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I would check/fold the river. I am not sure that the tag is capping with anything we can possible beat when the A comes on the river. (not to mention he 3bet the flop)

It looks like he had KK and called the river b/c the A scared him.

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This might be a better option if we are very certain villain checks behind with JJ / TT. Given my analysis above, this would have EV = 0 (better than above) if we are 100% sure he checks behind. If we think he bets JJ / TT even a small portion of the time then we risk giving up the entire pot, hugely -EV.