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again, they are happy for this pot to go multiway to win two bounties. We could go on, but instead, we suggest you do your own research by comparing Classic ICM spots to PKO spots in GTO Wizard . There are many interesting spots to compare in various endgame scenarios. Conclusion ICM in PKOs is one of the many complicating factors. Progressive Knockout Tournaments may never truly be solved, which is a good thing for those who study them. There will always be competing incentives from the two ends of the ‘ICM Dial’ that tighten and widen your ranges. The skill factors in PKOs may determine if ICM pressure or Bounty Power is the more influential force . The best way to study this conflict is to look at the same spot, in terms of chip distributions, in GTO Wizard for both Classic and PKO. Use the Classic spot as the baseline, then determine what the bounty adjustments are in the PKO example. Key Takeaways ICM and Bounties are two competing forces. Ask yourself which has more influence in any given situation. Payouts and bubbles will tighten your ranges; bounties will widen your ranges. Ranges are wider in PKO ICM situations. Fold equity is employed more often in non-PKO ICM situations. Solvers avoid high variance lines and multiway pots in classic ICM. They are happy to embrace variance and play multiway pots in PKOs. Ace blockers are more valuable in Classic ICM spots. Hands that play well multiway go up in value in PKO spots. GTO Wizard the #1 App for Poker players Study any spot imaginable Practice by playing vs. GTO Analyze your hands with 1-click START CRUSHING NOW JOIN DISCORD Author Barry Carter Barry Carter has been a poker writer for 16 years. He is the co-author of six poker books, including The Mental Game of Poker , Endgame Poker Strategy: The ICM Book , and GTO Poker Simplified . Latest article Preflop Raise Sizing: Examining 2 Key Factors It amazes me that, after nearly twenty years of playing no-limit hold ‘em professionally, I… How to Handle Loose-Passive Limpers Solver charts and presolved solutions do not offer much in the way of explicit guidance… Top 5 Mistakes in Spin & Gos As a Spin and Go poker coach, I regularly encounter common mistakes that players make,… An Introduction to Spin & Gos I was playing Tournaments for the first decade of my career. But after my first… Relationships and Poker In my more than 15 years of poker coaching, I’ve helped hundreds of clients improve… Do Multiple Sizes Matter? Should I work out the other tools or just stick to the crowbar? Solver results… The Science of Learning Applied to GTO Wizard The way we were taught to study in schools was flawed and has negatively impacted… Check-Raising a Single Pair In this article, I will address a question raised by Twitter/X user ’Matt Riley’, who… The Turn Probe Bet Imagine yourself defending as the BB caller vs BTN preflop raiser in a 100bb cash… When To Encourage Multiway Pots

has more incentive to block-bet, and can even value bet with hands that are slightly behind when called due to the EV of checking being lower. But this is a discussion for another article! Benchmarks Against Slumbot We were thrilled to find that when battling vs. Slumbot , the highest performing 150,000 hand trial was the one using 1-size dynamic sizing , meaning that we only used one bet size per node. Theoretically, a complex strategy should outperform a simple strategy, but the 7-second move limit allowed the simpler approach to reach higher accuracy. Here you can view the graphs of both matches against Slumbot. In both cases, Ruse (now GTO Wizard AI ), outperformed Sslumbot significantly, however the Dynamic algorithm had a 50% higher win rate and experienced less variance during the match. Complex Strategy vs Slumbot: Win rate: 13.1 bb/100 70% confidence interval: 8.8 to 17.3 bb/100 95% confidence interval: 4.5 to 21.6 bb/100 Dynamic Strategy vs Slumbot: Win rate: 19.4 bb/100 70% confidence interval: 15.3 to 23.5 bb/100 95% confidence interval: 11.2 to 27.6 bb/100 Conclusion Poker players sometimes fear that they will lose EV by simplifying their strategy, but we can confidently say from experience that the opposite is true. Rest assured that simplified strategies improve your learning experience and win rate . You will find improvements to both your accuracy and your confidence as you start to cut away unnecessary complications from your game and focus on what matters most. To recap the benchmarks: Poker players sometimes fear that they will lose EV by simplifying their strategy, but we can confidently say from experience that the opposite is true. Rest assured that simplified strategies improve your learning experience and win rate . You will find improvements to both your accuracy and your confidence as you start to cut away unnecessary complications from your game and focus on what matters most. To recap the benchmarks: Dynamic Sizing captures 99.95% of the available river EV compared to the optimal one-size betting strategy. Dynamic Sizing finds a near-optimal (less than 0.25% EV loss) bet sizing 95% of the time. Dynamic Sizing outperforms any fixed sizing strategy. Dynamic Sizing captures 99.7% of the available EV as compared to playing a very complicated strategy. Dynamic Sizing outperforms more complex strategies in practice when time/convergence is a factor. Dynamic strategies are easier to study, easier to implement, and less noisy than complex strategies. All tests were done on the river, where we anticipate the largest EV losses from simplifying. The Dynamic Sizing algorithm should perform even better on earlier streets! A simple strategy executed well will invariably outperform a complex strategy executed poorly. If you’d like to learn more about how our Dynamic Sizing Algorithm works, check out this article : GTO Wizard the #1 App for Poker players Study any spot imaginable Practice by playing vs. GTO Analyze your hands with 1-click START CRUSHING NOW JOIN DISCORD Author Tombos21 Tom is a long time poker theory enthusiast, GTO Wizard coach and YouTuber, and author of the Daily Dose of GTO. Latest article

Figure 1 - The EV Cycle Let's imagine that I played a 500 hand microstakes poker session one afternoon where the sum of every choice that I made earned me +$8 in EV . In the short-term, there exists a myriad of possible monetary outcomes for that session. In fact, this figure grossly underrepresents just how many different possibilities there are. Some days I'll win more than $8; other days I'll win less than $8. On more rare occasions, where the natural variance in poker has been against me over this small sample, I'll even lose money. My EV is still +$8, the actual results are just down to luck. Fortunately for us poker players, over an infinite sample of hands, we know this EV will translate exactly into money won and we'll get our $8 and not a penny more or less. Over large but not infinite samples, like a million hands, we can expect to come somewhere very near to making the same amount in money as we have in EV . It might be a little less or a little more, but the chances are it won't differ hugely like it does in the short term.

to act on each street… Crack the Shell of Nut Draw Strategy Nut draws hold obvious appeal as betting and raising candidates. They benefit from fold equity,… Preflop Raise Sizing: Examining 2 Key Factors It amazes me that, after nearly twenty years of playing no-limit hold ‘em professionally, I… How to Handle Loose-Passive Limpers Solver charts and presolved solutions do not offer much in the way of explicit guidance… Top 5 Mistakes in Spin & Gos As a Spin and Go poker coach, I regularly encounter common mistakes that players make,… An Introduction to Spin & Gos I was playing Tournaments for the first decade of my career. But after my first… Relationships and Poker In my more than 15 years of poker coaching, I’ve helped hundreds of clients improve… Do Multiple Sizes Matter? Should I work out the other tools or just stick to the crowbar? Solver results… The Science of Learning Applied to GTO Wizard The way we were taught to study in schools was flawed and has negatively impacted… Check-Raising a Single Pair In this article, I will address a question raised by Twitter/X user ’Matt Riley’, who… The Turn Probe Bet Imagine yourself defending as the BB caller vs BTN preflop raiser in a 100bb cash… When To Encourage Multiway Pots in PKOs I was recently shown this fascinating PKO hand from the GTO Wizard PKO library. Somebody… Protect Equity and Prosper When we think about the best hands to bet in a given situation, we tend… Do Solvers Have Targets? Targeting has long been a staple of exploitative poker thinking. When you’re value betting against… Disciplining Big Blind in Limped Pots When the BTN open-limps off a short stack, the postflop play against the BB should… I’d Rather Be Drawing Which is the better hand on a K♥8♦5♦ flop: K♠T♣ or 7♥6♥? OK, I’ll admit… The Curious Case of Open-Limping Buttons Before the advent of solvers, open-limping was considered the province of passive, gambley recreational players… Cleaning Out Sticky IP Callers A “sticky” player on your left, one who calls your preflop raises too often and… Defending Against Tiny 3-Bets Tournament poker is about precision. Cash games, where stacks typically run into the hundreds of… Heads up! Exploiting SB’s Preflop Mistakes Heads up (HU) tournament play presents unique challenges to the average player. Many tournament players,… C-Betting As the OOP Preflop Raiser Position is an extremely valuable advantage in poker. Most players would describe the comfort zone… Overchoice: Making Sense of Multiple Sizings Solver solutions with multiple bet sizes often involve a lot of mixing between those sizes,… River Refinements: When Your Opponent Won’t Check-Raise One of the biggest strategic differences between playing in versus out of position involves betting… Turn Barreling in 3-Bet Pots There are two articles on the GTO Wizard blog that make good prerequisites to this… The Right Way To Think About Protection Suppose Paul the Protector is in a 200bb cash game and opens A♠A♣ in the… The Importance of Board Coverage The first public version of the GTO Wizard announced AI

have different flops that fit them particularly well. Let's look at some typical hands and see what we think about different flops. Starting Hand No. 1: A♦A♣. You raised four times the big blind in third position, and got called by one player in sixth position. 124 This is the best possible starting hand, of course, but do you know what you'd really like to flop with this hand? The answer might surprise you! Flop No. 1. 3♠3♦3♥. This (and a few hands like it) is your best possible flop. You've made the nut full house, but more importantly, your opponent may have made a weaker full house! (Notice how much better this is than A♠3♦3♥, where you have an even better full house, but most likely your opponent doesn't have more than two pair, and he's going to be afraid of the ace showing.) Note that you don't need to slow play this hand. Just take the lead in the betting and wait for him to come after you. Flop No. 2. J♠5♦5♥. You're not going to see Flop No. 1 too often, but here's a flop that you will see frequently which is also excellent for you. This flop could give your opponent two pair, which in turn will be losing to your two pair. With this hand you want to check and trap a loose player, but bet against a tight player who might be afraid to bet. Make sure you don't give a free card to a player who you put on a pair and won't give action. Flop No. 3. A♠K♦Q♥. This is a good flop for you but may not yield a lot of profit. You wish he was holding kings or queens, but since he didn't reraise you before the flop, that's unlikely. Here you may as well simply bet into the pot. If he's holding a lower pair like T♦T♣, he knows he's dead, and a check won't fool him into betting. Just lead out and see if you can make any money. Flop No. 4. Q♠ J♦T♥. This is a flop you definitely don't like. The cards are high enough that they're likely to have hit many of the hands that would have stayed in against you. There are also likely to be straight draws out against you. Check to start, but be prepared to call two moderate bets with your aces. Flop No. 5. 9♠8♠7♠. This is reasonably good if you hold the ace of the suit, but otherwise it's very bad, with all the straight and flush draws floating around. Still, the fact that the cards are lower than in Flop No. 4 means it's less likely that they hit your opponent. Lead out with a bet and try to find out where you stand. Flop No. 6. Q♠9♦4♥. This is a good flop. Your aces are still almost certainly good. Just lead out and hope the flop hit him somehow. Starting Hand No. 2. K♦K♣. You raised in third position. This time you were called by two players behind you.

getting involved with a weaker hand. Be careful interpreting this tell, however. Some players always place a chip on their cards before the action has reached them. Your job is to ascertain which players do this only when they are going to play. Picking Up Chips Out of Turn Some players like to have their chips ready for action when it’s their turn. They count out the amount of the bet, or even the size of a raise. Again, by looking to your left, you may be able to accurately predict what each of your opponents is going to do. This can help you avoid making marginal calls, especially if you see that the pot is going to be raised behind you. Be aware of the reverse of this tell. Some players habitually pick up chips when they intend to fold for any bet, perhaps in an attempt to discourage those bets. Talking About Their Hands Some players like to talk about their hands, or offer friendly advice to their opponents in the midst of a pot. What you want to know is, do they speak the truth? Should you believe them? In most cases, talkers follow a consistent pattern. Some players consistently lie, while others tell the truth in an attempt at reverse psychology. Learning to discern who falls into which category will make you some money. Academy Award Performances There is a good reason why most poker players don’t get major roles in Hollywood. If you don’t know what that is, watch them as they try to convince you to call, fold, raise, or whatever it is that they want you to do. Some players act strong when they are weak, reaching for their chips as they see you preparing to bet. Others appear disinterested in the pot until the action gets to them, at which time they ease in a half-hearted raise (while holding the nuts). By observing the table when you are not involved in a hand, you learn to identify the actors. Then, when you do play a pot with them, you are able to decipher their acts. When to Look for Tells The best time to learn to identify and use tells is not when you are actually involved in a hand. Rather, this is one more part of your poker education that can be enhanced when you have folded and are waiting for the next hand to start. The vast majority of your opponents use this time to chat, watch television, or schmooze with the cocktail waitresses. If you use this time wisely, you will be miles ahead of the other players, even if it costs you a date or two with a waitress. Tip # 49 of 52 When to bluff in limit hold'em. Although it may appear that successfully bluffing in low limit hold’em is a next-toimpossible endeavor, you can take advantage of some opportunities. Here are some dos and don’ts to guide you as you prepare to steal: Dos Do bluff against two opponents or fewer. Often in situations against only one

Loose-passive Games (Social Poker) Once a month I get together with the same group of friends for a night of poker. We play unstructured "dealer's choice" games. Each chip is worth a dime and bets are rarely more than 50 cents. We do not play table stakes so we are constantly fishing green out of our pockets when our chip pile runs low. However, there is an "understanding" that if your hand is a monster, you won't be throwing down 10 and 20-dollar bills. We drink beer, munch salty snacks, at the half point eat a meal of cold-cut sandwiches, talk about sports, work, the stock market, and generally have a good time. On a really bad night, I might loose $30 and on a good night, I make that amount. It always feels better to win than to loose, but if you are the loser that night, where else could you have had such a good time for so little money? On poker night, we play Hold'em and Seven-Card Stud, but we also play many junk poker games with wild cards and antes high in relation to the final pot size. In high ante games where most of money in the pot has gone in before anyone sees their cards, it is impossible to gain an edge. Since the game consists of the same seven people, playing month after month, year after year, money just flows around the circle. Over time, no one wins or loses-a perfect social situation. The social game I play with my friends is an extreme example of a loose-passive game. The defining features of these games are few 76 THE INTELLIGENT GUIDE TO TEXAS HOLD'EM POKER raises and everyone plays until the end. There is always a showdown. If you go to a casino cardroom on a weekend, at the lower betting limits you will find games that are close to fitting the loosepassive definition. Tourists, beginners, and people out to have a good time populate these games. Money is not the main issue-entertainment is the attraction. The stakes are small compared with the costs of most entertainment/social activities. Loose-passive games are actually the easiest ones to beat. To win money, you must become antisocial: that is, not play every hand through to the end. Strategic Considerations for Loose-passive Games Primary reasons for the game---entertainment, socializing. Money-no one cares. Competitiveness-low. Safe Assumptions: Position is unimportant since everyone will call with every hand. There is little information to be gained from having an advantageous position. Cost will be small in relation to the pot. Just about every drawing hand will have decent pot odds. Number of players equals the number in the group. Everyone plays every hand. Playing styles are passive. People rarely raise, even with the nuts. Most Important Factor: Your Cards. The only way to get an edge is to do what the others will not: fold unproductive hands. STRATEGIES Frustrating Features of Loose-passive Games: Bad beats. After a long session of play where you end just about even, you will be thinking about the

11. Facing 3-Bets Hero has done it! Having become competent in the areas covered so far, he's managed to move up in stakes from 25NL to 50NL. There's a problem though. This game is awfully aggressive compared to what he's used to. It feels like he's being 3-bet every single time he opens a pot and, as of yet, he has no idea how to defend appropriately. If he calls, it seems like he just misses the flop and has to fold in a big pot. If he 4-bets, they always seem to shove. If he folds, then he feels like the aggressive 50NL population is abusing him. He's suddenly gone from hunter to prey. Facing 3-bets doesn't need to be so off-putting. In this chapter we'll be building a toolbox for competently dealing with 3-betting. We'll be talking about: What makes a hand +EV to flat against a 3-bet. How to design polar 4-bet ranges. What other adjustments can be made vs. rampant 3-bettors to increase EV . Designing ranges for opening and defending that meet minimum defense frequencies. When to mine against 3-bets. And finally we'll be cementing our newfound knowledge with a healthy dose of example hands.

should play You do this because: 1. Four people have come in. 2. There was no raise. 3. They play badly. 4. You are going to play it well. That means if you play K+5+, four people come in, you're to the right of the button, and the flop comes: The first guy bets, and someone calls, you fold. You use your skills to keep yourself from getting trapped. One of the reasons not to play K+5+ is that it can be a problem if a king flops. In other words you can be trapped with this hand. But, if you are a good player, you won't get trapped. You should be able to play K+5+, flop a king, and still often fold. If the flop comes 164 Part Four: Playing in Loose Games you are going to have to get involved. Likewise if the flop comes and everyone checks to you. But there are many cases where you would get away from the second flop. On the other hand, if you are playing against bad players who will call with any pair, you want to stay in,-and you will of course bet it in those situations where it appears that your hand is good. When they call with middle or bottom pair they are almost certainly wrong. Do you see why we advised earlier in the text to play a hand like Q5s if there is no raise and you are on the button? In the right spot, if you play this hand correctly, it can be profitable. But remember that "correctly" can mean that you hit your hand and still throw it away. Looking at Some Odds Continuing with the concepts of the previous chapter, if someone bets into a multiway pot on the flop and there was a preflop raise you would usually be getting approximately 12-to- 1 to call. If there was no preflop raise you would only be getting about 7-to-1. That means that it is often correct strategy to call with bottom pair if there was a raise, but not if there was not a raise. Bad players, however, will make this call no matter what the size of the pot. Therefore, with a hand like K+5+ it makes a big difference if you can get in for no raise. This is because if you flop a king and you get paid by the lower pairs, they are incorrectly paying you. You make money on their calls. So when the game is good, you should play more hands, specifically suited hands, but only if it appears that you can get in cheaply with them. (The extreme case of this is no limit. If you ever saw a good no limit player against weak players, you will find that he is constantly limping in. He is playing about 113 of the hands and limping with almost all of them. He's giving up a little bit before the flop because he can outplay them later.) The trap that you don 't want to get into is calling with

our hands also benefit by by getting protection and getting value from FL and other stuff and you know a PA and a straight Dr that will be calling a turn bed so yeah um which which is uh let's see how big of a mistake is here so it goes here and with the A10 is different so e wise uh we wouldn't be losing much e uh but I think um we can probably just get away with betting um more more often than um than equilib suggest mostly because we're just not getting raised at all here okay uh you goes check check and relase the do of Spates now now um jamming here is is definitely a big mistake um as plate on the do of Spades um now yeah there are some hands that want to go in but those hands are straights and then some Bluffs right so uh and some uh maybe a few uh strong two pairs uh that were played this way but um yeah for the most part we're just um Bluff or valuating right uh but um not not really using hands like two pairs or you know A10 for that A10 definitely prefers a um a small bet size a lot more so let's compare B going all in and B small here and see with A1 we are losing um 3.4 chips um so this is a relatively large um mistake given the size of the pot so this would be like 10% of the starting pot which is a lot um it's a very very uh big mistake um the hands that definitely I want to go in here are just the straight Combos and then the Bluffs definitely so yeah uh well we shove and good default now into the next one so here we have pocket kings the hero is on under again 900 table and he goes for the race now the hero range from under the G with 17 big BLS it's going to be something like this um just a a very tight range about 15% hands mostly focusing on high cards uh suited uh the weaker weakest PA that the solver opens here pocket sixes with a very small frequency against weaker players you can probably open them with 100% frequency but uh for the most part you want to um if you're a a tough table you want to probably go with S Plus A10 um ace5 sued plus so yeah it's is just very strong range uh that will connect a top pair very frequently which is key when you are short stock you want to be hitting a lot of top pairs or middle pairs not be hitting D that's why you don't see a lot of racing with you know um Su connector type of hands or even the weaker baby ax although um the sare doesn't open these hands I think in practice you can probably open them every time because um even uh in the toughest

