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Wouldn't someone with linear utility get swindled by the St Petersburg Paradox? And isn't Kelly not about utility at all, but about the fact that an individual receives the time average, not the ensemble average?

@ole_b_peters

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SBF

@SBF_FTX

Dec 11, 2020

12) In many cases I think $10k is a reasonable bet. But I, personally, would do more. I’d probably do more like $50k. Why? Because ultimately my utility function isn’t really logarithmic. It’s closer to linear.

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1) The answer starts to change if the upside case is > $10b; until then, linear is closer to correct for altruistic purposes 2) St Petersburg isn't a swindle if it's actual utility instead of $; yeah, sometimes you should trade it all for a small % of a huge gain

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as for what Kelly is "about" -- that's a subjective question, but I think the wikipedia article phrases it clearly: en.wikipedia.org/wiki/Kelly_cri

6:43 PM · Dec 13, 2020Twitter Web App

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Thanks. As an aside, I was floored to learn from

@ole_b_peters

that you can resolve the St. Petersburg Paradox (and recover Kelly) with no assumption about utility It really seems Bernoulli mis-specified the problem

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and

Yes, and when you try to apply linear utility to these kind of problems you're pretty much guaranteed to blow up. Its why utility is such a dangerous concept. Every "utility" riskier than ln utility is craziness, and that statement has nothing to do with risk tolerance.