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Kelly is not optimal if you can't estimate the probabilities with great precision, which you can't outside of contrived examples or casinos. In casinos you have negative expected value on every bet, and Kelly tells you to not play at all. Contrived examples don't matter.

You aren't addressing what I said, you are cherry picking things you find easy to rebut. You are right that I messed up and that you can't lose all your money with two 50% bets. However you ignore the stronger argument, which I opened with and repeatedly pointed out, which is that you can't estimate probabilities well enough to use it, and that if you can estimate probabilities well enough to benefit from Kelly, that ability to estimate probabilities itself almost always unlocks strategies that strictly dominate any benefit Kelly gives you. It's useless in practice.




I don't really care about winning any global arguments. I see bad logic and I try to point it out. If you didn't like that some of your points were easily rebutted then you shouldn't have written them. Leaving them unchallenged makes your position seem artificially strong.

I couldn't resist bringing up the poker bankroll example because I think your in-game-poker example was poorly chosen. To me, it looked like you came up with a situation where the criterion obviously had no hope of being applicable and then used it to argue that the criterion is useless. E.g. I could find a whole list of things for which calculus is not applicable, but that would not be a good argument for 'calculus is useless'. The example I gave is at least closer to the assumptions of the Kelly Criterion.

I think the main thing I wanted to do was to correct the misconception that Kelly is only maximizing expected log utility, because it is a shame if someone (including other readers) thinks that the Kelly Criterion is just a fancy name we gave for the argmax of E f(S) where f happens to be the logarithm.

After all this, you (and other readers) might still conclude that the criterion is useless. But the set of justifications, and maybe the certainty, in that position, should change.




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