> A not so obvious result that follows from making successive negative expected value bets, is that in the long run you are guaranteed to lose all your money (or ruin). Intuitively this makes sense as with each bet, you are losing money on average.
Expected value doesn't tell you much about the outcome of successive bets. Someone else can probably explain this better since it comes up on HN a lot (something about ergodicity and the difference between ensemble average and time average).
Quick example is if play a game of double or nothing on coin flips. This is a "fair game" because you pay x and get back 2x * 0.5 + 0 * 0.5 = x. But if you play more than one game you will very quickly get a "nothing" and can't continue.
Kelly staking criteria tells you how much to bet in such situations. in this case: nothing since it's a pointless bet, economically speaking. you may derive utility from the lols, though, in which case probably don't bet the whole bank in one go!
The Kelly criterion doesn't apply in this scenario. Imagine the same game, but it's triple or nothing (so, the odds are massively in your favour) and you can walk away at any time after resolving a bet, after which you go back to investing in Treasuries or low-cost index funds.
How much should you wager? Kelly says 25% (edge of 50% / odds of 2). But this is correct only under the assumption that you will have infinitely many opportunities to play the same game at the same odds for whatever stake you choose. If you only have one chance, you should bet more. It also assumes a linear utility value of money: assuming this is actually convex, you should bet less.
Expected value doesn't tell you much about the outcome of successive bets. Someone else can probably explain this better since it comes up on HN a lot (something about ergodicity and the difference between ensemble average and time average).
Quick example is if play a game of double or nothing on coin flips. This is a "fair game" because you pay x and get back 2x * 0.5 + 0 * 0.5 = x. But if you play more than one game you will very quickly get a "nothing" and can't continue.