Reasons for value betting in poker Sources of Value You’re probably accustomed to thinking of bets as either value or bluff. In this taxonomy, value bets are hands whose value comes from getting called, and bluffs are those whose value comes from getting folds. There are also semi-bluffs, hands that bet to make better hands fold but also have a substantial chance of improving to a winning hand. And there are thin value or protection bets, modest made hands that do reasonably well when called and also benefit from causing live equity to fold. While this terminology can be useful, these categories are ultimately human inventions designed to help our puny brains simplify the true spectrum of value. It is more accurate to say bets derive their value from some combination of the following sources : Growing the pot – Value derived from winning the pot if the bet is called (or raised). The most important measure of this value is how much equity a hand has against the opponent’s calling range, but as we will see, there are other considerations. Denying value – Value derived from causing other players to fold. The most important measure here is how much equity the bet causes to fold, but again, this is not the only consideration. All bets derive their value from some combination of growing a pot they are likely to win and denying value to opponents. Simple Examples Let’s take a look at a simple cash game scenario . This is a single raised pot, BTN vs BB, 100BB deep: After BB checks their entire range, the BTN mostly chooses between a large bet or a check . For our purposes, we’ll look exclusively at the 125% pot bet, which is the most commonly used option. As is usually the case with a large bet size, the BTN employs a fairly polar betting range, preferring to bet mostly very strong and very weak hands and check many medium-strength hands. The chart below shows a few example hands from BTN’s range along with how often they bet and what value they derive from the 125% pot bet: AK is a straightforward value bet ; almost all its value comes from calls. It gains only 6% of the pot in equity when BB folds, but with 84% equity against BB’s calling range, it earns a very nice return on every dollar that goes into the pot. At the opposite end of the spectrum, 9 ♣ 6 ♣ is a virtually pure bluff . It does terribly when called, retaining only 8% equity, but it can cause the Villain to fold 74% equity. In between the two are some semi-bluffs like 9 ♥ 6 ♥ , which derive their equity from both sources. 9h 6h has 36% equity against BB’s calling range, so it’s not as pure a bluff as 9 ♣ 6 ♣ , but it still folds hands that have, on average, 46% equity against it. Pocket 22s lies somewhere between a semi-bluff and a pure bluff : it gains more from folds

not getting value from those hands whether they're deep stacked or shallow stacked against weak opponents and against most opponents you just want that are like weaker players that aren't going to put you in tough spots you just want to be taking this you know raising like the top 20 to 25 percent of hands taking these pocket pairs to the connectors raising it up to four times the big blind and forcing your opponent to make a mistake either in that they're not going to defend enough or now you're getting value out of those bigger hands and I think that's the correct play and then limping this green range here that's going to be your biggest exploit probably against a lot of the opponents that you guys are going to be playing against is raising up all this red range limping the green and not worry about balance or anything like that being balanced doesn't matter much against these weak opponents I show you the ranges you want to play against good opponents because I think you need to know that Baseline in order to be able to make understand the adjustments and just realizing that no one really is Raising enough hands this range here being the big blind response to the small blind limp this range here is like 36 percent of hands and so this is what I'm trying to get at here if I'm playing in the big blind I'm going to be raising all of these red hands plus like 25 percent of the time I need to be raising up these hands like Queen six off Queen five off King five off Jack four suited Jack three suited Jack do student like all these hands I need to be raising and no one is Raising those hands enough and so this is kind of another counter exploit is when you're the big blind playing against small blinds that limp people on the big blind do not ISO raise enough um um someone and I I should probably uh point this out that these are all situations where it's a heads up pot now between the small blind and the big blind and so the other exploit being when you're in the big blind facing when the small block it falls to the small blind and they limp in is that people are not ISO raising enough to three and a half four times the big blind against a small blind limp and these are the types of hands you need to be raising um to punish that small blind to make sure they're not getting into play you don't want them to play all those ninety percent of hands um you're gonna there's a lot of money they're limping in with 90 of hands they're going to be doing a lot of Limp folding and you should be punishing them with raises to steal those limps and we're doing it with a lot of these lower suited cards obviously all our strong value

Up. No Change 4 4 7 7 K 7th player is dealt a J, making Aces Up. He improved. 2 A A J J The Betting 7th hand is High with Two Jacks Exposed. He bets, disregarding 1st hand's possible Straight. 1st player raises on a Six High Straight. 2nd foolishly calls, on Queens Up. Queens Up seldom win. He needs to make a Full House. 3rd is sucked in and also calls. 7th calls with Aces Up. The Deal Two Down Four Up 1st player is dealt a 10, making Six High Card Straight 2 3 4 5 6 10 2nd player is dealt a 10, making Queens Up. No Change Q Q 6 7 6 10 3rd player is dealt a J, making Sevens Up. No Change 4 4 7 7 K J 7th player is dealt a 3, making Aces Up. No Change 2 A A J J 3 The Betting 7th hand is High with Two Jacks exposed. He checks, fearing a Straight is held by 1st player. 1st bets on a Six High Straight. 2nd calls on Queens Up. He has lost all hope of winning unless he fills but it is about 11 to 1 he doesn't. 3rd calls on Sevens Up. He's in the same trap. 7th also calls. He's sure he has to fill to win with heavy odds against him. The Deal Two Four One Down Up Down 1st player is dealt a J, making 2 3 4 5 6 10 J Six High Straight. 2nd player is dealt a 4, making Q Q 6 7 6 10 4 Queens Up, no change. 3rd player is dealt a 3, making 4 4 77KJ 3 Sevens Up, no change. 7th player is dealt a 9, making 2 A AJJ3 9 Aces Up, no change. The Betting 7th player is still High with two exposed Jacks. He checks. With 7th player checking, unless he's checking a cinch, 1st player has only 2nd and 3rd players to deal with. He suspects that each of them has been drawing to two pair. If he is a mathematician he knows it is about 5 to 1 that neither one made a Full House. He bets. 2nd player is like so many card addicts he will call on anything. He calls. 3rd player is even worse than the 2nd player. He calls on Sevens Up, a hopeless call. 7th player with Aces Up has some reason for calling. He has a strong hand that will win most of the pots. But he should have observed the 1st player more closely. He started betting the moment he made his Straight. Winning Hand Small Straight, held by 1st player. 3RD DEAL The Deal Two Down One up 1st player is dealt J J J Three Jacks Concealed 2nd ,, ,, ,, 9 9 8 Two Nines Concealed 3rd ,, ,, ,, a bust 4th ,, ,, ,, K Q 7 King – Queen High 5th ,, ,, ,, Q Q 7 Two Queens Concealed 6th ,, ,, ,, a bust 7th

starting hand, especially if there were no pre-flop raises. This flop could have given someone a strong 2-Pair. Someone could have a Gut-Shot Straight draw if they were holding K Q, K 9, Q 9 or Q J and anyone holding an Ace will at least call on the River. Of course small to medium Wired Pairs always have to be considered if there was no pre-flop raises. This hand came down to the River in a showdown between A Q (in position) and A J (out of position). The player with A J decided his kicker was good enough and became very aggressive, A Q decided he had the better kicker and called every raise but did not re-raise. A Q won a nice pot at the showdown with the better kicker. A way to practice reading the flop is to list the top five hands in any given flop. For instance: A flop of Kh, Kc, Jc - The best possible hands are Four of a Kind of Kings then two different Full Houses, trip Kings and finally 2-Pair (if someone hold a pair in their hand. A flop of 7s, 8s, Td – The best possible hands are a Straight 7 to Ten, a set of tens and then a set of eights, then set of 7’s and then 2-Pair Tens and 8’s. A flop of 2d, 4,d, 6,d – The best possible hands are a Straight Flush of diamonds 2 to 6, then a Straight Flush of diamonds (a bicycle) of Ace to 5 Flush of diamonds, a set of 6’s You can also do this for the Turn: The previous flop of Ac, Tc, Jh, the Turn card is a 9h – the Straight of Ten to Ace is still the best but then we have an added Straight of 8 to Queen to think about and the Straight of 7 to 10. The board cards are Kh, Td, 7s, Ts – the best hand is a Full House of Kings and Tens, then a Full House of 7’s and 10’s and then a Straight 7 to 10. Here are some hand to look at and the win percentages on each street. I do not consider what the board cards are in this exercise. I am only considering what types of hands are out there. These are from actual hands I analyzed on Poker Tracker software. The main consideration in this analysis is to understand what the probability is of your hand winning pre-flop and down the streets depending on the types of hands your opponents may hold. All of the following hands were enumerated using Poker Tracker hand replay software and they are taken from actual hands. Starting Hand/Win % Flop/Type of Hand Win % A9s- 55.29% Top Pair 46.73% KJs- 44.27% Flush Draw 2nd Pair 53.27% The A 9 suited vs. the K J suited is an interesting example. On the flop, the A 9s has Top Pair vs. a Flush Draw and second Pair. The Top Pair is losing here in the win percentage

Art of Bluff Catching Bluff catching—calling a bet with a modest hand which you expect to win only if… Exploiting Excessive C-Betting by IP On some flops, it is simply not possible for the preflop raiser to continuation bet… Is Limping Pimping? In a past Discord post, one of our members noted that an upside of implementing… Exploiting Excessive C-Betting by OOP A preflop raiser who continuation bets too often is always a potential target for exploitation,… Preflop Button Mastery in PKOs Playing from the Button presents many unique opportunities in any tournament format, especially in PKOs.… The Worst Turn Card Greetings from GTO land. In today’s article, we will use the Turn Reports feature to… Navigating Range Disadvantage as the 3-Bettor Picture this: We’re playing a NL500 6-max cash game, and we’ve won a few pots,… Mastering Three-Bet Pots In Position in MTTs Playing in position against a three-better is a lesson in playing to your advantages. As… Mastering Three-Bet Pots Out of Position in MTTs Three-bet pots are scary. Playing out of position is scary. Put them together, and you’ve… The Greatest Final Table in Triton History Today, we’ll examine one of the most epic final table battles I’ve ever witnessed! Our… Mastering Thin Value Bets in Checked-Down Pots Valuing your hand appropriately—determining whether it’s strong enough to value bet or so weak you… Maximizing Value on Monotone Flops Monotone flops tend to provoke great anxiety among poker players. It’s easy to imagine that… How to Defend Against Turn Donk Bets Responding effectively to donk bets on the turn is tricky;, there’s no getting around that.… How and Why You Should Use Turn Donk Bets Donk betting–taking the betting lead away from the previous street’s aggressor–on the flop is rarely… How Stack Sizes Change Your Range In this series, we have looked at factors that can influence ranges in otherwise identical… How to Leverage GTO Wizard’s EV Comparison Tool With the advent of solvers, some troubling new turns of phrase have entered the poker… Should You Ever Cold Call a 3-Bet? When there’s been a raise and re-raise before the action is on you, you will… When ICM Breaks Down If you have read my previous GTO Wizard articles and my books, you’ll know I… When Is It Correct To Fold AA Preflop? One of the criticisms of ICM is that it is boring and robotic. In my… OOP C-betting vs Loose Cold-callers In a previous GTO Wizard article, I asserted that “Playing against an in-position cold-caller is… Short-Stacked Play in MTTs Playing a short stack well is an essential tournament skill. It is extremely rare to… When To Ladder in Tournaments In my last two articles, I wrote about the effect field size and payout structure… How Payout Structures Impact ICM Last time we discussed the ICM considerations in game selection, we looked at field size,… C-Betting IP in 3-Bet Pots When you three-bet before the flop and the original raiser calls from out of position,… C-Betting OOP in 3-Bet Pots Continuation betting from out of position can be

Okay, so here's a step by step template of how we decide what hands to bluff all-in with on the river.

bet sizes often involve a lot of mixing between those sizes,… River Refinements: When Your Opponent Won’t Check-Raise One of the biggest strategic differences between playing in versus out of position involves betting… Turn Barreling in 3-Bet Pots There are two articles on the GTO Wizard blog that make good prerequisites to this… The Right Way To Think About Protection Suppose Paul the Protector is in a 200bb cash game and opens A♠A♣ in the… The Importance of Board Coverage The first public version of the GTO Wizard announced AI upgrade already has some useful… How To Adjust When Villain Has No Bluffs “They always have it!” is a common, semi-joking expression in poker to describe the tendency… Adjusting on Later Streets After Exploiting Flop The key to exploiting opponents profitably is knowing when to stop. I’m not referring to… C-Betting IP vs Passive Poker Players A preflop raiser enjoys a significant range advantage over a BB caller, enabling them to… C-Betting Against ICM Preflop Ranges You raise from early position (EP) in a multi-table tournament and the BB calls. Both… The Art of Bluff Catching Bluff catching—calling a bet with a modest hand which you expect to win only if… Exploiting Excessive C-Betting by IP On some flops, it is simply not possible for the preflop raiser to continuation bet… Is Limping Pimping? In a past Discord post, one of our members noted that an upside of implementing… Exploiting Excessive C-Betting by OOP A preflop raiser who continuation bets too often is always a potential target for exploitation,… Preflop Button Mastery in PKOs Playing from the Button presents many unique opportunities in any tournament format, especially in PKOs.… The Worst Turn Card Greetings from GTO land. In today’s article, we will use the Turn Reports feature to… Navigating Range Disadvantage as the 3-Bettor Picture this: We’re playing a NL500 6-max cash game, and we’ve won a few pots,… Mastering Three-Bet Pots In Position in MTTs Playing in position against a three-better is a lesson in playing to your advantages. As… Mastering Three-Bet Pots Out of Position in MTTs Three-bet pots are scary. Playing out of position is scary. Put them together, and you’ve… The Greatest Final Table in Triton History Today, we’ll examine one of the most epic final table battles I’ve ever witnessed! Our… Mastering Thin Value Bets in Checked-Down Pots Valuing your hand appropriately—determining whether it’s strong enough to value bet or so weak you… Maximizing Value on Monotone Flops Monotone flops tend to provoke great anxiety among poker players. It’s easy to imagine that… How to Defend Against Turn Donk Bets Responding effectively to donk bets on the turn is tricky;, there’s no getting around that.… How and Why You Should Use Turn Donk Bets Donk betting–taking the betting lead away from the previous street’s aggressor–on the flop is rarely… How Stack Sizes Change Your Range In this series, we have looked at factors that can influence ranges in otherwise identical… How to Leverage GTO Wizard’s EV Comparison Tool With the advent of solvers, some troubling new turns

we're gonna be discussing how to make the most out of a small bankroll so here's a question i'm a new member with a small bankroll and struggle with knowing the best way to grow my bankroll can you give some advice i mean first things first most people as far as i can tell don't like to talk very openly about their finances why i don't know but they don't do it and i think you probably should especially whenever you are talking to a coach somebody you're asking for advice right now you certainly don't need to have your finances out for everyone to see there's probably no purpose in that but if you want to get good information from anyone you need to give them as much information as you can about your actual problem otherwise they're not gonna be able to help you right because like i don't know what this question actually is is this saying someone who's trying to become a full-time professional poker player if so my advice for them is gonna be very different than my advice for someone who is just playing for fun and you know i would ideally like to win but doesn't really care at the end of the day so anytime you are asking someone for help or for information you need to give them as much information as you reasonably can so they can give you as good of advice as they possibly can all right first things first figure out what you want are you trying to go pro is the goal to quit your job and only play poker right i think a lot of people get in their minds yeah i want to be a professional poker player but uh no you don't if you have a family and kids and responsibilities you probably don't want to be a professional poker player unless your other options are quite bad right the reason you see a lot of youngish people getting into poker or people my age who started when they were 18 getting into poker is because whenever you're that age you have no dependents right you have no kids typically you have no real responsibilities and you also don't really need to make money and and on top of that you don't really have any other good opportunities now some people do have good opportunities but like as a kid i had just like marginal opportunities i mean i like i was going to college i had a scholarship to where i didn't need to make money if i knew if i graduated college i'd get a job making like 50k a year being an engineer and there's nothing wrong with that fine perfectly fine good prospects but it's not like i'm going to get super rich doing that and also i probably didn't know if i enjoyed it that said if you are already in a career and you make a decent amount of money and it's very stable and it pays your

stack. Our range is stronger, and weighted toward more Ace-x type hands that not only make good one pair hands, but also block a lot of hands that call or 3-bet. Once again, the bet size has decreased, this time to a minimum bet (if the solver could bet less it probably would), because there should be no problem getting these stacks in the middle if need be. This is the range at 17bb : This is the tightest range so far, following the trend of being weighted towards high cards. Things get really interesting when we get to 14bb ; this is the UTG opening range: There is so much to unpack here, but the first thing to notice is that our range has slightly increased. We now play 16% of hands, compared to 15.8% in the 17bb example. Shoving has become a viable option. Our shoving range consists of middling pocket pairs, strong offsuit A x, and strong suited broadway hands. These are all hands that perform well when called, but taking down the pot preflop with them is also a good outcome. Our min-raising range is just 7.5% of hands. We open with most of our hands some of the time but our strongest hands do it most often. This is mostly what we would call an ‘induce’ range, ie. hands that want to entice more action (in the form of calls or reraises Reraise To raise after there has already been a raise on the current street. ). The really interesting thing is that a limping range has developed. We limp 4.6% of hands, which has never been an option in any previous range. Most hands limp some of the time. We limp with our strongest hands like AA and KK as traps, and to protect the limping range. Limping allows you to play a wider range. If we told a solver to adopt a raise-only strategy, the overall range would be tighter. We can see that this is the motivation behind the limp because at the margins, A4 s and 55 are occasional limps, and 66 is played all the time because it is limped some of the time. In the previous 17bb range A4 s and 55 were not in the range, and 66 was only played some of the time. The other reason why limping becomes an option at shallow stack depths (in chip EV) is that limping makes it less profitable for an opponent to 3-bet you. When you open to 2bb at 20bb effective, and an opponent shoves on you they can potentially win a maximum of 4.5bb without contest, which is a 22.5% stack increase for a 20bb stack. By limping we reduce that to maximally 3.5bb, or 17.5% of the effective stacks. At around 20bb, is when 3-bet shoving becomes very profitable. It is also easier for the limper because the limping range is somewhat polarized here. If they get shoved on they either have a snap call or a snap fold. When UTG gets to 8bb the strategy changes considerably:

a straight or flush draw, you will be at a disadvantage. In other words, you don’t want to give him the proper odds to call your bet. ADVANCED CONCEPTS When we talk about advanced concepts for high-stakes games, it should be clear that some of these work in medium and low-stakes games as well. No matter how high or low the stakes, you’ll profit from the pointers in this section. The Best Hands To Play 267 When you have good hands, you’re going to play most of them. I play the hands described in this section, and so does everybody else. Players like to debate whether A-A-K-K double-suited is a better hand than A-A-J-10 double-suited. I much prefer A-A-J-10, and I think that most other players do too. But it really doesn’t matter which hand is better because you should play both of them. Of course, there’s a big difference between hands that you can bet on after the flop, and those that you can’t bet on because you went all-in before the flop. I also like a hand with three connected cards and a suited ace, such as A? 8? 7? 6? or A™ J? 10? 9?. Three connected cards with one gap and a suited ace is also fine. With a hand like this, you’re either going to be in the hunt, or you’re going to throw the hand away. You can flop a very good hand, like a flush or a straight, or good draws to them. And many times you’ll pick up a monster draw, such as a flush draw combined with a straight draw. I like these hands because they’re not trouble hands. If they’re very good on the flop, play them. If not, throw them away. A double-pair hand, such as J-J-10-10, is also good. When you’re dealt a double pair, you will flop a set about one time in four. If you flop a set, you’ll probably be in a very profitable situation. If you don’t flop a set, you’ll probably just fold. You want hands in which all four of your cards are working together. If you have Q-Q-J-10 your hand is obviously superior to Q-Q-8-6. Suited cards look much better before the flop than after. If you don’t have the nut flush draw, you really don’t want to play them. But suited cards do have backdoor possibilities. Sometimes, if you turn a set, you still have a chance to make a backdoor flush. Suited cards also are very good from a defensive standpoint. For example, say you have two hearts in your hand and you flop a set with two hearts on board. Your hand makes it more difficult for an opponent to hit his hearts if he is playing the ace-high flush draw. If you have a good hand independent of the flush draw, your flush draw can play defense, as opposed to offense. For example, suppose you have the Q? Q? J? 10?, and the flop comes with the Q? 7? 4?. You have top set and a flush draw. With

types at the table, they want to exploit it by isolating certain opponents. For instance, they know the player who raised UTG is an aggressive player that will toss a pre-flop raise out with any two cards. You can identify this player by how many times he out plays his opponents after the flop. Ask yourself if he made the correct read more times than not on the streets after the flop and extracted the most money possible. If your answer is yes then you have met a TAG. A Loose Aggressive player will overestimate their hand, raising frequently, and their aggressive nature will drive the pot value higher, increasing potential winnings. A Loose Passive player will overestimate their hand, but due to their passive nature will rarely raise, preferring to call and allow other players to increase the pot. These are the weak players in the house, and you need to exploit them as often as possible. Their money is your money because they may be aggressive on the flop but are easily outplayed during the hand. A Tight Aggressive player will play to close constraints, participating in only a few hands which they have a high probability of winning. The hands they do play, they will raise frequently to increase the size of the pot. A Tight Passive player will participate in few hands, only considering playing those that they have a high probability of winning. The passive nature implies that they allow other players to drive the pot, never doing it themselves. Of course, after reading this book I hope that you will be a TAG instead of a losing poker player. Playing Your Best Poker Self-awareness is an important skill to have in poker. This chapter deals with playing when you are tired and ultimately needing the ability to check in on yourself to see if you are bored, frustrated, steaming, scared, or having fun. You want to figure out your optimal state of being for playing your best poker. When you are able to concentrate, be in the flow of the game and make the correct decisions. If you are preoccupied or distracted, you will not see the minute indicators and tells of your opponent’s style. You will be missing vital information when the time comes to go heads up with certain players. Your natural instincts will not be working, the part of you that sees things that your conscious awareness misses, like when a person takes a little more time before they check. Your unconscious may have already categorized that as being a trapping move. One of the more costly mistakes a poker player can make is playing a session for too long. When a player starts to get tired, they begin to lose interest, are unable to concentrate as much and start to force their play. One bad bet here, one overcall there and your bankroll could be halved in no limit. Lou Krieger says that the most important thing a poker player can do is to play their best game whenever they are playing

