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You are getting 11:1 on the river.
If an A hits his possible hands
uts
AA:1, KK:3, QQ:3, JJ:3, TT:6, AK:2, AQ:3
He wins: 10, you win:9 You tie:2.
Based on his betting and his smile he is most likely to have JJ or AQ. However, he could also have TT and have been smiling because he just took away 3 of your outs. Likewise, KK is possible too.
I would call an A with a bet on the river.
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Rick - i think we can remove AA and KK from his range of hands, he goes bananas with those holdings (saw both happen already). I also think we can slightly discount TT, not positive he would be the turn , perhaps discount that as part of his range by 20%.