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Is there anything here that leads you to believe he will call bets on the flop/turn and river with something that you are ahead of without a J? It seems unlikely to me. It also seems unlikely that he will bet anything you are ahead of that isnt a J. So either way I see no value from those hands. Your opponent will always call with a J on the river, but if you check he will pretty much always bet it also, so again I would be pretty much indifferent to betting v. checking. However, check calling on the river saves you money against sets/flushes 100% of the time (since i think if you bet and he pushes you have to call). So by checking, we lose value the times he has a worse J and pushes the river, but we gain value the times he has a set/flush. I think check calling is the better play.

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Yeah.. MLG's right.. I think this is an obvious check, and a slightly less obvious check/call.