“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.
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.