[Scarmiglio]

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On the other hand, if you bet out on the turn villain may just go away now reasoning that since the Ace didn't scare you, you can beat their big pocket pair. If villain does have a big Ace, they will almost certainly b/c and call the river.

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How likely is villain to have an overpair in this pot based on flop and pre-flop? If he does, how often is he laying it down to a single bet on each of the turn and the river?

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Lots of players will play an overpair this way preflop and on the flop. That being said, you will probably get him to call a bet on the turn and the river if he has TT - KK. I conceed that it's probably better to bet all the way here.