You are misunderstanding. Optimizing log wealth isn't because you have logarithmic utility... It's because doing so maximizes growth, which is more important t

You are misunderstanding. Optimizing log wealth isn't because you have logarithmic utility... It's because doing so maximizes growth, which is more important that immediate return in a game of repeated investment. Kelly maximizes your long term absolute wealth in such games. Edit: I see you last paragraph acknowledging but doubting this claim. Demonstrating an optimal strategy in a stochastic game is hard to make toy-like, because you have to somehow describe both the probability distributions and the entire range of strategies someone could take. In lieu, the end of this article does a good job of listing simple explanations of what that (provably) optimal strategy property entails: https://www.stat.berkeley.edu/~aldous/157/Papers/Good_Bad_Kelly.pdf https://www.stat.berkeley.edu/~aldous/157/Papers/Good_Bad_Ke...