200: AKs in the BB and the world wants a flop

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I totally understand what you are saying, but if we are going on the assumption, which we pretty much should, that we are pushing any flop here then the flop doesn't matter at all. I keep saying this but you always leave that out when you respond to me

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Sigh. I know how you feel about saying something again and again and not getting your point across. [img]/images/graemlins/smile.gif[/img]

First and most importantly. The point I am trying to make is that your plan of pushing any flop is a bad one. On this particular flop, if our opponents play as posited, pushing at this point is a mistake as I have shown. All of the rest of this is merely in support of that idea. If you want to argue that pushing *any* flop is correct, then you need to address this particular flop and these particular players.

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However, I am still fairly sure that your numbers are off.

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1) There are 9*6 = 54 ways they can both have sets.


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Where is the 6 coming from?

On any given flop there are only 9 total combinations of possible sets. Since each opponent's total combination of hands from JJ-22 is 54(on this flop) and there are only 9 combos of those that have sets, the probability that player A has a set is (9/54) 17%. Player B has the same probability. The probability that both have a set is merely (0.17*0.17) 3%.

This is the step, as mentioned above, that you are leaving out. You have to subtract the probability that they both flopped a set out as you are counting it twice.

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Actually, the line you point to is the one where I specifically include it. In the lines where I calculate the probability that only one has a set, I really do mean that only one has a set. (That is, I am excluding combinations where they both have a set.) Also, ironically enough, it is you who is over-counting. In your calculation, you are allowing them both to have the same set.

Here is where the 9x6 came from. Player one has a set. There are nine combinations of cards he can have which would give him a set: three each for each of the three cards on the flop. GIVEN THAT THE FIRST PLAYER HAS A SET, the second player has only 6 combinations of cards which make a set. (He can not have the same set as the first player, so there are only two flop cards remaining to give him a set.) Thus there are 9x6 possible combinations of hole cards which give them both sets.

(Also, there are actually only 51 total combinations of JJ-22 on this flop. There are 6 each for the 7 cards which do not appear on the flop and 3 each for the 3 cards which do appear.)

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I made a counting error with the 54, you are right. I just think you are making this harder than what it needs to be. Redoing my calc's...

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. They both have a set 3% of the time so the number is 33%, not 29% sorry.

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?

I see the point you are getting at now. I was trying so hard to get mine across that it was getting in the way. [img]/images/graemlins/smile.gif[/img]


The thing is this is one of the worst flops for us and there are tons of variables to take into consideration. You have a ton of FE here. If you aren't going to push then you might as well check-fold. Now, we probably didn't expect to get two callers here(preflop) and this is a terrible flop for a c-bet but I still think we have enough to make it when you consider that your opponents will make more mistakes than you think.

Put yourself in villains shoes, can you call JJ/TT here easily? 100%?

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? [img]/images/graemlins/smile.gif[/img]

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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.

[threads13]

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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]