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UTG Folds, Button calls (Hell yeah!)

Turn is a 7.

Hero beats himself to a pulp.... and does what?

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Well, bummer you 3-bet (although I guess if you didn't, you wouldn't be here. Calling that flop stinks). If you check, I assume he won't bet there at 10/20. You probably don't want to risk a river check. If you think a turn bet will fold this guy, I like checking the turn, expecting him to check behind. And then betting any river. If he bets that turn, you're a lucky, lucky man.