[AaronBrown]

I apologize, I read your initial post too quickly. With your definition of Q, your math is correct.

I'm still unconvinced about the theorem as a poker insight. On almost every no-limit hand, I think there's some chance I will stack another player and win. But that doesn't mean I'll call every bet from a big stack when I have a big stack. For one thing, the bigger are stacks are, the more I have to lose as well as win. For another, I'm not trying to maximize my EV every hand, I'm trying to win money for the session. I might feel that I'll have a better chance to take the stack on another hand, with less risk to my stack.

But most important, the intermediate bets go up with the stack sizes. Suppose I tihnk there is a 5% chance on a particular hand that I will stack another player and win $100,000. He bets $1,000 preflop. In your analysis I call, because the stacking possibility is worth $5,000 to me; plus I can win lesser amounts.

But I don't get to see his cards and the board, and then decide whether or not to stack him. He may bet $5,000 or $10,000 on the flop; or go all-in. I have to decide what to do without knowing his cards, or what the turn or river will be. The bigger our stacks, the bigger these intermediate bets are likely to be. The other guy knows as well as I do that we're playing for our full stacks.