The Skills for Success You can’t learn to be a good no limit hold ’em player until you understand what it means to be a good no limit player. What do good players do that mediocre or bad players don’t? This chapter will tell you what it means to be a good no limit player, and the rest of the book will show you how to think about the game so that you can acquire those skills. In many endeavors the answer to the question, “What makes someone good?” is at least somewhat transparent. You have to have quick reflexes to be a good baseball hitter. You have to be a good logical thinker to be a scientist. But what do you need to be a good no limit player? It’s not as clear. New players (and non-players) seem to think the game centers around two things: being a good liar and being keenly aware of tells. Don’t let that stone face crack, keep an eagle eye for your opponents’ nervous scratches and tics, and you’re on your way to riches and glory. Five buy-ins later, the neophytes realize that there’s a little more to the game than that. Then they concentrate on the cards they play. Now it’s about playing tight and out-folding the competition. That works a little better, but still it doesn’t produce results. So they switch it up and start playing loosely and raising a lot. Reading hands is the key skill now. That strategy produces some big wins — and some big losses. Some who get very good at it become consistent winners. Most don’t. They get hung up in their progression as players. They realize that reading hands is important, but they never get particularly good at it. Arid their notion of reading hands usually ends at “trying to put their opponents on a hand.” When asked what other skills are important to be a good no limit player, they’ll come up with a vast array of possibilities, but few that reflect what the good players really do. The strange truth is that many no limit players, even some experienced ones, don’t know what makes one player better than another. You will. Some of the most important no limit skills are: • Manipulating the pot size • Adjusting correctly to stack sizes • Winning the battle of mistakes 9

In Poker One of the most frequently asked questions in poker is how to calculate the size… Principles of River Play The river offers the least complicated strategy of any betting street. With no further cards… Exploitative Dynamics GTO solutions are designed to be unexploitable, performing reasonably well no matter how your opponents… How ICM Impacts Postflop Strategy Most players understand how the Independent Chip Model (ICM) in poker impacts their strategy preflop,… 10 Tips for Multiway Pots in Poker While lots of work has been placed into research and explanation of heads-up pot strategy,… What is the Bubble Factor in poker tournaments? The Independent Chip Model (ICM) shows us the real money implications of tournament chip decisions.… The Theory of Progressive Knockout Tournaments In poker, a PKO (Progressive Knockout) tournament is a type of tournament where a portion… How To Analyze Turn Textures In Poker Master the art of turn analysis in poker. Understand how the turn card changes the… Principles of Turn Strategy Learn the principles of turn strategy in poker and discover what makes the turn unique.… Poker Strategies: Tournaments vs. Cash Games Tournament poker is not as different from cash game poker as people sometimes assume. Most… How Solvers Work A Game Theory Optimal solver is an algorithm that calculates the best possible poker strategy.… The Most Powerful Play in Poker The central strategic implication of stack depth is the question of how much equity a… When does ICM become significant in MTTs? The Independent Chip Model (ICM) was invented in 1987 by M. Malmuth and is one… How to Study GTO Solutions Tools like GTO Wizard and other solvers should not be used to memorize specific strategies.… Principles of GTO Game theory, or GTO (for Game Theoretically Optimal), is best understood not as a rigid… Interpreting Equity Distributions GTO Wizard’s range vs range equity distribution graphs are an excellent tool for visualizing which… What is Leverage in poker? Leverage refers to the risk of future betting. When you call a bet on the… Reasons for value betting in poker You’re probably accustomed to thinking of bets as either value or bluff. In this taxonomy,… The Science of Poker Performance Poker is a game of small edges and big swings. Every hand is an investment… What is Valor in poker? Can a poker hand be courageous? How does your ability to value bet future streets… Pot Geometry “Pot Geometry” refers to betting an equal fraction of the pot on each street, such… A Beginner’s Guide to Poker Combinatorics Combinatorics is a fancy term for evaluating the number of possible “combinations” (combos) of any… Stack-to-pot ratio Stack-to-pot ratio, or SPR, is a way of measuring how deep the effective stack is… Equity Realization In poker jargon, equity expresses how much of the pot a hand will win, on… Variance and Bankroll Management Variance and Bankroll Management. Vital Soft Skills for Every Poker Player. How to Become a GTO Wizard Welcome to the wonderful world of game theory optimal poker! This article will serve as… The Three Laws of Indifference

Upswing A period during which a player has significant positive results, typically more than they would reasonably be expected to win. The opposite of a downswing.

unlike Seven-Card Low Stud, is a straight or a flush. A 2 3 4 6 is the lowest hand in this game. Low winning hands are quoted below. None of them are straights. Lowest Hand A2346 6 Low A 2 3 5 6 A2456 A3456 7 Low A2347 A2357 A2457 A3457 A2367 A3467 23467 A3567 23567 A4567 All cards which are below an eight, A23456 7, I call the Winning Zone. All others, 8 9 10 J Q K, I call the Losing Zone. You are dealt Two Down and One Up in Hi-Lo. If all three are in the Winning Zone, raise. Example 1: A 5 7 If two cards are in the Winning Zone and one in the Losing Zone, just call. Example 2: A 7 K If only one card is in the Winning Zone and two in the Losing Zone, fold. Example 3: A J K If all three cards are in the Losing Zone, fold. Example 4: 8JQ What you are trying to get for Lo are five cards out of seven in the Winning Zone; that is, five cards below an eight. In Example 1. A 5 7: If you draw another in the Winning Zone, A 5 7 4, then bet because you have four out of five in the Winning Zone. If the fifth card is also in the Winning Zone, of course you continue to bet. If in Example 1, A 5 1, you draw the fourth card in the Losing Zone, you can still make a low hand: A 5 7 K If you draw the fifth card in the Losing Zone, A 5 7 K J, your chances are not so good, but stay for another card. If the sixth card is in the Losing Zone, A 5 7 K J Q, then fold because you have only one more card to draw and you can't possibly make a Low Hand. Refer to Example 2, A 7 K. If you draw a card in the Winning Zone, A 7 K 3, then stay. Suppose on the other hand the fourth card is in the Losing Zone, A 7 K J. You now have two in the Winning Zone and two in the Losing Zone. To make a Low hand you would have to draw three consecutive cards in the Winning Zone and the odds are prohibitive against your doing so. Fold. Always fold with two in the Winning and two in the Losing Zone. Drawing a pair in the Winning Zone is the same as drawing a card in the Losing Zone. A 7 K J has the same value as A 7 7 K, or rather, it is even higher because you have a pair of Sevens for Lo. HIGH I ask you now to forget everything I have previously told you about Seven-Card High. This game has absolutely no relation to Hi in Hi-Lo. You don't stay on anything but the highest hands. In Hi, of Hi-Lo, go for Aces Up, Three of a Kind, Straights, Flushes, Full Houses.

3-betting range will consist of your best hands plus the next tier of hands that are not great calls, have equity or good blockers and can offer good board coverage. If you don’t have a flat calling range (mostly in the HJ, CO and SB), then your 3-betting range must be linear. If you are playing a 3-bet or fold only strategy, you want to put only your best hands in the 3-betting range and fold everything else. When you want to split your range into a calling range and a re-raising range, if stack depths are such that the Villain can re-raise all-in, you want your re-raising range to be polarized. This is because you want to put all high equity hands that you don’t want to re-raise/fold in your flatting range. Exploitative 3-betting When you suspect Villain is a weak player and or is opening more hands than they should, you should try to exploit them by increasing your 3-betting frequencies. However, you must be careful if there are other active players in the hand because if they pick up on what you are doing, they can start cold 4-betting wider and exploit you, even if the weak player never realizes you are exploiting them. The best way to assess quickly if a Villain might be over-folding to 3-bets is to use MDF and the Alpha number. Example Game: Live Cash Game Effective Stack: $500 Players: 8 Blinds: $2/$5 (no ante) Pre-flop: The action folds to the SB who raises to $15. You have seen him make some questionable opens with Q3o and 64o from SB before, so you estimate they may be opening approximately 76% hands (Hand Range 54).

mixed games or dealer’s choice games. Many home games and most of the biggest games are mixed games, in which the game changes after a set number of hands is played or a certain amount of time elapses. The most popular multi-game mix in casinos is H.O.R.S.E., an acronym for the combination of hold’em, Omaha eight-orbetter, razz, stud-high, and eight-or-better stud. Some common two-game mixes are stud and hold’em; no-limit hold’em and pot-limit Omaha; and high-low stud and high-low Omaha. With so many games to play, a hedgehog would have a lot of trouble competing at these tables. 5. Versatility A fox is much better prepared for any new games that develop than a hedgehog. The more versatile you become, the easier it will be for you to pick up a new variation when you are faced with it. WHAT TO LEARN What poker variations should you learn first? To some extent that depends on where you are and what game you normally play. No-limit hold’em is a good game to master first. Not only is it the most popular game, but it’s also growing faster than any other. If you intend to play a lot of tournaments, you should definitely learn no-limit hold’em, but don’t forget to study the limit and pot-limit variations. On the East Coast, stud is popular and should be your second choice. In Europe and the South, pot-limit Omaha should be your second choice. In 102 Vegas and California, Omaha high-low split is a reasonable second game to learn, but make sure you learn how to play both tournaments and live games. Eventually you should practice enough to feel comfortable playing limit, potlimit, and no-limit games. You should also strive to learn all the most popular games, including hold’em, seven-stud, Omaha high, Omaha high-low, sevenstud high-low, deuce-to-seven triple-draw, razz, and lowball draw—both aceto-five, usually played limit, and deuce-to-seven, usually played no-limit. The top players know and play all of them. Why shouldn’t you? I would even recommend the study of certain academic disciplines, especially mathematics and psychology. Psychology will help you better understand your opponents and what they are doing. It may also enable you to find, understand, and eliminate some of your own mistakes. Probability and statistics are extremely useful as well. Poker players have been known to use game theory to determine the percentage of bets that should be bluffs. Assuming you are extremely intelligent—and you must be if you are reading this book—and hard working, you should be able to master all of these games and academic disciplines in approximately five lifetimes. That’s why, in order to make the most money, you should master one or two games, while achieving high competence in the others. 103 LIMIT HOLD'EM POKER by Jennifer Harman Though Jennifer Harman is proficient in all poker games, I chose her to write the limit hold’em chapter because I’ve seen her win consistently at this game, often beating the best players in the world. Having played high-stakes poker with Jennifer the past few years, I’m convinced that she’s not only the

because Villain's most likely calling hands are top pair and draws and these hands are unlikely to start folding to bigger sizing. Villain's range is likely to be inelastic as is so often the case with Fish and so Hero makes sure not to lose out on any pot building value. On the river, these two groups of hands in Villain's range have now gone in very different directions. The top pair portion has become a very strong Full House that this player is unlikely to ever consider folding. Meanwhile, the draws have missed entirely leaving Villain with zero SDV and an easy fold when he has this part of his range to any sizing. There could also be a little bit of 6x in Villain's range, but these hands should be considerably outweighed by the other groups given the higher concentration of suited cards and high cards that Villain will prefer to play pre-flop. Moreover, 6x is now a full house and Fish with high WTSD stats tend to be quite bad at recognising their relative hand strength from their absolute hand strength. "You can't fold a full house!" Villain could of course also have 5x for quads, but this is so relatively unlikely that it's not a problem. When it happens Hero grits his teeth and moves on to the next hand knowing there wasn't much he could do about it. The upshot of this analysis is that Villain has an extremely inelastic range on the river. The vast majority of the time it's calling any size of bet or folding to any size of bet barring something absurdly small. As Hero has a value hand, he seeks to maximise his value vs. the chunk of Villain's range that will hardly ever be folding, ignoring the missed draws that don't call anyway. Hero shoves for 75BB. A nice line for Hero if he'd somehow got to this river with air himself would be to bluff a small size, just big enough to fold out the missed draw part of Villain's range while reducing his RFE and losing the minimum when Villain has the Kx portion.

SWAPPING MISTAKES 119 This strange “wait until the river and bet it all” strategy is the right way to play against this opponent; it’s the way that generates the maximum profit per hand. It significantly outperforms the “perfect” strategy. However, it doesn’t resemble the perfect strategy at all. If you played that way against typical opponents, you’d get slaughtered. It’s tailored to beat this specific opponent and no other. Your opponent makes huge mistakes; he calls all bets no matter how bad his hand is. If you want to beat him for the maximum, you must be willing to make some “mistakes” of your own: never bluffing, checking good hands on the flop and turn, giving free cards, overbetting marginal hands, etc. You trade your mistakes for your opponent’s mistakes, and since his mistakes are bigger than yours, you profit from the trade. If you refused to make mistakes, you’d have none to trade, and you wouldn’t make the most of your opponent’s willingness to make huge mistakes.33 You Can’t Win Them All In this heads-up game, the “swapping mistakes” theory doesn’t quite ring true. After all, is a mistake really a mistake if no one exploits it? The mistakes you trade to your opponent are worthless to him because he doesn’t do what it takes to profit from them. You capitalize on his mistakes, but he ignores yours. That’s fair enough. But if we extend our discussion to a three-handed game, you’ll see that you really are swapping mistakes. Say you’re playing in a game with the same “call every bet” opponent and another, savvier one. Your savvy opponent plays like a normal person. When you bet, she’ll call only if she thinks she’s a favorite. And she’ll bet when she thinks it’s the right play. The thing is, she’s underbankrolled. While you and the calling station play with $10,000 stacks, she plays with only $100 at a time. With the addition of a tough spot to your game, should you revert to a perfect strategy? No, you shouldn’t. You should play almost exactly as you played before; you check every hand to the river and then move in with hands favored over a random holding. The key is that the savvy player has only $100. Your crazy strategy is full of mistakes, and she’s going to exploit them for profit. When she actually bets her $100, both you and the other player will, on average, be big underdogs to her. She’ll make money from both of you. But she’s chipping away at you only $100 at a time, while you’re pummel- ing the other guy for $10,000. You’re making mistakes, and someone is now exploiting them, but that doesn’t matter. You’re trading small, $100-sized mis- takes for big, $10,000-sized mistakes.34 You’re much better offdoing that than making no mistakes and letting your calling station opponent keep his $10,000 too often. 33This is one time that we use the word “mistake” in a different way than the Fundamental Theorem of Poker way. 34The mistakes don’t actually cost you the full $100

Let's look at Villain's range. He probably gets to the river with a mix of pocket pairs, 5x, Jx and flush

Some players struggle to assimilate how a hand that was very strong on a previous street can be demoted and become weaker on a later street. They get emotionally attached to the initial value of their hand and feel entitled to win the pot just because they started with the strongest hand. Nevertheless, this is just all part of the game. Poker is a game of equities, how much we have, how it is distributed and how we realize it while preventing our opponents from realizing theirs. On countless occasions I have heard players say something along the lines of, “Every time I have AA, the flush or the straight card comes. I’m so unlucky.” You are supposed to have your strong hands demoted sometimes. It can be predicted mathematically and should be expected. So, you should be prepared for the times it happens. Know your range, as well as your opponent’s and understand that, even if on that occasion you might lose a big pot sometimes, you will be the one who has the best of it. The important thing is to play well and adjust correctly to how the situations change. This allows you to prevail in the long run. Flop Strategy 2: Turn Play after Flop C-bet and Call (x/b/c) OOP First Action: BB vs UTG on 9♥8♥4♦ (40bb) Diagram 119

while weaker players should not pass up on any profitable spots, even the very marginal ones. ICM doesn’t look into the future . It doesn’t account for blinds increasing or positions rotating. This is particularly important when the blinds coming back around and/or increasing puts you in a vulnerable position. ICM is an incredibly important strategic guide in tournaments and the players who ignore it are burning EV. But ICM is not a perfect model by any means, it has limitations you need to be aware of so you can deviate away from it when the circumstances merit a more comprehensive approach that will force you to think outside of the proverbial ‘ICM-box’. GTO Wizard the #1 App for Poker players Study any spot imaginable Practice by playing vs. GTO Analyze your hands with 1-click START CRUSHING NOW JOIN DISCORD Author Barry Carter Barry Carter has been a poker writer for 16 years. He is the co-author of six poker books, including The Mental Game of Poker , Endgame Poker Strategy: The ICM Book , and GTO Poker Simplified . Latest article Preflop Raise Sizing: Examining 2 Key Factors It amazes me that, after nearly twenty years of playing no-limit hold ‘em professionally, I… How to Handle Loose-Passive Limpers Solver charts and presolved solutions do not offer much in the way of explicit guidance… Top 5 Mistakes in Spin & Gos As a Spin and Go poker coach, I regularly encounter common mistakes that players make,… An Introduction to Spin & Gos I was playing Tournaments for the first decade of my career. But after my first… Relationships and Poker In my more than 15 years of poker coaching, I’ve helped hundreds of clients improve… Do Multiple Sizes Matter? Should I work out the other tools or just stick to the crowbar? Solver results… The Science of Learning Applied to GTO Wizard The way we were taught to study in schools was flawed and has negatively impacted… Check-Raising a Single Pair In this article, I will address a question raised by Twitter/X user ’Matt Riley’, who… The Turn Probe Bet Imagine yourself defending as the BB caller vs BTN preflop raiser in a 100bb cash… When To Encourage Multiway Pots in PKOs I was recently shown this fascinating PKO hand from the GTO Wizard PKO library. Somebody… Protect Equity and Prosper When we think about the best hands to bet in a given situation, we tend… Do Solvers Have Targets? Targeting has long been a staple of exploitative poker thinking. When you’re value betting against… Disciplining Big Blind in Limped Pots When the BTN open-limps off a short stack, the postflop play against the BB should… I’d Rather Be Drawing Which is the better hand on a K♥8♦5♦ flop: K♠T♣ or 7♥6♥? OK, I’ll admit… The Curious Case of Open-Limping Buttons Before the advent of solvers, open-limping was considered the province of passive, gambley recreational players… Cleaning Out Sticky IP Callers A “sticky” player on your left, one who calls your preflop raises too often and… Defending Against Tiny 3-Bets Tournament poker

bad with the idea that we're just not gonna fold so we bet luckily the short sack jams because then we just have a very very easy call and we get any gets a set so one of the few combinations that we actually do lose to and you know that's gonna happen understand that sometimes in poker tournaments you are just gonna run into it and there's not a whole lot that you can do about that notice funny given the run out and probably lose to everything unless your opponent ran delay on like eight seven of Spades but sometimes that's just how it goes so after this hand Mike blind it out a bit gutter all-in with pocket fours he jams were early position with pocket fours someone re-raise ace 10 off suit and the ace 10 off suit one which is like okay so that is how Mike the first person we backed from poker coaching calm cash in the $600 buy in Seminole Hard Rock Poker open event for one thousand three hundred seventy dollars Congrats to Mike

the amount of ev difference that you're able to generate in spots compared to the compared to that of your opponents so with that in mind i want to talk about you know when when you should apply that mindset to your current schedule uh in my mind you know just to [Music] kind of reiterate on the studying reiterate on it like i think it's a bad idea to binge 20 hours go play for a week be like oh crap i haven't studied in a while go study for 10 hours and then go play for another week it's much more important to have a constant desire to improve and spend high value time i put on here every week but really it's like it's every day every time you play you should spend high value time to improve after that session um so where i think this should fit into your schedule is in your post game so i think you should spend a little bit of time reflecting on your current postgame habits in my mind most people i know let their plus minus fuel their emotional state so it's like if they win they're happy if they lose their sad and then either way their post game typically ends up like you know taking a shower and going to bed or grabbing dinner grabbing a beer and going to bed and i think that's it's a pretty big mistake because right when you finish the session that's when things are freshest on your mind and so i would really encourage you to um spend that time like being really useful i think i might even yeah it's more even on this slide like you should have every single post game you should be getting rid of all the wasted thoughts and energy um like whatever you're feeling from the session right if if you're upset about a hand you played you need to kind of reflect like okay why am i upset about that you're just wasting your time and energy caring about things that don't matter when you could reset your mind and kind of focus on like get your mind back on the strategy every single session whether it's a good session or bad session you should spend 10 to 15 minutes focusing on the strategy and how you want to improve how you want to play spots differently the next session so i have that you should run or share marked hands like if you're using solvers um you should just run you know the three hands that were the biggest questions something i really liked from brad wilson's webinar he talked about the entry points right so this for me is like i you know i totally agree with it it's like once you finish a session if you find a couple spots that were tricky or you didn't know what to do you have to review it right you can't just imagine if every single time you have two players one of

