Yes, my position did indeed shift, as you changed my mind and I thought about it in more depth. My original position was very much pro-Kelly. On thinking about your points I now think it is the while my_money > 0 aspect where the problem really lies. I still stand by the difference between optimal global policy and optimal action at each step distinction, because at each step the optimal policy (for Kelly or not) is to shake the dice another time. But, if this is taken as a policy we arrive at the while my_money > 0 break condition being the only escape, which is clearly a bad policy. (It guarantees that in any world we walk away, we walk away with nothing.)
Nod. I think we basically agree at this point. Certainly I don’t intend to claim that optimal policy and optimal actions always coincide (I have more thoughts on that but don’t want to get into them).
Yes, my position did indeed shift, as you changed my mind and I thought about it in more depth. My original position was very much pro-Kelly. On thinking about your points I now think it is the
while my_money > 0aspect where the problem really lies. I still stand by the difference between optimal global policy and optimal action at each step distinction, because at each step the optimal policy (for Kelly or not) is to shake the dice another time. But, if this is taken as a policy we arrive at thewhile my_money > 0break condition being the only escape, which is clearly a bad policy. (It guarantees that in any world we walk away, we walk away with nothing.)Nod. I think we basically agree at this point. Certainly I don’t intend to claim that optimal policy and optimal actions always coincide (I have more thoughts on that but don’t want to get into them).