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Bet the flop. If you check behind on the flop, he's probably going to bet the turn no matter what comes, and you're going to be put to a very hard decision where you have no idea where you stand (like you were). If he has an ace, so what? If he calls or raises the flop bet you're done with the hand anyway.
Edit: Yeah this got a little math-filled from here on out. Just keep in mind you've got to put him to a decision or he's going to put you to one.
The pot on the flop is $15.75, I'd bet out and see what happens. This bet on the flop is +EV even if he's only folding 37% of the time.
I'm kinda bored so I'll show why:
If we say 37% of the time we win $15.75, and 63% of the time we lose $9.00:
37% of 15.75 = +5.83 (average gain when he folds)
63% of -9.00 = -5.67 (average loss when he continues in the hand)
The EV will actually be better than this, because sometimes he'll call and we'll hit our 2-outer on the turn.
Okay so, 2 cards out of 47 to come is 4.3%, 4.3% of 63% is 2.7% (% of the time he will call and the king will hit), and let's say when you hit the king on the turn you can extract on average another $10 out of villian:
37% of $15.75 = +$5.83 (average gain when he folds)
2.7% of $25.75 = +$0.70 (average gain when he calls and you hit the K)
60.3% of -$9.00 = -$5.43 (average loss when he calls and no K comes)
Average profit of the play: $1.10
Now, it's possible that a bet of $8 or $10 or something has a higher expected value, but I'm just trying to show the point. Also, if he's calling more than 37% of the time, then you're making more profit, and if he's paying you off more than an extra $10 when you hit the 2-outer then you're making more profit.
Wow this got long really quick. Just bet the damn flop.
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