THE FLOP CONTINUATION-BET (C-BET) Flop c-betting is one of the most important topics in poker. It is a complex subject that has been studied and discussed by poker players and theorists for decades. Contrary to most typical theory books, I decided to begin the flop discussion with the BB instead of leaping directly into c- betting. This is because I want readers to first develop a good conceptual understanding of betting in general, how the post-flop action is a function of the players’ relative positions, range distributions and SPR. After studying OOP betting and the power of position, all that is left in order to understand the flop c-bet is to analyze the situation from the IP player’s point of view. Just as we did when studying the donk bet, for this section we will use the aggregated data from thousands of GTO solutions with stack depths 20bb, 30bb and 40bb with standard GTO MTT starting ranges. The ranges in your own games might be different to the ones used for these simulations, but I have found that, as long as the ranges used are “reasonable”, the overall results for post-flop play won’t be significantly affected. If the standard ranges in your own games differ too much from the equilibrium strategies, you can still benefit by understanding equilibrium and then applying the principles discussed in this chapter to understand how your standard ranges are different from GTO and how you can deviate from equilibrium to further attack the imbalances introduced in the new strategies. Getting your own solver and running some custom simulations can help you better understand this effect and find good exploitative lines against population tendencies. In the previous section we found that, from a GTO point of view, there isn’t too much incentive for OOP to bet out on the flop, but what about IP? What is their equilibrium strategy? Are they incentivized to bet or check? Can they play a pure strategy that always checks back the flop without a significant EV loss in the way the BB can? Table 109: Result of IP Playing 100% Check Back

a 2.3bb open size won’t have a significant EV impact in your bottom line. The solvers are indifferent to using similar bet-sizings as long as the other player understands the best way to respond to each specific bet-size. Since different bet-sizes will have different optimal responses, and not all opponents will be capable of responding effectively to all bet- sizes, the best bet-size is the one that takes your opponents to a branch of the game tree with which they are unfamiliar, leading them to make the greatest number of mistakes. There must be a sweet spot for pre-flop bet-sizing that lowers your risk while maximizing fold equity. However, the game of poker is not fully solved yet, so there is no definite answer to the “correct” pre-flop bet-sizing. Furthermore, there is always room for exploitative bet-sizing against specific opponents, making applying the general bet-size guidelines more of an art form than a science. General Pre-flop Play Heuristics You will always take the highest EV action with each hand in your range at any decision point. Note the following points. From each position, you will play a distribution of hands that is strong relative to the random hands yet to act. If another player has voluntarily entered the pot, your hand distribution has to be strong relative to the remaining random hands and the hand distribution of the player who entered the pot. For example, the CO raising range vs an UTG limp has to be tighter than the raising range if the action was folded to the CO because CO has to be concerned about the UTG limper. From each position, you will play some variety of hands that will have a positive expectation against the remaining players (including the rake effect in raked games). In general, hands that use mixed strategies (sometimes raising and sometimes folding) are threshold hands. Given the card removal effects in Hold’em you can expect to see more hands having mixed strategies. The worst hands in your range will have zero EV and will be indifferent between raising and folding when playing against good/optimal opponents. However, you can increase your raising frequency by adding more weak hands to your range against weak opponents because they won’t be playing back at you aggressively enough to make the bottom of your regular raising range indifferent.

relatively recreational players and that is why the games are good so this is a situation where we can definitely expect this range to be far weaker than normal um this is probably a player who's raising their best hands and limping a lot of their junk maybe they limp with some nut hands but whatever king queen suit is definitely good enough hand to raise cut off three bets that's annoying I don't remember who this player is but we're certainly not folding the king queen suited very very easy call 10-4-2 hijack checks um I think we I'm sorry we check and then they bet 15K so they bet small this is a situation where you cannot fold against good players I know it may feel a little bit dicey checking and calling with the king queen High out of position but you can't go around folding this um you do want to consider finding some Bluffs because if we do have a hand like Jax in the scenario we probably want to just go ahead and check raise and get in maybe a hand like Ace 10. so what Bluff should we use well first off do we have a ton of value hands that want to check raise the answer is not really right we don't have a ton of combinations so we don't really need to have a ton of bluffing combinations so if we don't want to have a ton of bluffing combinations we probably want to be bluffing some high Equity draws but notice there aren't actually any of those and then some low Equity draws and I think a hand like Jack nine of diamonds or queen nine of diamonds makes a whole lot of sense to check Ray's tiny you may say could you really check raise to something like 32k and then fold to a shop and I think you could I think it's actually not not insane um that because whenever you do check raising like Jack nine of diamonds you're obviously going to fold if they shove you right and Jack nine of Dimes is probably not quite good enough to check and then call right so I think in the spot you want to have an over card with backdoor flush draw probably to check raise small and then fold some people saying Queen drag sooner I think Queen Jack scooter might be too good as well again you don't get to find all that many combinations right if you're only check raising finish value hands like Jackson Ace 10 which could be beat anyway plus um a few junky Bluffs you don't get to have all that many junky Bluffs and if you only are doing with six combinations is probably okay anyway this thing I think is probably too good to raise so we call turns into a heart's check folding out any bet Finance standard um also some people say they would raise small over the limp when somebody limps for 1500 you don't want to

understand solvers, or do proper off-table analysis. Having worked through different scenarios off the table gives you a much better sense of what is and is not a good strategy. GTO Wizard the #1 App for Poker players Study any spot imaginable Practice by playing vs. GTO Analyze your hands with 1-click START CRUSHING NOW JOIN DISCORD Author Tombos21 Tom is a long time poker theory enthusiast, GTO Wizard coach and YouTuber, and author of the Daily Dose of GTO. Latest article Preflop Raise Sizing: Examining 2 Key Factors It amazes me that, after nearly twenty years of playing no-limit hold ‘em professionally, I… How to Handle Loose-Passive Limpers Solver charts and presolved solutions do not offer much in the way of explicit guidance… Top 5 Mistakes in Spin & Gos As a Spin and Go poker coach, I regularly encounter common mistakes that players make,… An Introduction to Spin & Gos I was playing Tournaments for the first decade of my career. But after my first… Relationships and Poker In my more than 15 years of poker coaching, I’ve helped hundreds of clients improve… Do Multiple Sizes Matter? Should I work out the other tools or just stick to the crowbar? Solver results… The Science of Learning Applied to GTO Wizard The way we were taught to study in schools was flawed and has negatively impacted… Check-Raising a Single Pair In this article, I will address a question raised by Twitter/X user ’Matt Riley’, who… The Turn Probe Bet Imagine yourself defending as the BB caller vs BTN preflop raiser in a 100bb cash… When To Encourage Multiway Pots in PKOs I was recently shown this fascinating PKO hand from the GTO Wizard PKO library. Somebody… Protect Equity and Prosper When we think about the best hands to bet in a given situation, we tend… Do Solvers Have Targets? Targeting has long been a staple of exploitative poker thinking. When you’re value betting against… Disciplining Big Blind in Limped Pots When the BTN open-limps off a short stack, the postflop play against the BB should… I’d Rather Be Drawing Which is the better hand on a K♥8♦5♦ flop: K♠T♣ or 7♥6♥? OK, I’ll admit… The Curious Case of Open-Limping Buttons Before the advent of solvers, open-limping was considered the province of passive, gambley recreational players… Cleaning Out Sticky IP Callers A “sticky” player on your left, one who calls your preflop raises too often and… Defending Against Tiny 3-Bets Tournament poker is about precision. Cash games, where stacks typically run into the hundreds of… Heads up! Exploiting SB’s Preflop Mistakes Heads up (HU) tournament play presents unique challenges to the average player. Many tournament players,… C-Betting As the OOP Preflop Raiser Position is an extremely valuable advantage in poker. Most players would describe the comfort zone… Overchoice: Making Sense of Multiple Sizings Solver solutions with multiple bet sizes often involve a lot of mixing between those sizes,… River Refinements: When Your Opponent Won’t Check-Raise One of the biggest strategic differences between playing in versus out of position involves betting… Turn Barreling

a problem no mistake there um foreign but just still want to take a note that he's going to be not missing floats right that's that that's um and also that he blocked back the turn and this was a big note here because he blocked by the turn in order to check back the river and that's the note I end up taking here is it's so he can get the free check on the river so here with um top and bottom is going to always be a bet for us we don't block the main check back it's going to be jackets so we're not blocking that and his Heracles are going to be like Ace Jack and sometimes Queen Jack because it blocks are straight and doesn't block some of my Bluffs there might be some low diamonds or whatever so we still want to go all in because his ja is clear of course aren't interfered and he's still going to go with like Ace Jack type hands so he's definitely want to just be going all in here even though the straight complete and a lot of our Bluffs get there I'm still gonna have some Bluffs and it's going to be a good father and he doesn't end up having a nice Jack I don't actually remember in Revenue check because all this is going on I didn't actually see what handy had so it's good to see that yeah the bluff catches you'd expect them to have uh King five here I I told you if going all in I don't know him I think going or Lynn's pretty good but then I thought maybe a 2X pot he's gonna be really ballsy to go all in over top of it and he might treat it the same as an all-in uh and sometimes just fold some chops he doesn't fold a chop but we also get to see that he raised Jack Fireball suit on the bottom and so it's noteworthy I don't know if I do take a note on it but at least we get to see that what kind of range he is playing and definitely should be taken in here again a bit disorientated because trying to get tables get rid of tables um but definitely want to be taking those kind of notes because now we can Free Bet Jam a lot pre-flop against his opened uh and and yeah just like even like this is as wide as like Ace Ace X off suit like if it's on if someone shows me Jack five off in their opening range I would jam like ace2 or suit I would just jam it proof I'd play like someone that's playing heads up so here is another very interesting spot here so here we wouldn't want to go anything shy of getting all the chips here when he checks to turn um so yeah we set up we set up an SP of one so always thinking about spr um

Card removal The phase of a tournament when only a few players need to bust before the remainder of the players are in the money. When exactly one player needs to bust and the remainder will be paid, this is often referred to as the "stone bubble". The bubble often has strong ICM implications.

You should treat these hands as small quizzes, and try to answer the questions before moving on to the explanations. It would be easy to read through the text and convince yourself that, of course, you would have made exactly that play at the table, but you'll find the explanations much more informative if you wrestle with the questions on your own first. The hands have been compiled over the years from a variety of sources, including my own play, hands I've seen in major tournaments, satellites, and online events. In each hand I've laid out the table position and chip counts, as well as information about some of the players at the table, if known and pertinent to the hand. Study the hands, answer the questions, read what happens next, answer the next question, and in that way work yourself through the hand. Some of the hands hinge on the single crucial decision of whether or not to enter the pot. Others involve a series of difficult moves as the hand evolves. Take the hands seriously, study them carefully, and you'll be well rewarded. Poker on television needs to appeal to a wide audience of mostly casual players. As a result, the hands selected for inclusion tend to be dramatic all-in showdowns and major clashes. I don't have any quarrel with that; if I were a television producer I'd probably do exactly the same thing. But that's not real poker. Tournaments are won and lost in the trenches, where average-plus hands butt heads with average-minus hands. That's the workaday world of no-limit hold ’em, and most of the hands you'll find in this book are of that sort. My goal is to teach you how to think like a poker player. Anyone can win a pot when he flops a monster. It's how you play when you don't flop one that will decide whether you're a winner or a loser. With the help of this book, I hope you become one of those winners. ♣ ♦ ♥ ♠ This is not a beginner's book. I'm assuming that the reader already knows how to play no-limit hold ’em, either from actual play, online play, or just watching on television. However, this is not a complicated book either. I've tried to present the game the way I Play - with simple, 5 common-sense rules and a minimum of mathematical calculation. A little math facility is a good thing, and there are some simple percentages that you'd do well to commit to memory. But you don't need to be a math whiz to play good poker. Keeping your head at the table and thinking clearly is far more important. ♣ ♦ ♥ ♠ In many cases good arguments can be advanced for an alternate play to the one I recommend in this book. No-limit hold ’em is not an exact science. My recommendations are always reasonable but under certain conditions a different play could be slightly or even clearly better. Obviously, Bill Robertie and I can't enumerate every possible change in condition that would

that he called with he called with all his kings all his eights all his force all his flush draws all his strongest ace highs so all he's left with our pairs and draws and what it out of his imposition has everything that he bet with on the flop so in position saw his Queen Jack Jack Ted etc so now the outer position player on the deuce of Spades has a 52 percent equity advantage in position has a 48 percent so now let's look at the range composition here so on the right on the top we have the out of position player and on the bottom we have the imposition player now this is how we can take a look at this in position has a set 4 percent of the time out of position 1 percent of the time so that's still the same in the out of position basically never has a set now other than deuces so picked up two and a half combos reduces it peel it called with deuces with the deuce of clubs so that's that's where the set comes in to pair he only has six combos of two pair because he check-raise most of his two pairs remember he check raise with King eight and eight for the only two parry picked up was like King deuce suited eight deuce suited for do student so he picked up some of his this is his range after we went check bet call and the deuce of Spades came out so this isn't before the turn card it's after the turn card and there but here's the key part remember when we first looked at this out of position had pair 10% of the time right he had 11% top pair and 9% second pair and 3% so look at this between second pair and under pair he had 21% here now after the deuce of Spades comes out he went from 21% to now out of position has second pair 17 percent of the time and under pair 7 percent of the time and 20 percent top pair so he now has an 8 or better 23 43 percent of the time plus he has these two pairs instantly so almost half of his range is gonna be a pair of eights or better now versus before it was like 15% so that's why out of position is made up that big equity advantage because he's just folded all that junk that he had before and that's what we're gonna Matt we're gonna look at different turn cards and you'll see how the equities effects on different turn cards so this is and this is probably - what you're getting at Matthew this is probably what the equities are gonna pretty much be after it goes check bet call before the turn card comes out that's why I did the brick first cuz the brick really doesn't change anything other than Brees in a couple of more - pair combos so

9 9 9 A K No change. 5th stands pat on Eight High Straight. The Betting 2nd player checks Three Eights. 3rd checks Three Nines. 5th checks a Straight. He is satisfied to check since it just may be possible that the 2nd or 3rd hands might have made Four of a Kind. Winning Hand Straight, held by 5th player. Part Two Three Poker Stories 1 Five-Card Draw, Low Ball 2 Seven-Card Stud 3 Seven-Card Stud (Hi-Lo) 1 Five-Card Draw, Low Ball I I did not fulfil my ambition to become a criminal lawyer. Instead, I landed in the code room of the Department of State. Later, when World War I broke out, I organized a deciphering bureau to read intercepted enemy messages -the first of its kind since the Civil War. I had about 160 men and women under me. During the war and after, until the bureau was closed by a naive President, we deciphered around 200,000 messages to and from such nations as Japan, Germany, England, France, Mexico and all South American countries. I had received the Distinguished Service Medal for being the first to break the Japanese diplomatic cipher. In the 1930s I had written a book of my experiences. Upon the publication of The American Black Chamber, with its revelation of Japanese intrigue, I became a marked man in the Orient, and the Chinese authorities who had engaged me to organize a Chinese cipher bureau therefore decided to smuggle me in under the name of Herbert Osborn to avoid recognition and possible assassination by the Japanese. I choose China as the locale for the remainder of my story about how I win at poker because poker was instrumental in catching a secret agent whose mission was either to assassinate or to capture the Generalissimo. At Hong Kong I was met by my interpreter, Ling Fan, who was well supplied with money and instructed to provide everything for my comfort. He was a little man with a yellow skin, dressed in foreign clothes; his black hair was parted at the side and brushed back. My advance reputation was formidable and I had the difficult task of trying to live up to it. My resourcefulness was put to the test almost at once. Ling and I were drinking scotch and soda in the Hong Kong Hotel cocktail room and watching the beautiful and well-dressed Chinese women in their long coloured silk gowns, some split above the knee. I was about to put to Ling a question about the charms of Chinese women when he asked, a bit diffidently, 'Adviser, is it really true that a white woman's breasts are red?' When I didn't answer at once he explained, 'That's what a returned Chinese student from Paris told me.' 'Is that all he told you?' I asked. 'Well, no,' he said with some hesitation. 'He also told me - I don't know what you call it in English - but he told me it was also red.' Clearly it was up to me to show myself all-wise and all-powerful. I

be formed with a given set of community cards. For example, if you hold K4 K+, and the board has KV 10+ 74 5+ 2V, you can bet and raise to the maximum, knowing that you cannot be beat. No straights or flushes can be formed from this board, and, without a pair, neither can a full house or four of a kind. Your three Kings are the nuts. Suppose instead, with the same hand, K4 K+, the board has A+ A4 KV 7V 3+. Even though you have a much higher hand than in the previous situation (Kings full with Aces), you can be beat. Someone holding AV K+ wins with Aces full, but that is not the nuts. In this case, the nuts is A+ AV. The winner takes all. In Hold'em, the highest ranking hand wins the pot. It is not a split-pot game like some variations of poker. Split pots in Hold'em occur only if two or more players have identical high hands at the showdown. 2. Texas Hold'em in a Cardroom In a casino or public cardroom, poker games are dealt on a large, oval, felt-covered table. The table, shown in the figure below, seats the dealer and up to 10 players. There usually are no markings on the table. The dealer sits in front of a tray of chips. A plastic circle, imbedded in the table to the right of the dealer, provides a spot for separating the cardroom's percentage of the pot, called the rake. There is a slot in the table where the dealer deposits cash from players that are buying in, and a box to the dealer's left where tips are placed. A small plastic button is used to indicate which person acts last in Table Layout 1 Betting action moves to the left. Button and Blinds shift one position left after each hand. 16 THE INTELLIGENT GUIDE TO TEXAS HOLD'EM POKER the hand. The button starts with the player to the immediate left of the dealer. The person to the left of the button is the small blind, and the next person to the left is the big blind. Play proceeds from right to left: You act after the person on your right and before the person on your left. At the end of each hand, the button is passed to the next player on the left and the blind positions are shifted accordingly. The dealer conducts the game. All players receive their cards from the dealer, and the dealer exposes the community cards. The dealer collects the bets from each player and, if necessary, makes change. Players never reach into the pot or handle any chips but their own. Players never handle any cards other than the two that are dealt to them. If there is a showdown at the end of the hand, the dealer inspects the hands and awards the pot to the player with the highest hand. In cardroom poker, cards speak, meaning that you do not have to state the contents of your hand. If you mistakenly

