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I would bet/fold the river. You're going to get bluffed out a lot of times by check/folding a 4 flush board.

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By this logic, wouldn't you want to induce these bluffs that will occur a lot of the time? In this hand, I see myself calling should UTG+1 decide to fold. You can't overcall in this situation. What non-heart hands (that you beat) are calling you here if you bet the river?

To the OP: I think the river was played well, if you were intending to check/call.