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As played, open push the turn if he's got a made flush you're going to pay him off, if he's got JJ,77,33,44,56 that's just bad luck for you. The problem here is that we're dealing with microstakes.
Does BB know he's supposed to raise with the Ad and a made pair on the flop? Does he know he's supposed to raise if he made a baby to midsized flush to priceout a potential redraw? Inferring meaning from betting patterns is the key to online profitability, and unfortunately bets mean a lot less at 0.02/0.05 NL than they do at higher levels.
The whole idea here is to say to yourself "What would this particular villian (I can't stress that enough) have played the hand this way with?". If he's the least bit competent then you know that he knows that he should raise a set even on a flopped 3 flush board. This means 77,33,44 are all unlikely holdings. I'd like to think he would've raised with an overpair, so as of the turn JJ is unlikely as well. That being said there are three types of hands we're even considering him having AdX{c,s,h}, AdXd, KdQ{c,s,h}.
You've got too much equity against too many likely drawing hands here not to push the turn.
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