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Let me just agree with everyone that this is a pretty easy turn b/f. He has all kinds of combos that beat you and make sense on every street: JJ, 33, 66, AQcc, QJs. I can really only come up with AKdd, AJdd, and maybe JTdd as hands that you beat that he might play this way. You've shown strength on 3 streets.
I also think I would c/f the flop given 2 players and no reads. But, if I was going to bet, I would go .35. As matiusaa says, it will have the same effect. On that flop, no one is thinking "gee..I'd have called .35, but I better toss my hand for the extra dime." And, with that dry flop, you aren't worrying about pricing the draws. I know that 2 bb's may seem trivial when the bigger decision involved 57 bb's, but think about how many times in a session you have the opportunity to cbet. Poor cbet sizing really adds up quickly.
Also, it's not just the flop. Let's say you do cbet .35 and get called. The pot on the turn is now $1.32. A reasonable bet, which we all agree you should do, is about .80...give or take. The board now has some draws and a slightly larger % bet is warranted. Now, think about the hand. Assuming you fold, you have saved 8bb's by pot controlling a little better. That really adds up over the course of a session.
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