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Are lottery tickets ever a wise investment provided the jackpot is large enough?
The other answers here do an excellent job of laying out the mathematics of the expected value. Here is a different take on the question of whether lottery tickets are a sensible investment. I used to have the snobbish attitude that many mathematically literate people have towards lotteries: that they are "a tax on the mathematically illiterate", and so on. As I've gotten older I've realized that though, yes, it is certainly true that humans are staggeringly bad at estimating risks, that people actually are surprisingly rational when they spend their money. What then is the rational basis for buying lottery tickets, beyond the standard explanation of "it's cheap entertainment"? Suppose you are a deeply poor person in America. Your substandard education prepared you for a job in manufacturing which no longer exists, you're working several minimum wage jobs just to keep food on the table, and you're one fall off a ladder from medical-expense-induced total financial disaster.  Now suppose you have things that you would like to spend truly enormous amounts of money on, like, say, sending your children to schools with ever-increasing tuitions, or a home in a safe neighbourhood.  Buying lottery tickets is a bad investment, sure. Name another legal investment strategy that has a million-dollar payout that is accessible to the poor in America. Even if you could invest 10% of your minimum-wage salary without missing the electricity bill, that's still not going to add up to a million bucks in your lifetime. Probably not even $100K.  When given a choice between no chance whatsoever at achieving your goals and a cheap chance that is literally a one-in-a-million chance at achieving your goals the rational choice is to take the bad investment option over no investment at all.