following table compares Big Blind’s defense frequencies at 40bb and 20bb effective stack depths: Conclusion After calling a raise from the blinds, you should almost always check to the preflop raiser, regardless of whether you are in the BB or the SB. The major exceptions are on very specific flops or as an exploit against players who do not bet often enough. When facing a bet, you should recognize you are at a significant range disadvantage. Unless the bet constitutes a large fraction of the effective stack, your choice is mostly between calling and folding, though you should raise somewhat more often against smaller continuation bets. But beware of the “Jedi mind trick” where you anchor the size of your raise as a multiple of your opponent’s bet . Against a very small bet, it is generally correct to raise a larger percentage of the pot to avoid offering extremely good odds. GTO Wizard the #1 App for Poker players Study any spot imaginable Practice by playing vs. GTO Analyze your hands with 1-click START CRUSHING NOW JOIN DISCORD Author Andrew Brokos Andrew Brokos has been a professional poker player, coach, and author for over 15 years. He co-hosts the Thinking Poker Podcast and is the author of the Play Optimal Poker books, among others. Latest article Preflop Raise Sizing: Examining 2 Key Factors It amazes me that, after nearly twenty years of playing no-limit hold ‘em professionally, I… How to Handle Loose-Passive Limpers Solver charts and presolved solutions do not offer much in the way of explicit guidance… Top 5 Mistakes in Spin & Gos As a Spin and Go poker coach, I regularly encounter common mistakes that players make,… An Introduction to Spin & Gos I was playing Tournaments for the first decade of my career. But after my first… Relationships and Poker In my more than 15 years of poker coaching, I’ve helped hundreds of clients improve… Do Multiple Sizes Matter? Should I work out the other tools or just stick to the crowbar? Solver results… The Science of Learning Applied to GTO Wizard The way we were taught to study in schools was flawed and has negatively impacted… Check-Raising a Single Pair In this article, I will address a question raised by Twitter/X user ’Matt Riley’, who… The Turn Probe Bet Imagine yourself defending as the BB caller vs BTN preflop raiser in a 100bb cash… When To Encourage Multiway Pots in PKOs I was recently shown this fascinating PKO hand from the GTO Wizard PKO library. Somebody… Protect Equity and Prosper When we think about the best hands to bet in a given situation, we tend… Do Solvers Have Targets? Targeting has long been a staple of exploitative poker thinking. When you’re value betting against… Disciplining Big Blind in Limped Pots When the BTN open-limps off a short stack, the postflop play against the BB should… I’d Rather Be Drawing Which is the better hand on a K♥8♦5♦ flop: K♠T♣ or 7♥6♥? OK, I’ll admit… The Curious Case of Open-Limping Buttons Before the advent of solvers, open-limping

And: It's now time to look at what happens when stacks are smaller than 100BB.

encounter common mistakes that players make,… An Introduction to Spin & Gos I was playing Tournaments for the first decade of my career. But after my first… Relationships and Poker In my more than 15 years of poker coaching, I’ve helped hundreds of clients improve… Do Multiple Sizes Matter? Should I work out the other tools or just stick to the crowbar? Solver results… The Science of Learning Applied to GTO Wizard The way we were taught to study in schools was flawed and has negatively impacted… Check-Raising a Single Pair In this article, I will address a question raised by Twitter/X user ’Matt Riley’, who… The Turn Probe Bet Imagine yourself defending as the BB caller vs BTN preflop raiser in a 100bb cash… When To Encourage Multiway Pots in PKOs I was recently shown this fascinating PKO hand from the GTO Wizard PKO library. Somebody… Protect Equity and Prosper When we think about the best hands to bet in a given situation, we tend… Do Solvers Have Targets? Targeting has long been a staple of exploitative poker thinking. When you’re value betting against… Disciplining Big Blind in Limped Pots When the BTN open-limps off a short stack, the postflop play against the BB should… I’d Rather Be Drawing Which is the better hand on a K♥8♦5♦ flop: K♠T♣ or 7♥6♥? OK, I’ll admit… The Curious Case of Open-Limping Buttons Before the advent of solvers, open-limping was considered the province of passive, gambley recreational players… Cleaning Out Sticky IP Callers A “sticky” player on your left, one who calls your preflop raises too often and… Defending Against Tiny 3-Bets Tournament poker is about precision. Cash games, where stacks typically run into the hundreds of… Heads up! Exploiting SB’s Preflop Mistakes Heads up (HU) tournament play presents unique challenges to the average player. Many tournament players,… C-Betting As the OOP Preflop Raiser Position is an extremely valuable advantage in poker. Most players would describe the comfort zone… Overchoice: Making Sense of Multiple Sizings Solver solutions with multiple bet sizes often involve a lot of mixing between those sizes,… River Refinements: When Your Opponent Won’t Check-Raise One of the biggest strategic differences between playing in versus out of position involves betting… Turn Barreling in 3-Bet Pots There are two articles on the GTO Wizard blog that make good prerequisites to this… The Right Way To Think About Protection Suppose Paul the Protector is in a 200bb cash game and opens A♠A♣ in the… The Importance of Board Coverage The first public version of the GTO Wizard announced AI upgrade already has some useful… How To Adjust When Villain Has No Bluffs “They always have it!” is a common, semi-joking expression in poker to describe the tendency… Adjusting on Later Streets After Exploiting Flop The key to exploiting opponents profitably is knowing when to stop. I’m not referring to… C-Betting IP vs Passive Poker Players A preflop raiser enjoys a significant range advantage over a BB caller, enabling them to… C-Betting Against ICM Preflop Ranges You raise from early position (EP) in a multi-table

constructing ranges to better deal with facing 3-betting. For now though, I'll say in more general terms that the less hands we open in the first place, the easier it is to defend and prevent these player types from exploiting us when we're out of position. If opening and then folding to 3-bets is -EV , let's not do it so much when we're expecting to get 3-bet often. There are of course other options available for adjusting to avid 3-bettors including getting up and finding a better table to play on, but for now we're concerned with how we should adapt our opening range in light of this problem. See the model below for a more conservative 12.5% HJ range that will be able to stand more heat and bleed less money vs frequent 3-betting. Figure 9 - A Defensive HJ Range

what… What is Equity in Poker? The term “Equity” is ubiquitous throughout poker theory. Equity refers to your chances of winning… Range Morphology “Morphology” is the study of form or structure. You’ve probably heard terms thrown around such… What is Expected Value in Poker? Expected value (EV) is the most fundamental metric in poker. Every decision you make is… Why doesn’t my solution match GTO Wizard? So, you’ve got your own solutions to some spot, compared it to GTO Wizard, and… Understanding Nash Distance Understanding Nash Distance. One of the most common questions when studying with solvers is “Why… Combinatorics Poker Puzzle Today we have a special puzzle for you that will test your intuition as a… The 10 Most Important Concepts for New Poker Players The 10 Most Important Concepts for New Poker Players. Fundamentals are one of the most… What is GTO in Poker? The meaning of GTO in poker is Game Theory Optimal. Game theory is a study… What does GTO aim to achieve? So what exactly is a GTO strategy? What makes it “unexploitable”? What does it try…

You can win the SB stack of 15bb plus the dead money (the big blind plus 2bb that you raised). So, $W = 15+1+2 = 18bb The frequency with which you lose the pot is: %L = 100% - 43.31% = 56.69% The amount you need to call is: $R = 13bb Putting this all together: You decide to call with A♠5♠ because it is the higher EV option. When you call, you have an EV of 0.4 and when you fold, you have an EV of 0. Win Rate Another way to visualize EV is in big blinds won or lost per 100 hands (bb/100). Since we are calculating EV in big blinds, all that is needed is to multiply EV by 100 (EV × 100). Poker winnings should be measured over the long run. The ability to consistently make better decisions allows the best players to win in the long run. They take the highest EV action over and over again. As seen in this example, a player who calls every time with A♠5♠ will make on average 40 big blinds per every 100 hands more than a player who always folds. Even if 0.4bb might seem like a small reward-to-risk for calling Villain’s all-in for a big

have common cards, you'll be an underdog to win. Important exception: Limp if a raise behind you is fairly likely. JJ, TT: Treat these hands like the premium pairs, and put in a healthy raise. As before, you don't want to encourage a multiway pot. Here's a sobering statistic: a pair of jacks, facing four 88 opponents with randomly weak hands (ace-small, king-small, and two low flush draws) is only about 30 percent to win if the hands are played down to the end. 99: Play the hand, but with a 50/50 mixture of raises and calls. 88 through 22: In this situation, the small pairs benefit from what's called the umbrella effect. With one extra caller in the pot, calling with the small pairs gets you slightly better pot odds. As a result, you can call with eights, sevens, and sixes. On the button instead of fifth position, I would call with all these pairs. With the lower pairs, you're hoping to flop trips or catch an otherwise exceptionally favorable flop. AK, AQ: With ace-king raise whether the hand is suited or unsuited. With ace-queen, I would raise only with suited cards, and call with unsuited. AJ, AT: Call with ace-jack whether suited or unsuited. With ace-ten I would call only if suited. Fold an unsuited ace-ten. A9 through A2: Fold all these hands. This may seem an exceptionally conservative strategy, but if you are playing these hands, you'll often find yourself up against an initial caller who had acex and x is a higher kicker than yours. You're a huge underdog in these hands, and you'll find yourself losing many big pots when an ace flops. KQ, KJ: With a suited king-queen I would call. Fold an unsuited king-queen. I would play a suited king-jack only if I thought the opener were a loose or weak player. Suited connectors: Fold them. The problem here is that you don't have enough players in the pot yet. Be alert, though, for the ideal hand with suited connectors: you're late to act and several limpers have already entered the pot. In that case you want to limp in as well. You'll mostly be throwing your hand away after the flop, but when you do hit your flush or straight, you'll have a chance to win a very large pot. Case 4: You are on the button. The player in third position raised three times the big blind, and the player in fifth position raised nine times the big blind. One player announced he had a strong hand. Knowing that, a second player announced he had an even stronger hand. Under these circumstances, what do you need to hop into the pot? Answer: You need a monster hand. The first player just might be bluffing, but the second player certainly isn't. Don't forget, too, that the blinds have yet to be heard from, and the first player still has the right to reraise no matter what you do. AA, KK: Reraising with aces is obvious; this is the dream scenario for a pair of

which you expect to win only if… Exploiting Excessive C-Betting by IP On some flops, it is simply not possible for the preflop raiser to continuation bet… Is Limping Pimping? In a past Discord post, one of our members noted that an upside of implementing… Exploiting Excessive C-Betting by OOP A preflop raiser who continuation bets too often is always a potential target for exploitation,… Preflop Button Mastery in PKOs Playing from the Button presents many unique opportunities in any tournament format, especially in PKOs.… The Worst Turn Card Greetings from GTO land. In today’s article, we will use the Turn Reports feature to… Navigating Range Disadvantage as the 3-Bettor Picture this: We’re playing a NL500 6-max cash game, and we’ve won a few pots,… Mastering Three-Bet Pots In Position in MTTs Playing in position against a three-better is a lesson in playing to your advantages. As… Mastering Three-Bet Pots Out of Position in MTTs Three-bet pots are scary. Playing out of position is scary. Put them together, and you’ve… The Greatest Final Table in Triton History Today, we’ll examine one of the most epic final table battles I’ve ever witnessed! Our… Mastering Thin Value Bets in Checked-Down Pots Valuing your hand appropriately—determining whether it’s strong enough to value bet or so weak you… Maximizing Value on Monotone Flops Monotone flops tend to provoke great anxiety among poker players. It’s easy to imagine that… How to Defend Against Turn Donk Bets Responding effectively to donk bets on the turn is tricky;, there’s no getting around that.… How and Why You Should Use Turn Donk Bets Donk betting–taking the betting lead away from the previous street’s aggressor–on the flop is rarely… How Stack Sizes Change Your Range In this series, we have looked at factors that can influence ranges in otherwise identical… How to Leverage GTO Wizard’s EV Comparison Tool With the advent of solvers, some troubling new turns of phrase have entered the poker… Should You Ever Cold Call a 3-Bet? When there’s been a raise and re-raise before the action is on you, you will… When ICM Breaks Down If you have read my previous GTO Wizard articles and my books, you’ll know I… When Is It Correct To Fold AA Preflop? One of the criticisms of ICM is that it is boring and robotic. In my… OOP C-betting vs Loose Cold-callers In a previous GTO Wizard article, I asserted that “Playing against an in-position cold-caller is… Short-Stacked Play in MTTs Playing a short stack well is an essential tournament skill. It is extremely rare to… When To Ladder in Tournaments In my last two articles, I wrote about the effect field size and payout structure… How Payout Structures Impact ICM Last time we discussed the ICM considerations in game selection, we looked at field size,… C-Betting IP in 3-Bet Pots When you three-bet before the flop and the original raiser calls from out of position,… C-Betting OOP in 3-Bet Pots Continuation betting from out of position can be a dicey proposition in single-raised pots. Cold… Dynamic Sizing: A GTO Breakthrough

Overplay A term used to describe a situation where a player has unintentionally over-valued the strength of their hand relative to their actions.

Figure 22 - C-Bet Sizing Guide As the flop in Hand 23 is about as dry as flops can be and Hero's range very weak since he's opened from the BU, and given Hero is c-betting pretty much everything in his range here, he should opt for a size comfortably within the small zone. Half pot will do nicely. Hero bets 2.25BBs. Important: Remember that as Villain is an aware player in this hand, Hero will want to use balanced sizing. This means that he will also use this bet-size with top pair, a set and with total air. Let's have a look at an example that's not so clear:

THE IMPORTANCE OF IMPLIED ODDS 26 you’ll both flop a set, and if you don’t know he has pocket aces, you’ll almost certainly get stacked. Now your EV for a $65 reraise is −$4.80. −$4.80 = (0.88)(−$65) + (0.11)($520) + (0.01)(−$480) The remote threat of getting stacked if you both flop a set costs you almost an extra $5 a hand. That means that your opponent with secret pocket aces doesn’t have to raise as much to keep your call from being profitable. Also, if your opponent sometimes will reraise preflop with smaller pairs or unpaired hands like ace-king (as almost everyone will), then your implied odds situation is much weaker still. Sometimes when you hit your set, you won’t get your opponent’s stack. Meanwhile, when you don’t hit your set, the raiser will get you to lay down what turns out to be the best hand. In this situation, the most typical in real play, the raiser needs to raise less still to avoid offering you too high implied odds. 7 So, putting you in the raiser’s shoes for a moment, the more your opponent can narrow down the range of hands you might have, the larger of a percentage of your total stack you must bet immediately to avoid rewarding your opponent’s ability to take advantage of his knowledge. 8 The more your opponents know about the ex- act nature of your hand, the more you have to bet immediately to avoid offering them too high implied odds. Here’s another example. Say you are playing $5–$10 blind no limit with $2,000 stacks. Someone raises to $30 in early position, and you call on the button with 6♢5♢. Both blinds fold ($75 in the pot and $1,970 left to bet). The flop comes J♣7♣3♠, giving you a gutshot. Your opponent bets $100. At that point, he tells you (he’s not lying) that he has a set of jacks. Furthermore, he promises to bet all the rest of his money on the turn no matter what comes. If you call and miss your straight, you lose $100. If you call and make your straight, you still have to dodge a board pair on the river to win. Ten cards out of forty-four pair the board, so 23 percent of the time (10/44) you’ll lose $1,970, and 77 percent of the time (34/44) you’ll win $1, 970 + $75 = $2, 045. So your expected win if you catch your straight on the turn is $1,132.50. $1, 132.50 = (34 44 ) ($2, 045) − (10 44 ) ($1, 970) Thus, your implied odds are $1,132.50-to-$100 or about 11.3-to-1. Your chance to catch your straight is 4/45 or about 10.25-to-1. Since your implied odds are greater than your chance to make the straight, you should call. 7Also in this situation, the player with aces need not reraise so much because he has to balance out the threat of giving a pair the right implied odds with the risk of scaring out hands like ace-king, ace-queen, or king-queen. 8Again, when the stacks are deep,

Hand Range 316: UTG 25bb (2x vs HJ 2.75x 3-bet) • All-in 24.4% / • Call 40.5% / • Fold 35.1%

yeah whoever just said eights and nines let me ask demetrius why did you say eights and nines are the worst cards a couple other people said it too but i'm gonna ask demetrius because i have them so it's not because straight draws are blocked like so a lot of people are saying busted straight draws you know okay yeah but just think of it you're making it way too simple what's the bottom of the button opening range on queen 76 jack what's the bottom of the opening range [Music] like what is almost every single bluff from the button what cards do they have to contain so off two dates right okay every single bluff in the button is probably not every bluff but almost every bluff is either gonna contain an eight a nine or a ten okay so what would be a better hand to call with queen three or queen eight i don't know if either are gonna be a call i'm just saying what would be a better hand to call with queen three or queen eight okay good most of you are saying queen three why why would queen three be better than queen eight someone said don't block bluffs and where are the bluffs coming from i don't even know what this hand was i just made it up but where do the bluffs have to come from from the button the button has to block with bluff with off suit eights off so they're gonna block with eights first nine seconds tens third and then king's fourth potentially so they're gonna bluff with those ants because that's where they have to bluff from so when they check okay and we check when the small blind button goes all in okay here's queen eight pure fold here's queen three pure call why are we folding queen nine pure fold almost there's some blocker stuff here the queen nine's folding queen eight's folding but queen five off is calling queen three off queen deuce off so you guys see right away um let's look at another one um let's see here what's another hand you see king seven's folding why they might bluff with some king heis um here's queen yeah so the main thing right away i just noticed like i told you right away queen eight's gonna fold because why they have to bluff from eights nines and tens so we're folding all those hands and we call with queen three off because we don't block any bluffs when we have a three okay but i know that because i know what the bottom of the opening range is they bought with eight nines and sentences they can't bluff with a jack because that has a pair they can't bluff with the queens that has a pair it's hard to bluff with the king high like king tens of straight they can have king nine or king eight so again they have to have a king why do we fold queen five

Figure 78 - A Bluff Heavy Polar 3-bet Range BB vs. UTG Hero's bluff portion of his range outweighs his value portion by 40 combos to 12 or 3.33:1. No doubt this range is very exploitative, but 68% is a huge fold to 3-bet stat and so such an imbalance is easily justifiable. Bluffs are once again chosen from the best of the 'would be fold' hands based on which have the best blockers + post-flop playability. [A2s-A5s] here should outperform [A8s-A9s] due to their extra playability and similar pair flopping power. Villain is unlikely to be defending weak Ax or medium pocket pairs like 77 and 88 here and so whether or not we have a 9 or a 5 with our ace does not matter from a pair-making perspective. It does matter from a straight making perspective though and only the wheel aces have a shot at doing this. Q2. What's our river value range?

