When 4 bet/call on a paired board ...

[TheRempel]

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Case 5 for UTG, SB is slow-rolling 7-7 and MP1 took a card off with straight flush draw or an overpair.

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Man, you like looking for those monsters huh? It's certainly quite possible that the other three players have it completely boardlocked, but it is much more likely that you are up against another five (or 77, or both), a couple of overpairs, and a draw, or some combination of the three. I'd raise it up here a bit, fold to a push from most players, and block the river if it got HU. Unless my opponents are total crap, getting two callers would have me check-folding to all but the tiniest of bets on the river.