[Jerrod Ankenman]

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we know that the optimal bluffing frequency is s.t the odds against bluffing are the same as the pot odds the opponent receives. At the optimal bluffing frequency it doesn't matter if the opponent always calls or always folds. But suppose the opponent wavers somewhere in between (i.e sometimes calls, sometimes folds). Will he not be playing optimally? how does 1 prove that the opponents optimal strategy is to always call or always fold?

thanks.

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The opponent's optimal strategy isn't determined by your play at all, remember. He calls with some fraction of hands so that you are indifferent to bluffing at a particular threshold hand.

If either of you play a mixed strategy with any hand, then the equity of playing that hand in each way against the opponents' optimal strategy must be equal. So in a sense, if you will continue to play optimally no matter what your opponent does, he can call or fold with his threshold hand as he wishes. (In fact, there's a fairly large region of hands that are like this in most examples like this).

But if he just folds all his hands, you can exploit him. BTW for those of you who do study games, this fact is pretty useful for finding the value of games once you have the strategies. You can just pretend that one side just folds at all mixed strategies, which usually trims the game tree a lot.

Jerrod Ankenman