Expected log utility? Kelly says to maximize expected log money. (The fact that wealth-derived utility seems to go roughly like log of wealth is largely coincidence, so far as I can see, though I wonder vaguely whether, precisely because of Kelly, brains that value things logarithmically tend to accumulate most in the long run, in which case the Kelly criterion might actually explain why utility is roughly logarithmic in wealth. I’m pretty sure I don’t actually believe that, though.)
Maximizing expected utility also gives the right answer in “win or die”, of course.
Expected log utility? Kelly says to maximize expected log money. (The fact that wealth-derived utility seems to go roughly like log of wealth is largely coincidence, so far as I can see, though I wonder vaguely whether, precisely because of Kelly, brains that value things logarithmically tend to accumulate most in the long run, in which case the Kelly criterion might actually explain why utility is roughly logarithmic in wealth. I’m pretty sure I don’t actually believe that, though.)
Maximizing expected utility also gives the right answer in “win or die”, of course.