♦ Always be aware of the Villain’s bet-size and pot odds offered. Be realistic about your outs and equity. ♦ Your flop x/r range won’t necessarily consist of your strongest hands but, instead, hands that benefit from lowering the SPR and that have the right blockers (forward and reverse). ♦ Don’t be afraid to play aggressively on a flop where you have a lot of strong hands in your range. ♦ Flush draws and OESD are good hands, but they are not the nuts. You don’t have to x/r the flop every time you have a decent draw. It is important to have good board coverage in your x/c range too. ♦ Before snap folding your hand when you miss the flop, think for a few seconds about the way the equities are distributed on the flop. Consider how often the Villain should be betting the flop and how likely they are to fold to a flop x/r. BB C-bet Defense Examples Flop Strategy Example 1 BB vs 2/3-pot c-bet: BB vs UTG on A♥Q♦3♠ (40bb) Diagram 99: BB vs 2/3-pot c-bet: BB vs UTG on A♥Q♦3♠ (40bb)

Hand Range 254: HJ vs UTG (40bb) • 3-bet 4.9% / • Call 8.9% / • Fold 86.3%

Big blind (bb) The big blind (bb) is the largest mandatory bet before cards are dealt. It's also the name of the seat that places this bet (BB), who acts after the small blind (SB).

Rake cap The maximum amount the house is permitted to charge for rake per hand.

price but on a pretty weak hand suited six High three gapper says let's take a flop it's bottom pair for welcome Inferno top pair for the jonic backdoor diamonds for the both of them certainly a strong enough hand for dijonik to bet here he wants to get protection from over card hands he wants to charge the draws he wants to charge the worst Pairs and he wants to get value from the worst pairs I do Sephora are going to call all sevens or Worse sevens and Johnny probably gonna be wanting to just go for three streets with this hand if he gets a good run out goes for 1.4 the small bat size I think a large bat size is also reasonable here to get more protection and welcome Inferno doing a check raise Bluff your reason he's making this play is twofold first he thinks to jonik is betting with pretty much his entire range there are going to be a lot of hands that to Johnny has just missed with which are the over card type hands things of that nature second is if he is up against a pair that is not top pair top kicker an even top pair top kicker maybe we'll just call but a lot of one pair hands are just going to call here uh which means welcome Inferno is effectively semi-bluffing with the five outer so on the occasions where dijonik is just betting the parts of his range that have missed uh welcoming friends looking to take the pot down right now risking 3.5 to win 5 million nice odds and even when he is up against a pair he's semi-bluffing with the five outer which will improve by the river a little bit over 20 of the time with the back door straight draws and backdoor flush draws working for him as well so this is a play you can make on dry boards where you think your opponent's going to be betting a lot of Misses now the question is well did johnik re-raise here for protection or will he call we certainly know he's not folding by calling he keeps in the worst Hands by shoving yeah I think I think if he shoves even a seven is going to be really considering things because it is a significant amount of chips so I think he's kind of stuck just calling and allowing welcome Inferno to to keep betting we said it's probably he's probably looking for three streets and one face with that check race he got two of the streets right there now welcome Inferno checks the turn I think it's a spot to jonik probably wants to bet uh not too many of the two pair hands are checking and when welcome Inferno has one of these One Pair of Hands he still has a 10 chance to improve on the river and I think to jonik wants to bet for to charge those hands but he decides he's going to

have read The Theory of Progressive Knockout Tournaments you already know why we… Understanding Blockers in Poker Often when looking through a solver’s meticulously crafted grid of deception, one of the following… Flop Heuristics: IP Cold-Caller in MTTs A Cold-call refers to the act of calling a preflop raise when you don’t close… Flop Heuristics: IP C-Betting in MTTs In the world of poker, the flop is a crucial stage of the game that… Flop Heuristics for Defending the Blinds in MTTs The field of Game Theoretically Optimal poker is extensive, and thus, to simplify our strategy,… Multiway strategy in Progressive Knockout Tournaments Progressive Knockout (PKO) tournaments are much more complex than traditional MTTs. The fact that players… How To Calculate Raises In Poker One of the most frequently asked questions in poker is how to calculate the size… Principles of River Play The river offers the least complicated strategy of any betting street. With no further cards… Exploitative Dynamics GTO solutions are designed to be unexploitable, performing reasonably well no matter how your opponents… How ICM Impacts Postflop Strategy Most players understand how the Independent Chip Model (ICM) in poker impacts their strategy preflop,… 10 Tips for Multiway Pots in Poker While lots of work has been placed into research and explanation of heads-up pot strategy,… What is the Bubble Factor in poker tournaments? The Independent Chip Model (ICM) shows us the real money implications of tournament chip decisions.… The Theory of Progressive Knockout Tournaments In poker, a PKO (Progressive Knockout) tournament is a type of tournament where a portion… How To Analyze Turn Textures In Poker Master the art of turn analysis in poker. Understand how the turn card changes the… Principles of Turn Strategy Learn the principles of turn strategy in poker and discover what makes the turn unique.… Poker Strategies: Tournaments vs. Cash Games Tournament poker is not as different from cash game poker as people sometimes assume. Most… How Solvers Work A Game Theory Optimal solver is an algorithm that calculates the best possible poker strategy.… The Most Powerful Play in Poker The central strategic implication of stack depth is the question of how much equity a… When does ICM become significant in MTTs? The Independent Chip Model (ICM) was invented in 1987 by M. Malmuth and is one… How to Study GTO Solutions Tools like GTO Wizard and other solvers should not be used to memorize specific strategies.… Principles of GTO Game theory, or GTO (for Game Theoretically Optimal), is best understood not as a rigid… Interpreting Equity Distributions GTO Wizard’s range vs range equity distribution graphs are an excellent tool for visualizing which… What is Leverage in poker? Leverage refers to the risk of future betting. When you call a bet on the… Reasons for value betting in poker You’re probably accustomed to thinking of bets as either value or bluff. In this taxonomy,… The Science of Poker Performance Poker is a game of small edges and big swings. Every hand is an investment… What is Valor in poker? Can a poker hand be courageous?

of how much equity a… When does ICM become significant in MTTs? The Independent Chip Model (ICM) was invented in 1987 by M. Malmuth and is one… How to Study GTO Solutions Tools like GTO Wizard and other solvers should not be used to memorize specific strategies.… Principles of GTO Game theory, or GTO (for Game Theoretically Optimal), is best understood not as a rigid… Interpreting Equity Distributions GTO Wizard’s range vs range equity distribution graphs are an excellent tool for visualizing which… What is Leverage in poker? Leverage refers to the risk of future betting. When you call a bet on the… Reasons for value betting in poker You’re probably accustomed to thinking of bets as either value or bluff. In this taxonomy,… The Science of Poker Performance Poker is a game of small edges and big swings. Every hand is an investment… What is Valor in poker? Can a poker hand be courageous? How does your ability to value bet future streets… Pot Geometry “Pot Geometry” refers to betting an equal fraction of the pot on each street, such… A Beginner’s Guide to Poker Combinatorics Combinatorics is a fancy term for evaluating the number of possible “combinations” (combos) of any… Stack-to-pot ratio Stack-to-pot ratio, or SPR, is a way of measuring how deep the effective stack is… Equity Realization In poker jargon, equity expresses how much of the pot a hand will win, on… Variance and Bankroll Management Variance and Bankroll Management. Vital Soft Skills for Every Poker Player. How to Become a GTO Wizard Welcome to the wonderful world of game theory optimal poker! This article will serve as… The Three Laws of Indifference Indifference in poker is one of the most misunderstood concepts. The word “indifference” means that… Poker subsets and abstractions An “abstraction” is a way to simplify the game of poker. This game is so… Mathematical Misconceptions in Poker Pot Odds and MDF are foundational mathematical formulas in poker. How to solve toy games Poker is a complicated game. It’s impossible to calculate GTO strategies on the fly. By… The Value of Fold Equity – Experiment The term “fold equity” is ambiguous in the poker community. Firstly, it’s an EV equation,… MDF & Alpha MDF & Alpha. Minimum Defence Frequency and Alpha are metrics on poker that determine how… What are Pot Odds in poker? Pot odds are a fundamental calculation in poker. In the simplest terms, pot odds tell… Does your range affect your strategy? Advanced players will often tell you that your range affects your strategy. Visualizing implied odds Implied odds are the value you expect to gain over and above your raw equity.… ICM Basics As a tournament player, you may have heard about the concept of “ICM”, but what… What is Equity in Poker? The term “Equity” is ubiquitous throughout poker theory. Equity refers to your chances of winning… Range Morphology “Morphology” is the study of form or structure. You’ve probably heard terms thrown around such… What is Expected Value in Poker? Expected value (EV) is the most fundamental metric in poker.

they just fold well in that scenario you should actually raise with any two cards all of your hands because the player in the big blind is going to fold way too often what if the player in the big blind will re-raise or raise every time you put a chip in the pot from the small blind well now you want to be much more conservative from those from the small blind because you're going to frequently face aggression and you don't want to put in money with the marginal hands and just have to fold them right so you're going to want to adjust significantly especially from the later positions and the small blind is definitely where that is most true however from the small blind this is the proper chart in theory that involves some limping some calling of the big blind and the reason for that is because you're putting in half of a big blind to try to win two big blinds in the pot which means you're only putting in 25 of the pot which is not all that much and whenever you're getting essentially a discount to try to play the pot you get to play a much wider range and the reason you're just calling with some of the absolute best hands up here is because you want to make it to where when you do just call the big blind you don't have all garbage right a big mistake a lot of players make is they always raise and re-raise with their absolute best hands and they always call with their marginal hands and their garbage but that's a big mistake and it turns out limping just calling with the best hands here allows you to also profitably limp with some of these weaker hands in the bottom because your opponent just can't mindlessly raise your limp because you're going to show up with aces and kings and ace king some portion of the time in terms of other adjustments you can make away from these charts like i said from the later positions that is when you should be making more adjustments so usually from the cutoff or the button you can't really make a whole lot of adjustments from the early positions and that's because from the early positions you just have to worry about everyone yet to act waking up with a strong hand just purely based on chance right but from the button let's say you know the player in the small blind and the player in the big blind are both pretty tight they only play the best hands well in that scenario instead of raising 54.8 percent of hands on the button you should actually raise much more perhaps 100 of hands depending on how tight they are and you know alternatively if you know they're going to be re-raising you if you raised to let's say six dollars at a one-two game you know they're gonna make it 25 every time well now you would not

this scenario, however, a bluffis relatively unlikely. After a bet and two or more calls on the flop, the pot is protected. Enough players still remain that

strategy. You always stand to lose more equity than you gain in tournaments Bubble Factor shows you the equity you need to call an all-in Required Equity = BF / (BF + 1) Payout structure, stage of tournament and chip stacks influence Bubble Factor Bubble Factor is highest on the money bubble and final table Bubble Factor is different against different stack sizes Big stacks should avoid big stacks and target mid stacks Mid stacks should avoid big and mid stacks Small stacks should target everyone, but especially other short stacks GTO Wizard the #1 App for Poker players Study any spot imaginable Practice by playing vs. GTO Analyze your hands with 1-click START CRUSHING NOW JOIN DISCORD Author Barry Carter Barry Carter has been a poker writer for 16 years. He is the co-author of six poker books, including The Mental Game of Poker , Endgame Poker Strategy: The ICM Book , and GTO Poker Simplified . Latest article Preflop Raise Sizing: Examining 2 Key Factors It amazes me that, after nearly twenty years of playing no-limit hold ‘em professionally, I… How to Handle Loose-Passive Limpers Solver charts and presolved solutions do not offer much in the way of explicit guidance… Top 5 Mistakes in Spin & Gos As a Spin and Go poker coach, I regularly encounter common mistakes that players make,… An Introduction to Spin & Gos I was playing Tournaments for the first decade of my career. But after my first… Relationships and Poker In my more than 15 years of poker coaching, I’ve helped hundreds of clients improve… Do Multiple Sizes Matter? Should I work out the other tools or just stick to the crowbar? Solver results… The Science of Learning Applied to GTO Wizard The way we were taught to study in schools was flawed and has negatively impacted… Check-Raising a Single Pair In this article, I will address a question raised by Twitter/X user ’Matt Riley’, who… The Turn Probe Bet Imagine yourself defending as the BB caller vs BTN preflop raiser in a 100bb cash… When To Encourage Multiway Pots in PKOs I was recently shown this fascinating PKO hand from the GTO Wizard PKO library. Somebody… Protect Equity and Prosper When we think about the best hands to bet in a given situation, we tend… Do Solvers Have Targets? Targeting has long been a staple of exploitative poker thinking. When you’re value betting against… Disciplining Big Blind in Limped Pots When the BTN open-limps off a short stack, the postflop play against the BB should… I’d Rather Be Drawing Which is the better hand on a K♥8♦5♦ flop: K♠T♣ or 7♥6♥? OK, I’ll admit… The Curious Case of Open-Limping Buttons Before the advent of solvers, open-limping was considered the province of passive, gambley recreational players… Cleaning Out Sticky IP Callers A “sticky” player on your left, one who calls your preflop raises too often and… Defending Against Tiny 3-Bets Tournament poker is about precision. Cash games, where stacks typically run into the hundreds of… Heads up! Exploiting SB’s Preflop Mistakes Heads up (HU)

Hand Range 214: BN vs CO (25bb) • All-in 5.9% / • 3-bet 3% / • Call 13.5% / • Fold 77.5%

Pots The last thing you want to do when on a draw is narrow down the field. The more players in the pot the better. Attempting a long shot raise in hopes of bluffing everybody out is just a bad play. It’s not going to work nearly often enough to make it profitable. When To Raise Raising the turn in marginal situations can be an expensive play, but it’s one you’ll need to make more often if you are playing in higher limit games. Before you go raising up a storm, consider the following four situations where this play is most effective. 1. To Maximize Your Profit You should only make this play when you feel you have the best hand. Your 147 goal isn’t to drive your opponent out of the pot, although that wouldn’t always be a bad thing; rather, you are simply trying to get maximum value for your hand. Let’s look at an example. In the middle position with K-K, you raise, and only the big blind calls. On a J? 7? 3? flop, the big blind check-raises you. Reraising on the flop wouldn’t be a bad play, but what about just calling? By simply calling on the flop, you will entice your opponent to bet the turn unless a scare card hits. When he does bet the turn, you can go ahead and raise him. This would be considered a variation play. You should only use it on a relatively safe flop. If there is a flush draw or straight draw present, there are too many potential scare cards out there that would cause your opponent to check the turn, thus costing you a bet. For example, on a flop like 9? 10? 5?, any heart or any overcard may scare your opponent into checking. So on a dangerous flop, you’re better off playing the K-K fast. 2. Semi-Bluffing on a Scare Card Earlier, I advised you to avoid fancy plays when the straightforward play will work. That still holds true, but there are certain situations where a well-timed fancy play will win you the whole pot with little risk. Consider the following situation. You have J? 10? from early position. Although you’d often just call, this time you mix up your play and raise, and only the big blind calls you. The flop comes 7? 9? 2?. The big blind check-raises you on the flop, and you decide to just call. Now the turn card comes the K?, and your opponent bets. If you don’t think your opponent can beat a pair of kings, this wouldn’t be a bad spot to try to take the pot from him. Since you raised from early position, you could easily be representing A-K. You are playing the J? 10? exactly as you would the A-K, and if your opponent believes you’ve got A-K, he may decide to fold a pair of nines. If not, oh well. You were going to call the turn anyway, so it only cost you one extra bet. If he does in fact have a

back to death The Simple Solution to this situation is to play less hands out of position that works fine in the short term but as we get better however we need to learn how to defend ourselves out of positions such as the hand we saw today I prefaced it with this person has been loose aggressive so we probably did need to call down a lot more than normally we'd like to one rule of thumb we can use is most people can't triple barrel block that that really goes through especially with I find that if the person has recreational markers at all like they're just limping in a little bit more they're calling a little bit more pre-flop than they should a lot of those folks do have a problem triple barrel bluffing as much as they should so in general I'll give them the benefit of the doubt the first time but continuing obviously we showed a situation where we did not give someone the benefit of the doubt so that does happen too if you see the person is capable of being loose aggressive so recapping one rule of thumb we can use is most people can't triple barrel Bluff almost everybody can continuation bet Bluff on the Flop some people can bet the turn is a bluff not many people can fire the river as an absolute Bluff when we're playing an unknown player we should give them the benefit of the doubt the first time especially if we're playing lower Stakes if we're a little too tight on later streets to start the session that's fine once we identify a player as a maniac we can change our strategies we can pick any halfway decent top pair and called out and we do have to really be prepared to call down if we believe the person is going to identify while this person is weak here uh their their range is capped I better fire calling down without a plan however until a player proves themselves to be capable of advanced play we're not going to give them credit we'll play our big pots in position until further notice playing too many hands from early position playing too many hands from early position is a great way to lose a ton of money in online cash games some players like to limp their small Pairs and suited gappers from early position this is generally a losing play it would would be better to raise or fold with those hands when you're starting to play online cash games you should strive to play tighter from early position when you open with so many players to act behind you it is likely someone will pick up a solid hand if they three bet you then they have put you in a disadvantageous position if you call out of position you're only trying to save the big lines you already put in the pot it will be massively difficult to make a profit from out of position

Hand Range 39: CO vs BN 3-bet • 4-bet 20.6% / • Call 20.4% / • Fold 59%

Using New Skills at the Poker Table How many times has it happened to you that you make a mistake only to realize immediately – perhaps even while you’re putting the chips into the pot – that you should have known better? How many times has your performance at the table failed to live up to the knowledge you know you possess, based on all your off-the-felt study? Away from the table, it’s easy to nod along and convince yourself everything makes sense when you read articles as beautifully written and explained as this one. You’re not alone , many students of the game report difficulty accessing their knowledge when under poker’s many stresses, which include time, financial, emotional, and social pressures. This leads to what I call “boneheaded” mistakes, errors owing not to a lack of understanding of the relevant concepts but rather a failure caused by the heat of the moment . The good news is that everyone experiences some deal of struggle with this, and it’s a skill that can be practiced like any other. Leveling up your capacity for putting knowledge into practice will give you an edge over the competition just as surely as improving your hand reading or range construction. Let’s learn some concrete strategies you can practice . Some of these may work better for you than others, so feel free to pick, choose, and remix them as needed. Focus on a Single Skill Working on everything at once usually results in very little progress on anything. Instead, pick a single skill to focus on for a given session. If you choose to focus on value betting, for instance, give yourself permission to think less deeply about bluffing opportunities. When studying, instead of passively consuming whatever the latest strategy video or blog post happens to be, seek out material related to your chosen skill. Come into each session with a list of specific things related to that skill you’d like to practice. Once you make some progress on your chosen skill, or just find yourself getting bored, pick a new focus for a while. You can always return to the original one later. Your development as a poker player will be a constant back-and-forth. There is no mastery, only progress. Practice in Slow Motion Before you practice a new skill over the table, practice in “ slow motion ” first. When reviewing a hand history or playing against the GTO Wizard trainer , you can strip away all the time and financial and social pressure and focus solely on your thought process. Practice this way until you are satisfied with your ability to access your newfound knowledge effectively in a matter of seconds . Then, you can take it to the next level by deploying your skill in real-time, against real opponents, for real money. Focus on Focus Playing deliberately is a skill just as surely as hand reading and value betting are. Like those other skills, you can practice and get better at it. Playing deliberately is a skill just as surely as hand

