Yeah, I wasn’t trying to claim that the Kelly bet size optimizes a nonlogarithmic utility function exactly, just that, when the number of rounds of betting left is very large, the Kelly bet size sacrifices a very small amount of utility relative to optimal betting under some reasonable assumptions about the utility function. I don’t know of any precise mathematical statement that we seem to disagree on.
Well, we’ve established the utility-maximizing bet gives different expected utility from the Kelly bet, right? So it must give higher expected utility or it wouldn’t be utility-maximizing.
Right, sorry. I can’t read, apparently, because I thought you had said the utility-maximizing bet size would be higher than the Kelly bet size, even though you did not.
Yeah, I wasn’t trying to claim that the Kelly bet size optimizes a nonlogarithmic utility function exactly, just that, when the number of rounds of betting left is very large, the Kelly bet size sacrifices a very small amount of utility relative to optimal betting under some reasonable assumptions about the utility function. I don’t know of any precise mathematical statement that we seem to disagree on.
Right, sorry. I can’t read, apparently, because I thought you had said the utility-maximizing bet size would be higher than the Kelly bet size, even though you did not.