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.
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.