Yes, for some classes of games in some sense… MDP/POMDPs are a very general setting so I don’t expect any helpful simple exact answers (although to my surprise there were for this specific game), so I just have qualitative observations that it seems like when you have quasi-investment-like games like the coin-flip game, the longer they run and the higher the cap is, the more the exact optimal policy looks like the Kelly policy because the less you worry about bankruptcy & the glide-in period gets relatively smaller.
I suspect that if the winnings were not end-loaded and you could earn utility in each period, it might look somewhat less Kelly, but I have not tried that in the coin-flip game.
Yes, for some classes of games in some sense… MDP/POMDPs are a very general setting so I don’t expect any helpful simple exact answers (although to my surprise there were for this specific game), so I just have qualitative observations that it seems like when you have quasi-investment-like games like the coin-flip game, the longer they run and the higher the cap is, the more the exact optimal policy looks like the Kelly policy because the less you worry about bankruptcy & the glide-in period gets relatively smaller.
I suspect that if the winnings were not end-loaded and you could earn utility in each period, it might look somewhat less Kelly, but I have not tried that in the coin-flip game.