Ah, yeah, this looks pretty close to what I was looking for.
OK, so if I’m understanding correctly, the basic idea is EV maximization with a cap on total possible winnings? (Which makes sense—there’s only ever so much money to win.)
So is the claim that this approaches Kelly in the limit of simultaneously increasing cap and horizon?
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.
Ah, yeah, this looks pretty close to what I was looking for.
OK, so if I’m understanding correctly, the basic idea is EV maximization with a cap on total possible winnings? (Which makes sense—there’s only ever so much money to win.)
So is the claim that this approaches Kelly in the limit of simultaneously increasing cap and horizon?
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.