[cartman]

[ QUOTE ]

Where is Cartman when I need him?!

[/ QUOTE ]

Like any poker situation, the most thorough way to analyze this is with a comprehensive tree diagram, which sometimes gets big enough to cover a football field. You can usually short-circuit the process with assumptions. Obviously the more of them you make and/or the broader you make them, the less accurate your conclusion will be.

In this situation, your first set of branches would only have two choices: CHECK and BET. When your diagram is complete you just pick the branch with the higher EV and do it. Lets say in this case that you find out that the CHECK branch has the higher EV so you do it and he bets. Now you find in your diagram that exact path (first branch CHECK, second branch HE BETS). There will be 3 branches coming out from that spot: RAISE, CALL, and FOLD. Again you pick branch with the highest EV and do it. You use the same process for determining whether to call if you CR and he 3 bets.

In this particular case, I would use a simpler approach than the full analysis I described above. For example, lets assume that we check and he bets, and we are trying to determine whether to raise or to call. We will always call if he 3-bets. Here are the parameters we need:

1) how often does he have a better hand
2) given that he has a better hand, how often does he
a) 3-bet
b) call
c) fold
3) given that he has a worse hand, how often does he
a) 3-bet
b) call
c) fold


Now since if we just called his bet, we would always lose 1BB when he had a better hand and win 1BB when he had a worse hand, I would look at the analysis of the CR decision relative to the call. For example, find the probability he both has a better hand and 3-bets and multiply it by -2, because we will be 2BB worse off than if we had just called. Then find the probability that he both has a better hand and just calls and multiply it by -1, because we will be 1BB worse off than if we had just called. Etc. Find each of these probabilities and multiply it by its relative result to checking and calling and then add up the terms. If the sum is positive then you conclude that, given that we check and he bets, raising is better than calling.

Sorry to be vague, I'm in somewhat of a hurry.

Cartman