If you’re trying to maximize expected money at the end of a fixed number of rounds, you do that by betting everything on every round (and, yes, almost certainly going bankrupt).
If that’s not what you’re trying to do, the optimal strategy is probably something else. But “how do we maximize expected money?” seems to be the question Gwern’s post is exploring. It’s just that with the $250 cap, maximizing expected money seems like a good idea (because you can almost always get close to $250), and with no cap, maximizing expected money seems like a terrible idea (because it gives you a 10^-67 chance of $10^92).
You don’t do Kelly because it’s good at maximizing expected money. You do it (when you do it) because you’re trying to do something other than maximize expected money.
Oh, I see. Yes, I agree. The idea to maximize the expected money would never occur to me (since that’s not how my utility function works), but I get it now.
(e: posted overlapping with Oscar_Cunningham)
If you’re trying to maximize expected money at the end of a fixed number of rounds, you do that by betting everything on every round (and, yes, almost certainly going bankrupt).
If that’s not what you’re trying to do, the optimal strategy is probably something else. But “how do we maximize expected money?” seems to be the question Gwern’s post is exploring. It’s just that with the $250 cap, maximizing expected money seems like a good idea (because you can almost always get close to $250), and with no cap, maximizing expected money seems like a terrible idea (because it gives you a 10^-67 chance of $10^92).
You don’t do Kelly because it’s good at maximizing expected money. You do it (when you do it) because you’re trying to do something other than maximize expected money.
Oh, I see. Yes, I agree. The idea to maximize the expected money would never occur to me (since that’s not how my utility function works), but I get it now.