Game Theory: Unusual Question #3 and #4

[Aisthesis]

Yep, checked it through, and you're right. Thanks!

It's rather interesting that the ONLY thing making the raise profitable at all is the bluff. If B never bluffs, then A can always find a (tight) calling criterion to make it in fact unprofitable for B to raise (as opposed to the just calling with 1/2 or better and never raising). So, if B never bluffs, A can successfully punish B for raising.

On the other hand, it doesn't take very much bluffing to force A into dramatically looser calls, hence making the raise profitable for B. Moreover, the bluffing criteria and raising criteria for B always force A into an exact call point. It would be kind of interesting to figure out (given B's optimal value-raise threshold) just what the correlation is to A's call treshold if B bluffs more or less than is optimal.

On the other hand, while B's optimal values force A into an exact calling/folding strategy, it doesn't seem to me that this applies the other way around: If A didn't know that B was switching strategies and hence kept calling the raise on the top 1/3 of his hands, instead of bluffing, B could increase his winnings by value-betting only.

I guess what I'm basically saying is: B's optimal strategy forces A into exactly one optimal betting strategy. If B sticks with his optimal strategy and A changes his, A will just lose more money.

But A's optimal strategy by no means forces B into his true optimal strategy. It only does so under the assumption that A will adjust his strategy if B changes his. If A is incapable of adjusting to changes in B's strategy, then B can also capitalize on his inflexibility.

Or yet another way of putting it: A has no way to punish B for inflexibly sticking with the optimal (bluffing) strategy, but B can punish A for inflexibility.