dynamic. SB has no pure bets, but the hands they best often are either already strong (middle pair or better) or drawing to something strong (flush draws, straight draws, backdoor draws). Hands as strong as A ♥ 3 ♥ and K ♣ 5 ♣ are pure checks, with the intention of folding to even a small bet. The problem with these hands is not that they lack equity. A ♥ 3 ♥ flops nearly 45% equity and retains about 40% equity vs BB’s 33% pot bet. The trouble is equity realization . Ace-high will be a difficult hand to take to showdown, as BB will be able to bluff and value bet effectively on many runouts. Even when A ♥ 3 ♥ improves, it improves mostly to marginal hands that will still be tricky to play. Turning third pair when an open-ended straight draw comes in is nothing to celebrate. Turning an Ace is nice, but one of the three Aces will also put three diamonds on the board. Even backdooring a straight can get dicey, as it will be the low end of a four-card straight on the board and there may well be flushes to worry about as well. Being likely ahead is a reason not to bet. This gets at another common misunderstanding. Many players believe they should bet the flop with hands like A ♥ 3 ♥ that are likely ahead but vulnerable to both free cards and bluffs. In fact, being likely ahead is a reason not to bet. SB is better off bluffing with weaker hands, those that benefit more from fold equity but also have more potential to improve when called. Even though A ♥ 3 ♥ and similar hands will fold if they face a flop bet, checking them is not the same as giving up. BB checks back more than half the time at equilibrium, in which case these hands retain their value. Common Exploits Though we have identified certain types of hands that many humans bet more often than a solver would, these bets are not necessarily mistakes. Precisely because blind versus blind play is so tricky, it is also very possible your opponents will make big mistakes which could make these bets profitable exploits. For example, at all stack depths, the BB’s equilibrium strategy involves a polar raising range versus the SB’s limp, with hands like 72 o and T4 o raising very aggressively. Many human players, however, raise a more linear range from the BB, preferring to check their worst hands and grow the pot with only “good” hands. This results in an overly weak checking range and a much larger equity advantage for the SB in a limped pot, which increases the value of many of SB’s flop bets relative to the equilibrium. Many human players are also prone to undervaluing their own weak or unpaired hands when facing a flop bet in the BB, leading to too much folding and not enough raising . This, too, will increase the value of many of SB’s bets, turning hands that

top pair makes the cut. UTG had considerable incentive to bluff their worst hands and to value bet their strongest hands on the turn . When they decline to bet the turn, their range consists mostly of medium-strength hands, with very few slowplayed or rivered monsters. Their lack of weak hands to bluff with means they don’t do much overbetting, even with the nuts, after BB checks. Conclusion River play cannot be evaluated in a vacuum. Which player has the range advantage and thus prefers to bet more frequently, how large they should bet, and how strong hands must be to value bet all depend heavily on the previous action. Calling decisions are also highly contextual and depend on the composition of the betting range and the characteristics of specific cards, not merely the pot odds and the board texture. Understanding these concepts should enable you to avoid big, expensive river mistakes, but you will nevertheless face many tough river decisions with no clearly correct choice. That can be frustrating, but it helps to remember solvers face the same dilemma. Every mixed strategy in a solver solution represents a tough decision, and struggling with these spots over the felt does not necessarily constitute a leak in your game. GTO Wizard the #1 App for Poker players Study any spot imaginable Practice by playing vs. GTO Analyze your hands with 1-click START CRUSHING NOW JOIN DISCORD Author Andrew Brokos Andrew Brokos has been a professional poker player, coach, and author for over 15 years. He co-hosts the Thinking Poker Podcast and is the author of the Play Optimal Poker books, among others. Latest article Preflop Raise Sizing: Examining 2 Key Factors It amazes me that, after nearly twenty years of playing no-limit hold ‘em professionally, I… How to Handle Loose-Passive Limpers Solver charts and presolved solutions do not offer much in the way of explicit guidance… Top 5 Mistakes in Spin & Gos As a Spin and Go poker coach, I regularly encounter common mistakes that players make,… An Introduction to Spin & Gos I was playing Tournaments for the first decade of my career. But after my first… Relationships and Poker In my more than 15 years of poker coaching, I’ve helped hundreds of clients improve… Do Multiple Sizes Matter? Should I work out the other tools or just stick to the crowbar? Solver results… The Science of Learning Applied to GTO Wizard The way we were taught to study in schools was flawed and has negatively impacted… Check-Raising a Single Pair In this article, I will address a question raised by Twitter/X user ’Matt Riley’, who… The Turn Probe Bet Imagine yourself defending as the BB caller vs BTN preflop raiser in a 100bb cash… When To Encourage Multiway Pots in PKOs I was recently shown this fascinating PKO hand from the GTO Wizard PKO library. Somebody… Protect Equity and Prosper When we think about the best hands to bet in a given situation, we tend… Do Solvers Have Targets? Targeting has long been a staple of exploitative poker thinking. When

than getting sucked down the tube. Remember, big pairs play well against one low hand but poorly against multiple low hands. This basically sums up concept seven but I want to touch on one other situation briefly. What do you do when you pick up a hitchhiker who is also going high when you have the big pair? Example Two You: Q-7 Q Player One: x-x 4 Player Two: x-x J The first thing you need to ask yourself is, what kind of player is your opponent? Would he play two jacks here? Would he play a three-flush here? Hopefully for your sake, the answer to either of these questions would be yes. But if I happen to be Player Two, the answer is no, and you are in for a world of hurt. I may have an ace-baby suited, but chances are I have a concealed high hand. Again, in this situation, you should fold and run screaming from the table. This leads us into our next concept. 240 CONCEPT 8: PLAYING A CONCEALED HIGH HAND When you play a concealed high hand such as rolled-up trips, buried aces, or a buried pair bigger than anyone else’s upcard, play your hand according to what your upcard represents. In other words: (1) If you have a high card, raise as you normally would with a big pair. (2) If you start with a middle card, raise. If a bigger card reraises you, just call until you get to bigger betting on future streets. (3) If you catch low, represent a low hand and play accordingly. If heads-up against a high hand, you might be lucky enough to catch bad on fifth street. This will allow you to raise and get a double bet in on a big bet street. (4) If you catch what appears to be a bad card in a multiway pot, allow yourself to be put in the middle, never showing strength, which would tip your hand. If you are fortunate enough to start with a rolled-up hand and make quads on fourth street, remember this: In seven-card stud-high, you should almost always check this hand on fourth street. No matter how obvious it may seem, you want to give your opponent a chance to make something or some kind of draw to call you with. Conversely, in stud eight-or-better, you want to bet out right away, no matter what. If your opponent is going low, bet whether he catches good or not. Make him pay to draw to his low, especially if he’s trying to backdoor it. Also, even if it appears he is going low, he may also have a concealed high hand and might be able to continue. CONCEPT 9: DISPELLING A LONG-HELD MISCONCEPTION This is an extremely important concept, not just in eight-or-better, but in almost all forms of stud. Curious yet? Okay, let me break it down for you. You’re playing in an eight-handed stud game and a very tight player raises with an ace-up. Since your such a good player, you throw away

to avoid ending up in a marginal spot where you’re making decisions about whether to call or fold with a bluff catcher. You don’t want a K in the AKQ game ; you want an A . Sometimes, in pursuit of an A , you end up with a K . When that happens, you must make the best of it. But the chance of improving to an A is worth a lot. Could this hand improve to something nutty? Here is BB’s turn strategy facing a 125% pot bet on A ♥ T ♦ 6 ♥ 4 ♠ : With the exception of AQ and AK , which beat some value hands, top pair is indifferent between calling and folding. Nut flush draws always fold unless they have a straight draw as well. Yet lower flush draws with a pair like 5 ♥ 4 ♥ and Q ♥ T ♥ never fold . Despite being lower ranked and having worse blockers than A9 , these hands always call (or raise). Neither the draw nor the bluff catching value alone is enough to make calling profitable. It is the combination of improving to a flush or showing down the best hand unimproved that gets these hands over the line. In fact, BB starts folding top pair as early as the flop when they don’t have a significant redraw Redraw To have a made hand but also a draw to a better hand. to go along with it. Notice that A5 is indifferent to calling the 76% pot continuation bet unless it also has a backdoor flush draw: You may be more familiar with this concept than you realize. Suppose you’re on the button preflop, facing a raise from UTG. Would you rather call with 87 s or K7 o? It could go the other way if the bet were all-in, but with money behind, you probably prefer the 87 s. K7 o is a (slightly) above-average hand preflop, but it rarely turns into anything nutty. It often misses the flop entirely, and when it does hit, it makes tough-to-play hands like bottom pair or top pair with a bad kicker. 87 s may be the lower-ranked hand, but its potential to turn into a straight or flush makes it a better candidate for playing after the flop. It is never too soon to fold top pair. The same principle applies when you’re facing flop and turn bets. The more money remaining to be wagered, the more you should concern yourself with what the hand could turn into on later streets rather than its current rank. Contrary to popular belief, there is no prize for being ahead on the flop , nor is it “too soon” to fold top pair. Practical Bluff Catching What makes these two cards good for calling? Start with a rough sense of how often you ought to continue . This is primarily a function of the bet size relative to the pot—you should be more stubborn facing smaller bets—and range dynamics. If you started with a weaker range

Figure 74 - River Barrel Factors The first factor is identical to that described for turn barreling, it's just that now Hero's range can only have been improved by making a made-hand not by making a draw. Having four cards to a flush is not so much use with zero cards still to come. Rivers are scary for Fish in the same way that turns are. Overcards complete the AK (a hand Fish love to assume their opponent holds) and flush cards complete flushes. That said, Hero has to be more careful when bluffing random Fish on rivers as showdown is tantalisingly close. Many Fish will just click call with their bluff catchers knowing that they get to see Hero's hand immediately without having to invest any additional money on the next street. As a result, river fold equity vs. Fish is generally a lot lower than on the turn. It is for this reason that Regs at the microstakes are very used to adopting unbalanced, value-heavy river betting ranges. These work very well against Fish but are very exploitable against more solid players.

you will stop noticing when your opponents change gears from loose to tight or passive to aggressive. You may even miss when players leave the table and new players enter the game. This is important because a few different players can change the whole table dynamic very quickly. 2. Thinking, perhaps I am not a very good poker player. I have coached players who fall into this syndrome and I have thought this way for a short period. You have to realize that the cards will not always go your way. There are ups and down when you play poker and if you are a good player your bankroll will increase in increments, not all at once. Your bankroll will go down because of bad beats, short bad streaks or even long durations of having the second best hand. This does not mean you are a bad poker player; it is just poker. Try to remember this; remember when you were doing well and always had the best hand at the showdown. Use this time to study the game and increase your skill instead of beating yourself up. Feeling bad about your game is really just a waste of time if it takes away from the time you could be spending learning more about being a good player. 3. Changing your game style to a tight/weak game for fear of another bad beat. This is another way to feel bad about yourself because you will always be losing. You can break out of a slump if you take some swings at the pot when you have an advantage. 4. Changing your game style to a loose/aggressive to make up for the lost money or have the "any two cards can win" mentality. This is called “steaming” and is a sure fire way to lose the rest of your bankroll. The cards have no memory and they do not owe you a few big wins to make up for your losses. Good players will notice that you are steaming and happily step up to the plate with better hands pre-flop. You become a target when you steam. 5. Slowing the process of rebuilding your bankroll. When you are far ahead after the flop, you over-bet the pot shutting everyone else out so you do not get full value for your good hands. This happens when you are afraid someone will draw out on you and do not let the pot build to a decent amount. Essentially, you want the victory but are not being patient enough for the fruit to grow on the vine. For the beginner player, having one or more bad beats inflicted upon you in any few sessions can lead to any of the above feelings. You must remember that bad beats are a part of the game and the probabilities always even out. If you have a solid game, and the bad beat was not because of making bad decisions, then you have to stick with your game. The cards will turn around; you cannot make them change. When

Table 77: HJ Action Frequencies (40bb) With 40bb, the HJ 3-bets 5.48% on average with a polarized range. The 3-bet/folds are mid to low suited Ax, AJo, ATo, KQo, and some Kxs. The calling range includes pocket pairs, AQo, AJo, KQo, suited broadways and suited connectors. The frequency with which the suited connectors are called increases as the initial raiser’s range is wider (Hand Ranges 252-255).

One-gapper Describes preflop hands where there is one card rank between the ranks of a player's hole cards. For example, 86 is a "one-gapper", as the 8 and 6 are gapped by a 7.

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model since they are so often profitable calls and hands that want to keep the price of seeing a flop low and have little interest in thinning the field. Realising implied odds is the goal of these hands in multiway situations. Difference 2: Big offsuit hands tend to depreciate in value since they prefer to be heads up in order to have good relative hand strength with the one pair hands they flop most often. These hands are, therefore, often better choices to turn into double blocker bluffs as flatting them may become -EV in three and four way pots. Difference 3: Fold equity is usually more limited due to the multiway nature of the situation and so linear ranges are more commonly applied in squeeze spots than polar ones are, though of course, there's a time and a place for both. With these points in mind let's build ranges for a couple of squeeze spots. Just like before we'll be using Figure 49 to construct out of game ranges. In the third and fourth example hands to follow we'll be zooming in and going back to Figure 58 to practice our in game decision making. Have a look again at Figure 49 and have a think about what kind of range we'd be inclined to adopt here and what the different parts of that range would look like. Starting at the top, this is an extremely clear spot in which to be polar. Both players are folding a substantial amount to 3-bets and Hero is thrilled to have a very wide flatting range with incredible pot odds closing the action. Moreover, SB is probably folding much more out of position with a capped range than he would be in most other situations facing 3-bets and so we can expect his Fold to PF 3Bet After Raise stat to increase dramatically in this specific spot. This illustrates the dangers of having a flatting range from the SB in the first place. Now onto Hero's subranges:

Ok so what does this have to do with having a raising range in open action spots? When we want to be balanced, it may be better to just call everything we're continuing with or it may be better to balance bluff raises with value raises. Against Regs, we need to ask ourselves if we want a raising range at all since our overall strategy and balancing it are important to us. When we're going all out exploitative against a Fish, however, we simply don't care about balance and should revert to the table in Figures 42 and 43. Against weaker players, it's usually better to consider the hand in a vacuum, not caring about the shape of our range since these players are not likely to be aware or skilled enough to exploit that shape. In fact, it's because these players are normally very unbalanced themselves that we want to be unbalanced in the way that best takes advantage of this. Against Regs we have much more incentive to make sure our ranges aren't wildly out of sync because we expect these players to be observant and skilled enough to exploit us if they are. As we saw earlier in Hands 57 and 58, protecting our calling range and leaving our range uncapped with strong made-hands was a good idea to ensure that our range wasn't skewed too much towards weak hands when we merely called the flop bet. When we zoom out away from our actual hole cards in one hand and see that, in general, we don't want to be raising a flop at all for value, it follows that we don't really want to be bluff raising the flop either as this would make our raising range obviously weak and to do this would be to adopt a highly unbalanced and exploitable strategy. This is something we want to avoid without good reason to think it's higher EV , for example, with the read that Villain folds too much to flop raises, and even then, we'd probably want some value in our raising range to avoid being so blatantly out of line. It's easy to notice and counter such an unbalanced strategy in such a commonly recurring spot.

are constrained not only by the size of the raise but also by the risk of players behind them calling or squeezing. Only the BB who’s closing the action makes calling decisions based solely on the pot odds, and so their decisions are more sensitive to changes in those odds. Players facing a raise are constrained not only by the size of the raise but also by the risk of players behind them calling or squeezing. Raise Size and Fold Equity This data puts in perspective the compromises entailed in choosing a raise size. Larger raises increase your risk against IP players in exchange for greater fold equity against the BB and, to a lesser extent, the SB. Larger raises increase your risk against IP players in exchange for greater fold equity against the Blinds. Larger raises do buy additional fold equity from IP players as well, but not in an efficient way. A 3bb open risks 50% more than a 2bb open but gets only 5%–10% more folds from HJ, CO, and BTN. And that’s in the unraked game! In the raked game, raise size barely affects these IP players’ VPIP frequencies . Only the BB folds 50% more often to a 50% larger raise. Growing the Pot But doesn’t a larger raise also grow the pot for your stronger hands? Yes, but very few hands count as “stronger” in this context. In the raked game, AA has an EV of 10.15bb when opened for 3bb versus 9.48bb when opened for 2bb. KK and AK s are the only other hands to have higher EVs with a 3bb open. AK o has the same EV with both sizes, and QQ already shows a significant preference for the smaller size , 1.13bb as opposed to 0.95bb when opened for a 3bb raise. EV Comparison LJ Open-Raise Sizings @100NL Rake 2 bb LJ open-raise 3 bb LJ open-raise These EVs assume 200bb effective stacks and 100NL rake, but the results are not much different at 100bb or in an unraked game . Your best hands have lower EV with shallower stacks, but everything else performs better in early position when there is less money to be wagered. Hands as strong as QQ still perform better with a 2bb open than a 3bb open. When open-raising, you almost always prefer to take it down immediately or get heads up against one of the Blinds. Getting called or 3-bet by an IP opponent costs you EV with all but your strongest hands. When opening from early position, small raises hedge your risk against the less good outcomes while giving you the opportunity to achieve the better ones. Smaller raises steal the blinds less often and yield lower EV if you get heads up against the BB (you’re heavily favored in this scenario, and so would prefer a larger pot), but they also lose less when an in position opponent enters the pot. Opening the Button The situation is different when opening from the BTN, but only slightly. Larger raises still do not yield proportionately more

you’ve established a firm and profitable foothold at the higher level. But you always have to be willing to come back down. And you can’t get too hooked on labels. A lot of people do, you know. They get this sense that they’re, for example, a $10/$20 no-limit player and even if the $5/$10 game looks really good, they won’t play it, because in some existential sense, it’s beneath them. I don’t need to tell you how ridiculous that is. That’s the ego talking and nothing more. People think they’re a big deal and in the name of preserving some counterproductive self-image, they look off profitable opportunities in smaller games. It happens every day. You walk into the casino and see that the $10/$20 game is filled with players you know you can’t beat. If you’re honest, you admit this to yourself, then play in a good $5/$10 game or even the $2/$5 blind game, which is full of deep-stacked drunks. If you’re not honest, if you’re all up in your ego, you play in the big game and get crushed. How does your ego feel now? It’s simple. You’re not a $10/$20 blind player. You’re not a $1/$2 blind player. You’re a poker player. You’ll play in the best game you can find, where “best” is a function of your bankroll, state of mind, and opponents you face. Remember that the smaller game has several tangible advantages. Worse players. Less variance. And an opportunity to do something that’s really great for your game: play your best, no matter what the stakes. A lot of people just can’t do this. They get into a small game and figure that the money doesn’t matter—they really can’t get hurt too bad—so their discipline and strategy go out the window and they basically fart around. You know what? I could be playing in a $.01/$.02 game—hell, I could be playing in a no-money game—and still be committed to doing the only thing that matters: making good decisions. I don’t need the money there to keep my attention. The game itself keeps my attention. Solving thedecision-making problem keeps my attention. And it should for you, too. In other words: DON’T DEFINE YOURSELF BY THE MONEY DEFINE YOURSELF BY THE GAME When that happens, it’s the decision-making process, not the money, that gets your rocks off, and then a lot of negative stuff tends to go away. Among other things, bad beats don’t bother you at all (well, not much). When you get your opponent to take the wrong price on the flop and again onthe turn, but he sucks out on the river, oh well. You forced two mistakes. If you’re only about the results, you hate that. But if you’re there to play correctly and make the other guys do otherwise, you don’t care. You know that money’s coming back to you, purely as a function of your decisionmaking edge. Losing Streaks Bad things happen to good people. It’s a fact.And losing streaks happen to the best players in the world. So the question is,

doesn't make much sense to change the strategy the other thing people are so scared to bust out of the main event it's one tournament is it an important tournament like yeah it's a cool tournament and stuff but like for my year it's less than five percent of the total buy-ins i'm gonna play for the whole year it's less than five percent you know i'll play probably somewhere between like a quarter million i mean in a normal year without the pandemic like quarter million in buy-ins like people just like lower their ev so much because they're trying to adjust their their pain to adjust their strategy what you're paying with is ev and that literally is what makes the main event so like good and like i've noticed it through the first two days where there's spots where i'm just getting two three four times the value like no one wants to bet big people aren't getting value with their good hands they're like checking behind with like six high and pots because they don't want to bluff off their chips and stuff so um yeah it's just um just food for thought you know and for you guys like maybe it's not the main event let's say you satellite into like a you know big online tournament or you satellite into a wpt tournament or a thousand dollar live tournament you know don't go in changing your strategy go in and play the game that you know and don't like just try to like be careful and survive like that's not how you make money in tournaments so all right um cool we're gonna start with this hand which isn't doesn't seem that exciting on the surface but i think this uh spot is one of the most important spots in poker so button makes it two and a half x uh anyone folding here pre-flop um i call uh 109.5 two clubs we check this parabet's 1 000. uh what do you guys think in here so how do we think about this well first off folding is not an option here that's number one um that's like you always want to start in spots with like eliminating one of the options if you can so i think folding is definitely versus the button not an option here that's number one so we got check race or check call so we gotta weigh the merits of those two options um obviously we have a gut shot we have a club if we didn't have a club check raise would not be an option here why is folding not an option well we're up against the button who's raising with h4 offsuit a6 off suit all this stuff we got a gut shot you know if we had a pair we have way too much equity to fold yes we have eight high but we have a lot of equity against the opponent's range they can have ace king you know base queen like it's a disaster

