Re: Book at Pokerstars???
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Question re bluff-raising in the toy game on page 204: in what sense does bluff-raising with the top of your check-behind region "dominate" bluff-raising with the bottom of that region?
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In the situation described, the opponent has already bet, and we're trying to decide what to do with our hands that are too weak to raise for value or call. Some of them will be folded; others will be bluff-raises.
Most of the time, it won't matter which hands we bluff-raise with (as long is it is the proper frequency); our opponent won't call with any hands that can't beat a bluff-raise anyway, so whatever. In fact, choosing any subset of hands (such that you raise-bluff with the proper frequency) from the folding region to bluff-raise is a co-optimal strategy. The opponent can't exploit it -- try it and see!
However, suppose you're playing against someone silly, who will bluff with his worst hands and then call your bluff-raise. Then it's better for you to bluff when the very strongest hands of your (fold+bluffraise) region, since you get some extra value from the silly guy. You don't lose anything against reasonable players by doing this - they only call with hands that can beat you anyway.
So raise-bluffing with the best of the hands you would fold dominates other strategies because it performs better against silly strategies and the same against reasonable ones.
This is different than the case where the guy checks to you. Now you should bluff your worst hands in your "check behind" region, because they have less value from checking than the others. But if we're selecting bluffs from a region which would otherwise be folded, we select the strongest hands to bluff.
jerrod
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