No, it is true if you want to have the highest expectation value of utility in your life, and the answer to ciphergoth’s question is you use all your wealth.
If instead of wanting to maximizing utility, you might prefer to minimize the probability that your utility will fall below a certain level. In this case, the bad tails of the distribution of Kelly criterion strategies matters to you and the expected utility does not. You might come up with some modification of Kelly criterion that meets this criterion of avoiding really bad outcomes with high probability. Or you might find some entirely different criterion or policy that meets the avoidance of bad outcomes that you are trying to achieve.
The OP’s original question hides a lot of complexity in its “in the real world” clause. In the real world, are we expected-utility maximizers? Or are we low-utility-probability minimizers? Or are we something else? Until we know we can’t evaluate investment/betting strategies.
That is only true if you are making lots of bets and expect them to be your main source of income. But that assumes away Ciphergoth’s question.
No, it is true if you want to have the highest expectation value of utility in your life, and the answer to ciphergoth’s question is you use all your wealth.
If instead of wanting to maximizing utility, you might prefer to minimize the probability that your utility will fall below a certain level. In this case, the bad tails of the distribution of Kelly criterion strategies matters to you and the expected utility does not. You might come up with some modification of Kelly criterion that meets this criterion of avoiding really bad outcomes with high probability. Or you might find some entirely different criterion or policy that meets the avoidance of bad outcomes that you are trying to achieve.
The OP’s original question hides a lot of complexity in its “in the real world” clause. In the real world, are we expected-utility maximizers? Or are we low-utility-probability minimizers? Or are we something else? Until we know we can’t evaluate investment/betting strategies.
A little knowledge is a dangerous thing.