The Kelly criterion, as a bet-sizing optimum, makes a few assumptions, which are not true in most humans.
- Future bets will be available, but limited by the results of the currently-considered wager. That is, there is a bankroll which can grow and shrink, but if it hits zero, the model ends. Kelly phrases this requirement as "the possibility of reinvestment".
- Utility of money is logarithmic in the ranges under consideration (that is, you're considering lifetime resources, not just the amount in your pocket right now).
It's a little unclear whether the log utility is an assumption or a result of the bankrupcy-is-death assumption. The original paper, http://www.herrold.com/brokerage/kelly.pdf , says:
The gambler introduced here follows an essentially different criterion from the classical gambler. At every bet he maximizes the expected value of the logarithm of his capital. The reason has nothing to do with 926 the bell system technical journal, july 1956 the value function which he attached to his money, but merely with the fact that it is the logarithm which is additive in repeated bets and to which the law of large numbers applies. Suppose the situation were different; for example, suppose the gambler’s wife allowed him to bet one dollar each week but not to reinvest his winnings. He should then maximize his expectation (expected value of capital) on each bet. He would bet all his available capital (one dollar) on the event yielding the highest expectation. With probability one he would get ahead of anyone dividing his money differently.
This all implies that the special-case is the last wager you will ever make. And from there the more complicated cases of the penultimate wager and the probabilistic-finite cases. I don't know how big the chain needs to get to converge to Kelly being the optimum, but since it's compatible with logarithmic utility of money in the first place, for some agents it'll be the same regardless.
My strong suspicion is that Kelly always applies if your terminal utility function for money is logarithmic. But I don't see how that could be - the marginal amount of money/resources you'll control at death is tiny compared to all resources in the universe, so your utility for any margin under consideration should be close to linear.