> I assume that no one's utility
> function is exactly logarithmic, but that everyone's approximates it,
> which I believe is required for the Kelly Criterion to be in
> contention as the optimal approach to gambling.
I think that's correct, assuming your primary goal is to grow your bankroll. It could be that you gamble for other reasons. If you were more risk-seeking you could "press your bet" beyond Kelly. If you were risk-neutral (linear function) the optimal would be to bet it all if possible. But when would you stop? If you continue with betting it all, wouldn't that be risk-seeking, since you would be increasing your odds of busting out? Does long term risk-neutral entail betting less than the full bankroll, perhaps a long term ROR of 50%? And if you were more risk-averse you could bet any fraction of Kelly since you would be getting a reasonable tradeoff of less risk for less reward. A lot of people recommend betting a fraction of Kelly, so perhaps a lot of people are a bit more risk-averse than log utility? Steve Jacobs if he's still around would know for sure.
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