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Are lottery tickets ever a wise investment provided the jackpot is large enough?
You can have a positive expected return on a lottery ticket purchase, but only if the lottery requires all players to pick their own numbers and doesn't have an option to buy a ticket with a randomly generated set of numbers. This is because people are very bad at picking random numbers, and will tend to pick numbers that are fairly evenly spaced or based on dates rather than genuinely random numbers. For example in January 1995 the UK national lottery happened to have fairly well-spaced numbers (7, 17, 23, 32, 38 & 42), and there were 133 winners with all six numbers. So they way to win is to wait for a draw where a rollover jackpot is high enough that your expected winnings are positive if you are the only winner, and pick a set of numbers that looks stupidly non-random, but is not so very non-random that people will have picked it anyway, like 1, 2, 3, 4, 5, 6. For a "pick 6 in the range from 1-49" lottery you might pick something like 3, 42, 43, 44, 48, 49. But it doesn't work if there's a random option, since a significant number of players will use it and get genuinely random numbers, and so your chances of being the only winner get much smaller.