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Player A has 9/51(18%) probability of hitting a set on the given flop as does player B.

Therefore, the probability that they both have a set is found just by multiplying the two together. I don't think you need to go through all the fancy hoops.

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But that is just it. You are right that they each have an unconditional probability of hitting a set of 9/51, but those events are not independent. The probability that they both have a set is not P(A has a set) * P(B has a set). It is P(A has a set) * P(B has a set GIVEN that A has a set). If A has a set, there are now only 6 combinations of cards which B can have which make a set. His probability of having a set given that player A has one is actually only 12.5%.

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Now, they are going to fold JJ/TT some portion of the time here. Maybe 20% of the time they will fold. I think that is being conservative. I am curious, what does it look like if you introduce that factor into your math? Does that alone, with the decrease in the set percentage, make a big impact?

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I think THIS is the discussion we should be having (if indeed we have not long since devolved into a math argument no one else cares about).

I think it actually goes the other way. With stacks this size and players who would make that call pre-flop with a pocket pair, I think we get calls not only from JJ-TT, but also from underpairs a fair amount of the time. If they will always fold JJ-TT and the other underpairs, then this is a push. If they never will fold JJ-TT it is a fold. If they sometimes do not fold underpairs, even more so. If they sometimes have other cards, then it turns toward a push. If they will sometimes call with them then even more so. Pick your assumptions and we can do the math. (Also note that, as far as the original post goes, we have assumed away a large portion of one of our opponents stacks. That works against us.)

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I don't think the plan to push any flop is a bad one if you look at it on a whole. Some flops will come that will hit you and they will call incorrectly. Some will not hit you but they look dangerous(QJT) and give you more outs. This is one of the worse flops, given. Although, I do agree that the EV of this particular hand is very neutral.

Are we on the same page now?

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I think we are pretty close. You are saying that if we had to pick a plan before the flop cards came out, then always pushing is +EV. I agree. I am saying that some flops make that plan a pretty close decision, perhaps even non-optimal. I think you agree.

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I agree with everything. I could be off on my probability stuff. Now the unconditional stuff I have a glimmer of a memory back there somewhere.

I think we are on the same page now. I agree this is a bit closer given the flop hits a good part of their range. The real debate is over what they do with JJ-TT on this flop. I definitely don't think they will call with it 100% because our hand is going to be an overpair so often here. They actually probably should call this flop with JJ-TT given that our range is probably JJ+/AK when we push. Of course, if they narrow our range that much they shouldn't have called preflop. [img]/images/graemlins/smile.gif[/img]