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I think bet/folding the river is much better than check/calling. His turn check is either a trap or he wants to see a cheap showdown with his 10x, A3 or whatever. If he was free carding you on the flop with a draw there is no way that J didn't improve his hand enough to bet the turn.

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I like bet/folding this river aswell, I think this is a spot where he will only bet hands that beat you, so if you aren't check/folding then I don't think you should be checking at all.

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