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I ended up breaking Zeebo theorem and folding. I knew there was no way he was bluffing, and I decided that he wouldn't make the play with just AAA. That said, when I went over the math later I realized that he only has to make the play with AAA a small percentage of the time to make calling profitable. I don't think he ever puts me on a draw that hit btw, he knows I have trips or a full house/quads when I raise him, even if that isn't completely accurate.

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if you had jacks-full instead, it would be much
harder to fold.

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I'm interesting in seeing the math here. If he only pushes with a full house+, and his preflop range is AA,KK,QQ. What's my equity against his range with JJJ33, given that I dumped a king.