[Buzz]

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the times he calls with a worse hand need to outweigh the times he raises me with a better one by 2:1 for betting just to break even.

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Donger - Seems a good way to think.

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His hand is basically random. My hand isn't. Since I raised before the flop, I'm more likely to have a low-oriented hand that will miss this board completely. This makes him more likely than normal to try to bluff at a busted-low board.

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Yes. As I think about it, exactly.

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P.S. - Do you have some sort of fast method for whipping out those cominations, or do you just do it the old fashioned way?

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I don't think I have any particular systematic method. I thought of the forty sevens involved here sort as a collection of clumps, kind of collecting some of them on my fingers. Didn't take long. Then I reflected for a while. I thought it was very interesting that Villain somehow coincidentally had about the same number of hands involving two pair or better that win as lose.

You have top and third top pair. I'll think about this scenario some more while I do my walk, but off-hand it seems like that's probably always the case when there are two ways of sixteen each for an opponent to make a straight and when you have top and third pair. Then we can go up and down from there... da da da. Whatever. I think this might turn out to be a very practical reference post for me.

As Chaos opines, what to do depends a lot on your opponent.

Just my opinion.

Buzz