Yes, I would agree with this. If we suppose our utility function is bounded, then when given unlimited access to a gamble in our favor, we should basically be asking “Having been handed this enormous prize, how do I maximize the probability that I max out on utility?”
Hm, but that actually doesn’t give back any specific criterion, since basically any strategy that never bets your whole stack will win. What happens if you try to minimize the expected time until you hit the maximum?
Optimal play will definitely diverge from the Kelly criterion when your stack is close to the maximum. But in the limit of a large maximum I think you recover the Kelly criterion, for basically the reason you give in this post.
“Having been handed this enormous prize, how do I maximize the probability that I max out on utility?” Hm, but that actually doesn’t give back any specific criterion, since basically any strategy that never bets your whole stack will win.
That’s not quite true. If you bet more than double Kelly, your wealth decreases. But yes, Kelly betting isn’t unique in growing your wealth to infinity in the limit as number of bets increases.
If the number of bets is very large, but due to some combination of low starting wealth relative to the utility bound and slow growth rate, it is not possible to get close to maximum utility, then Kelly betting should be optimal.
Yes, I would agree with this. If we suppose our utility function is bounded, then when given unlimited access to a gamble in our favor, we should basically be asking “Having been handed this enormous prize, how do I maximize the probability that I max out on utility?”
Hm, but that actually doesn’t give back any specific criterion, since basically any strategy that never bets your whole stack will win. What happens if you try to minimize the expected time until you hit the maximum?
Optimal play will definitely diverge from the Kelly criterion when your stack is close to the maximum. But in the limit of a large maximum I think you recover the Kelly criterion, for basically the reason you give in this post.
That’s not quite true. If you bet more than double Kelly, your wealth decreases. But yes, Kelly betting isn’t unique in growing your wealth to infinity in the limit as number of bets increases.
If the number of bets is very large, but due to some combination of low starting wealth relative to the utility bound and slow growth rate, it is not possible to get close to maximum utility, then Kelly betting should be optimal.