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Personally I can't imagine our EV when an overcard flops and he cbets is much better than 0, but idk.
I think this is the key. If you assume this, then raising pretty much has to be better than calling. Those in favor of calling are assuming that we still make plenty of money on overcard flops exploiting our tight image and position.
I guess we could try to assign weighted probabilities to all the hands in his range, and see how often he has a hand that will want to continue oop on a dry overcard flop, and try to estimate the EV in this case, but I'm thinking we'll have to make so many assumptions that our conclusions won't really tell us anything meaningful. Suffice to say that his range includes lots of hands that aren't necessarily wanting to continue OOP on a high-card flop, so I think it's wrong to assume our postflop EV against overcards is 0. It's basically the same as saying that having position against his range is worthless, which seems pretty clearly incorrect.
Fundamentally, I think it just is wrong to break the hand down in terms of flop types, and how often we flop sets. If you look at this just in terms of the equity of our button calling range vs his CO opening range, our range should have positive equity, especially considering the advantage of position.
On the other hand, when we raise, we have the EV of winning right away (which is good) plus the equity we have postflop against not his opening range, but his calling range. (This has been mentioned before).
Of course, as I said before, I don't think there is really a huge EV difference between calling and 3betting here, but I don't think you can prove 3betting better via this line of analysis.
Last edited by well named; 12-14-2007 at 07:38 PM.