Just an aside: the first scenario you suggest, in which you have a 1% chance to 1000x your money and a 99% chance to lose it all, has an expected value of 10. I

Just an aside: the first scenario you suggest, in which you have a 1% chance to 1000x your money and a 99% chance to lose it all, has an expected value of 10. It is absolutely rational to make that bet if you have enough capital to withstand a drawdown of let's say, 5x your initial bet. For example, suppose you model this as a game with the following rules: - you start with $1,000,000 - each turn you may bet $10,000 - if you bet, you roll a d100 - if you roll a 1, you earn 1000x your bet, if you roll anything else you lose your entire bet - the game ends after 1000 turns or you lose all your money, whichever happens first If you bet every turn, on average you'll end the game with approximately $60,000,000. EDIT: Did you edit your comment to be 100x or did I misread? Oh well, leaving this here for posterity. If the win outcome is 100x, the EV is still 1.