by Aisthesis » Fri Aug 11, 2006 12:35 pm
The way to calculate the probability of his having an A is this: Determine the range of hands on which he'll play the hand as he did up to your all-in check-raise. I don't think he's 3-betting pure junk, since you've now shown strength, but players have different tastes here.
Then, given the board, you can simply count the number of times he can call and the number of times he can't.
My own theory is that he can have KK, QQ, and AK here. I think JJ and AA are both fairly rare--AA mainly because of the fairly solid CB, but a read could change that. And a read could also put AQ or even AJ in there, the latter being moderately rare, but I've seen players willing to go that far with AQ and a few with AJ or even weaker aces.
Anyhow, if his hand range on the 3-bet with that particular CB is KK, QQ, and AK, this board (together with your hand) means there are 6 each of KK and QQ, and 12 AK hands. If that's the case and he folds KK and QQ always, calls AK always, then half the time you get a call (and lose your stack), and half the time you get a fold (and win $190).
More than anything else (barring cases where you know a player CAN'T have a piece of a scary board), what I think this hand shows is how much more desirable it is to bluff with outs. In actuality, you have near 0 outs against his entire hand range. Hence, in case he calls, you ALWAYS lose. If you were able to pick up even 25% of those pots, the bluff would become much more attractive--and in fact pretty clearly +EV.