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Try putting opp. on a range of hands based on his call preflop (will be big lv1 w/no reads-- any pp, any Ax, any suited connectors/gappers...). Based on his call on the flop, narrow that range. The check on the turn and river IMO tell me that he probably doesn't have the nuts, but it doesn't mean he doesn't have you beat. He may just be taking a check call line with trips or 2 pair. How many hands in the ranges you came up with, and narrowed down, are you ahead of on the river but will still call a value bet(very few)? How many better hands are folding (none)? I think the bet on the river will cost you money in the long run because it won't extract value from beaten hands very often, and will lose you more when you are beaten.
A side note: what if this guy is truly a fish who has called down with AQ and hit his gin card on the river. He can't wait to reraise your river bet ai. I have seen countless people get ai in the first level with Ax on an A high f/t/r.
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