[vmacosta]

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I'm almost always going to showdown here

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I don't see how I can call a river bet, unless the board pairs or I hit my A.

River 3, no diamond.
UTG bets, MP1 screams and calls, there is no way I can call, not even getting 21:1.

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Well, that's a particularly bad sequence, so I won't blame you for folding. But in general we should not be looking for reasons to fold aces on any street for one more BB in a pot of this size. FWIW, I'd probably still call on the river you described and not feel real bad about it. Even live players do stupid/courageous crap and folding the best hand in a pot of this magnitude will likely ruin (or at best end) the rest of the session for you.