if you drop the gambler’s presentation of kelly, and just maximize expected log utility, you immediately get the correct answer for the “win or die” scenario. the second scenario lightly touches on kelly, and would also be aided by considering the situation as log utility maximization. (expenses going out every month like clockwork, decision is work (small guaranteed return), and/or how much to allocate to various bets.)
some of your concerns in the last post can also be modeled properly.
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.
if you drop the gambler’s presentation of kelly, and just maximize expected log utility, you immediately get the correct answer for the “win or die” scenario. the second scenario lightly touches on kelly, and would also be aided by considering the situation as log utility maximization. (expenses going out every month like clockwork, decision is work (small guaranteed return), and/or how much to allocate to various bets.)
some of your concerns in the last post can also be modeled properly.
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.