How do you respond to an inept table coaching?

[smarterthanyoda]

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1)Never correct an idiot.

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I know not to do this on strategy points, but when it's something so factually incorrect I'm wondering if embarrassing him with a comment to the effect of, "If you're going to criticize my play maybe you should remember what I actually did?" would be better than just playing dumb like I would if he had said something like "You raised with ace-king? No one was about to fold, you know! That's a drawing hand!"

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You still shouldn't say anything because you might be giving a wake-up call. Obviously this player isn't paying a lot of attention to the game. He may have his mind in a million different places, but it's probably not on poker. Pointing this out to him might make him realize this. By focusing on the game he won't just remember the action, he'll also start analyzing his play and make more correct moves. His level of play will go up, and your EV will go down.