Hand Range 239: CO vs LJ 4-bet (40bb) • Call 50.9% / • Fold 49.1%

our flushes well we check a lot we check a lot with our flushes why well let's take a look here if we bet 75 percent of the pie what is our opponent call with well they call with a6 they call it ace five they call it queen nine they call it jack nine they call it nine eight they call it nine seven they call with a pair of aces they even fold they say pretty cool uh they call sometimes with a pair of tens but most of their calling range is a pair of aces trip nines right you guys see that here what if we check let's go back say it's the nine of hearts still now if we check what's their betting range what are they with ace eight they check what are they bet with they bet with a nine the betting the the the betting range is almost the same as the the the calling range it's pretty much like yeah they have a couple flushes here but now they bet say that they bet two thirds here they bet seven big blinds do we play it safe we got seven high flush draw what do we do we have a seven high flush draw what do we do we don't call we raise they bet seven big blinds we make it 44 big blinds i'm gonna make it huge here we go there's all these are all flushes flush flush flush flush flush flush flush full house full house flush what do we check raise bluff with here here's ten eight with the eight of clubs you're ten seven with the seven of clubs sometimes ten six with the six of club sometimes queen of clubs five king of clubs five five four like pear and a flush blocker or something yeah so this is how you get a lot of money in the pot this is how you get like 30 40 big blinds in this pot on the river okay now let's look at a different river instead of the nine of hearts let's say it's the deuce of hearts now what are we gonna do with our flushes we already talked about this before and i haven't looked at this but i'm assuming we're gonna mostly bet with our flushes now we're gonna check sometimes maybe we check like 15 of the time 20 percent of the time but now we're mostly going to bet why because they're not going to bet if we check yeah they'll bend and ace but it's not like they're not going to bet call with an ace anyways like some of our flushes are still checking but like we're betting a lot more with our flashes gears king eye flush queen eye flush queen eye jack high flush yeah we check sometimes with a flush still we still check sometimes but let's like also too like we're betting like massive sometimes like this is 30 big blinds or something we're betting here this is

a team of Canadian programmers from Quebec, developed… GTO Wizard AI Explained We are excited to introduce GTO Wizard AI, formerly known as Ruse, the world’s best… GTO Wizard AI Benchmarks GTO Wizard has combined the power of artificial intelligence with traditional solving methods to bring… Table Management in PKOs Perhaps the most important strategic consideration in Progressive Knockout Tournaments (PKOs) is making sure you… Overcalling From the BB In poker, overcalling refers to calling a bet or raise after another player has also… Understanding Which Mistakes Cost You the Most Money I am fortunate enough to have worked for many years with the mental game coach… Overbetting The Flop in Cash Games Although most commonly analyzed on turns and rivers, flop overbetting can be a devastating weapon… Using New Skills at the Poker Table How many times has it happened to you that you make a mistake only to… Flatting Ace-X Hands Shortstacked Playing out of position is tricky, but it’s an essential part of tournament play. With… Playing Limped Pots as the BB in MTTs Success as the BB in limped pots begins before the flop. The BB’s equilibrium strategy… The Absurd Game Theory of Chopped Boards A “chopped board” in poker is one where the community cards make up the best… Playing Limped Pots as the SB in MTTs MTT confrontations between the small blind and big blind force no-limit players into uncomfortable situations,… The Art of Learning Poker In his book The Art of Learning, chess and Push Hands champion Josh Waitzkin describes… Is Donk Betting for Donkeys? “Donk betting”, or betting from out of position into the player who was the aggressor… Delayed C-Betting This is a companion piece to Probe Betting. It stands on its own, but understanding… Probe Betting As far as rules of thumb go in poker, “check to the raiser” is a… ICM and Blind Battles: The Big Blind This is a companion piece to this article on the SB’s strategy for blind vs… ICM and Blind Battles: The Small Blind ICM incentivizes more conservative play, which means that at stages of the tournament where risk… The Initial Bettor’s Advantage The mathematics of poker holds a little-known secret: the first bettor enjoys better bluffing odds… Mastering the Chiplead: The Scalpel and the Sledgehammer When you have a lot of chips at a final table or in another situation… Flop Heuristics: IP C-Betting in Cash Games Our never-ending quest for money and fame leads us to the flop. We open the… How ICM Impacts Restealing From The Blinds When I first started working with preflop solves, one of the features I found most… The ICM Benefits of Late Registration in Poker Tournaments Why do so many professional poker players register late for tournaments when they clearly would… Flop Heuristics: OOP C-Betting in MTTs Playing against an in-position cold-caller is dramatically different–and dramatically more difficult–than playing against a caller… Counterintuitive Calls Solver outputs such as those provided by GTO Wizard are models of no-limit hold ‘em,… How To Negotiate Final Table Deals Most people’s first

MODERN POKER SOFTWARE Computer programs and apps have taken over modern society. Now you can find apps that do pretty much anything, including gaming, social media, communication, fitness, health, yoga, meditation, cooking, learning new languages, playing music and videos and even dating! No matter your need, there is a good chance that you can find an app that can fulfill it and if you can’t, you can be sure that there is someone somewhere in the world developing it right now. The world we live in has changed, and with it so has poker as we knew it. As technology progresses, the tools used by poker players to analyze and study the game have become more and more sophisticated. In this chapter we will analyze some of the most important programs and applications used by poker players to improve their strategies, keep up with modern developments, and crush their opponents. Equity Calculators Poker equity calculators have been around forever, and they are undoubtedly the most essential tool in any serious player’s arsenal. Understanding how equities interact for hand vs hand, hand vs range and range vs range is the first step towards a successful poker career. Equity calculators have come a long way since 2008 when the now deprecated PokerStove was first released. Back then, the calculators were unpolished and offered extremely limited functionality. Now, equity calculators such as Power Equilab (power-equilab.com) offer a wide variety of features that go beyond simple equity calculations, including equity graphs, heatmaps, range analysis and more. Pros ♦ The process of entering ranges and calculating equities is intuitive and simple to use ♦ Multiway equity calculations ♦ Ability to create custom playability profiles ♦ Fast equity calculations

the action is on you, you will… When ICM Breaks Down If you have read my previous GTO Wizard articles and my books, you’ll know I… When Is It Correct To Fold AA Preflop? One of the criticisms of ICM is that it is boring and robotic. In my… OOP C-betting vs Loose Cold-callers In a previous GTO Wizard article, I asserted that “Playing against an in-position cold-caller is… Short-Stacked Play in MTTs Playing a short stack well is an essential tournament skill. It is extremely rare to… When To Ladder in Tournaments In my last two articles, I wrote about the effect field size and payout structure… How Payout Structures Impact ICM Last time we discussed the ICM considerations in game selection, we looked at field size,… C-Betting IP in 3-Bet Pots When you three-bet before the flop and the original raiser calls from out of position,… C-Betting OOP in 3-Bet Pots Continuation betting from out of position can be a dicey proposition in single-raised pots. Cold… Dynamic Sizing: A GTO Breakthrough Dynamic Sizing is a revolutionary new poker algorithm that automatically simplifies your strategy with the… Dynamic Sizing Benchmarks Dynamic Sizing is a revolutionary new poker algorithm that automatically simplifies your strategy with the… Understanding The Impact Of Field Size On ICM In Poker When people talk about game selection in multi-table tournaments (MTTs), they invariably talk about the… Defending vs BB Check-Raise on Paired Flops This is a companion piece to Attacking Paired Flops from the BB; you will get… Mastering PKO Final Tables Final tables can be the most exciting and rewarding phase of a tournament, and being… Attacking Paired Flops From the BB Paired flops present unique challenges to both a preflop raiser and a BB caller. The… KK vs QQ vs JJ at WSOP Main Event With only fourteen players remaining in the 2023 WSOP Main Event and blinds of 400K/800K/800K,… Responding to BB Squeezes You open raise, someone calls, and the BB squeezes. How should you construct your strategy?… Crushing a Top HUNL Poker Bot In 2022, Philippe Beardsell and Marc-Antoine Provost, a team of Canadian programmers from Quebec, developed… GTO Wizard AI Explained We are excited to introduce GTO Wizard AI, formerly known as Ruse, the world’s best… GTO Wizard AI Benchmarks GTO Wizard has combined the power of artificial intelligence with traditional solving methods to bring… Table Management in PKOs Perhaps the most important strategic consideration in Progressive Knockout Tournaments (PKOs) is making sure you… Overcalling From the BB In poker, overcalling refers to calling a bet or raise after another player has also… Understanding Which Mistakes Cost You the Most Money I am fortunate enough to have worked for many years with the mental game coach… Overbetting The Flop in Cash Games Although most commonly analyzed on turns and rivers, flop overbetting can be a devastating weapon… Using New Skills at the Poker Table How many times has it happened to you that you make a mistake only to… Flatting Ace-X Hands Shortstacked Playing out of position is tricky, but it’s an

Hand Range 266: UTG+1 vs UTG 4-bet (60bb) • All-in 40.5% / • Call 4.4% / • Fold 55.1% 09 MTT EQUILIBRIUM

Pre-flop: We're getting closer and closer to the very important 3-betting chapter of this manual. These decisions will seem much more automatic after reading it, but for now, we can suffice to say that this is not a hand strong enough to 3-bet and get in a stack with vs. a 4-bet in these positions and that to 3- bet for value is somewhat thin. This hand is much better as a flat, partially to set mine and partially to get to showdown without a set on the better run outs for us. Flop: Calling is incredibly standard here. Hero does not desire a raising range in this spot with range disadvantage and the board being so dry and even if he did, it would be too thin to build a huge pot

bet on fourth if I 397 was the original raiser. You’ll recall that even if I missed this hand completely, I’d bet it on the flop as long as I was the raiser. But if my bet on the flop was called, I’d try to check it out from then on, unless I thought my opponent was drawing. Now that I’ve gotten a little help on the flop, however, I’d bet again on fourth despite the fact that my bet on the flop was called. I don’t like to keep betting when I’m on a complete bluff, but I do like to keep betting when I’ve got an out. In this case, I know that if I catch that other 6 or a 7, I’d likely have a stronger hand than my opponent. So I wouldn’t show any weakness with my hand on fourth street. I’d go ahead and make a reasonable bet. If I still didn’t get any help on fifth street, I’d probably stop betting. If my opponent was drawing and he didn’t make his hand, I’d know that my pair of sixes is more than likely good, so I’d check. And if they aren’t good, there’s no sense in losing any more money with them. If I happen to get some additional help on fourth, such as a 7, well, then I’d make an oversized bet, one that’s larger than what’s in the pot. I’m always out to win a big pot, and now I’d have a hand to do it with. I wouldn’t try to sell my hand for a small amount of money. I’d make a very big bet on fourth, and a very big bet on fifth. If I didn’t catch that 7 until the end, then I might try to sell it on fifth street for whatever I thought I could get. Whether I caught the 7 on fourth or fifth, I’d play a hand this way only if I was the original raiser coming in and I stayed in the lead by betting on every turn of the cards. Assuming I was a caller coming in and had checked and called on the flop, I’d play the hand differently if I caught a 7 on fourth street. If there was a lot of money in the pot, this is another one of the few times I’d check-raise. I wouldn’t want to take my opponent, the original raiser, out of the lead, especially if I know the size of the pot will make him bet again on fourth and since he’d have no idea the 7 helped me. He’d surely try to shut me out, and when he bets, I’d raise him. I’d want to win the pot right there, because if a queen or deuce comes on the end, the board will pair, killing my two pair. If I caught a 6 on fourth street, my strategy would be different still. The two 398 sixes on the board would look very threatening, so my hand would be harder to conceal than if I caught

Assuming Bill wins: (20% chance) Now we multiply the 2nd place equity by the probability of each scenario: Total 2nd place equity: Now we can simply add the first and 2nd place equity together to figure out the total equity: As you can imagine, this process gets exponentially more complex as we add more players and payouts. Luckily there are plenty of quick and easy ICM calculators online. It is nearly impossible to calculate ICM during play. The process is far too complex. Tournament professionals build their ICM intuition by studying thousands of ICM spots and playing with variables. Here’s the same calculation done with a free online ICM calculator ( Holdem Resources Calculator ): Tournament Equity Prizes How to leverage this information Let’s ask ourselves how this information can affect the strategy. Amy folds BTN, Tom shoves in the SB, Bill calls in the BB. What will their tournament equity be if Tom or Bill wins? You can calculate this by plugging the resulting stacks into any ICM calculator: Tom wins: Tom’s equity is $58 (+$12.82) Bill’s equity is $0 (-$22.57) Bill wins: Tom’s equity is $30.85 (-$14.33) Bill’s equity is $38.29 (+$15.72) In other words, Bill is risking $22.57 to win $15.72. Tom is risking $14.33 to win $12.82. ICM has the effect of creating an uneven downside relative to the shortstack. Bill is risking more tournament equity in this situation, so they need a stronger range to defend. This gives the big stack an advantage. Risk Premium To put it simply, chips won are worth less than chips lost . This uneven risk/reward ratio creates the effect of “risk premium”. You are risking more than a straight chip-EV calculation would suggest. Total required equity Let’s use the example above to figure out Bill’s risk premium facing Tom’s shove. We can imagine the blinds are 25/50, with Bill in the BB facing a shove from Tom in the SB. A simple pot odds calculation tells us how much equity Bill needs to call, in a cash game. We can call this amount the “Chip Equity”. Tom: 500 chips Bill: 200 chips Bill needs to call 150 more chips, and their stack will be 400 if they win. 150 / 400 = 37.5%. In a cash game, Bill should call any hand that had at least 37.5% equity against Tom’s range. But as we know, chips gained do not equal chips lost. Bill needs to weight the cost of a fold against the risk of calling. There are 3 situations, Bill folds, calls and wins, or calls and loses. Here is the tournament equity in each case: Bill can fold and retain $17.93 of tournament equity. So Bill is risking $17.93 by calling, and will have a stack worth $38.29 if they win. Let’s do a new pot odds calculation: $17.93 / $38.29. In other words, Bill actually needs about 47% equity to call! Because of ICM pressure, Bill needed an additional 12% equity. That additional 12% represents his risk premium. This extra risk premium allows Tom in the SB to

is that it is boring and robotic. In my… OOP C-betting vs Loose Cold-callers In a previous GTO Wizard article, I asserted that “Playing against an in-position cold-caller is… Short-Stacked Play in MTTs Playing a short stack well is an essential tournament skill. It is extremely rare to… When To Ladder in Tournaments In my last two articles, I wrote about the effect field size and payout structure… How Payout Structures Impact ICM Last time we discussed the ICM considerations in game selection, we looked at field size,… C-Betting IP in 3-Bet Pots When you three-bet before the flop and the original raiser calls from out of position,… C-Betting OOP in 3-Bet Pots Continuation betting from out of position can be a dicey proposition in single-raised pots. Cold… Dynamic Sizing: A GTO Breakthrough Dynamic Sizing is a revolutionary new poker algorithm that automatically simplifies your strategy with the… Dynamic Sizing Benchmarks Dynamic Sizing is a revolutionary new poker algorithm that automatically simplifies your strategy with the… Understanding The Impact Of Field Size On ICM In Poker When people talk about game selection in multi-table tournaments (MTTs), they invariably talk about the… Defending vs BB Check-Raise on Paired Flops This is a companion piece to Attacking Paired Flops from the BB; you will get… Mastering PKO Final Tables Final tables can be the most exciting and rewarding phase of a tournament, and being… Attacking Paired Flops From the BB Paired flops present unique challenges to both a preflop raiser and a BB caller. The… KK vs QQ vs JJ at WSOP Main Event With only fourteen players remaining in the 2023 WSOP Main Event and blinds of 400K/800K/800K,… Responding to BB Squeezes You open raise, someone calls, and the BB squeezes. How should you construct your strategy?… Crushing a Top HUNL Poker Bot In 2022, Philippe Beardsell and Marc-Antoine Provost, a team of Canadian programmers from Quebec, developed… GTO Wizard AI Explained We are excited to introduce GTO Wizard AI, formerly known as Ruse, the world’s best… GTO Wizard AI Benchmarks GTO Wizard has combined the power of artificial intelligence with traditional solving methods to bring… Table Management in PKOs Perhaps the most important strategic consideration in Progressive Knockout Tournaments (PKOs) is making sure you… Overcalling From the BB In poker, overcalling refers to calling a bet or raise after another player has also… Understanding Which Mistakes Cost You the Most Money I am fortunate enough to have worked for many years with the mental game coach… Overbetting The Flop in Cash Games Although most commonly analyzed on turns and rivers, flop overbetting can be a devastating weapon… Using New Skills at the Poker Table How many times has it happened to you that you make a mistake only to… Flatting Ace-X Hands Shortstacked Playing out of position is tricky, but it’s an essential part of tournament play. With… Playing Limped Pots as the BB in MTTs Success as the BB in limped pots begins before the flop. The BB’s equilibrium strategy… The Absurd Game Theory of Chopped Boards A “chopped board” in

Freezeout A tournament where rebuys are not allowed, and once a player loses all of their chips and is therefore eliminated, they are unable to re-enter and thus “frozen out”.

Pre-flop is a clear cold call. It's not that we want to play this hand 100BB deep OOP against the Reg's likely linear 3-bet value range that dominates us, it's that we want to get into a pot 200BB with a whale who is extremely likely to be calling the 3-bet. Our hand thrives from implied odds rich multiway situations with these stacks so calling should be obvious. Now onto post-flop, but first remind yourself of the difference between floating and chasing, if there is any doubt.

pat flush before the draw, his correct play would be to throw away a pair of aces when you bet. Calling would be a mistake, but it is a special kind of mistake. We do not mean your opponent played the hand badly by calling with a pair of aces; we mean he played it differently from the way he would play it if he could see your cards. This flush example is very obvious. In fact, the whole theorem is obvious, which is its beauty; yet its applications are often not so obvious. Sometimes the amount of money in the pot makes it correct to call, even if you could see that your opponent's hand is better than yours. Let's look at several examples of the Fundamental Theorem of Poker in action. Examples of The Fundamental Theorem of Poker The Fundamental Theorem of Poker 19 This example may also seem too obvious for serious discussion, but it is a general statement of some fairly sophisticated plays. Let's say in no-limit hold 'em you hold the and your opponent holds an offsuit The flop comes: Example 1 Suppose your hand is not as good as your opponent's when you bet. Your opponent calls your bet, and you lose. But in fact you have not lost; you have gained! Why? Because obviously your opponent's correct play, if he knew what you had, would be to raise. Therefore, you have gained when he doesn't raise, and if he folds, you have gained a tremendous amount. You check, your opponent bets, and you call. Now the ace of diamonds comes on fourth street, and you bet, trying to represent aces. If your opponent knew what you had, his correct play would be to raise you so much it would cost too much to draw to a flush or a straight on the last card, and you would have to fold. Therefore, if your opponent only calls, you have gained. You have gamed not just because you are getting a relatively cheap final card but because your opponent did not make the correct play. Obviously if your opponent folds, you have gained tremendously since he hasthrown away the best hand. 20 Chapter Three Example 2 Suppose there is $80 in the pot, and you have two pair. You are playing draw poker, and you bet $10, which we will assume is all you can bet. Your single opponent has a four-flush — that is, four cards to a flush. The question is — are you rooting for him to call or fold? Naturally you want him to do what is most profitable for you. The Fundamental Theorem of Poker states that what is most profitable for you is for your opponent to make the incorrect play based on complete information about both hands. Since your opponent is getting 9-to-1 odds (his $10 call might win him $90) and is only about a 5-to-1 underdog to make a flush, it is correct for him to call because a call has positive expectation. Since it is correct for