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As played, you should have bet river since you both only have $1.50 behind. It's really too late to stop here unless you're set on folding. With your reads, he looks like he has a strong hand, but you also look really weak on the river so he knows his flush is good. You've got 1.5:5 pot odds, so it only needs to be a bluff or a jack 1/5 of the time. Then again, if he really is weak, we expect a check behind with a jack or less, so I don't think calling is ever the right option despite the good odds. If you think he would call with a jack, or he's able to fold a flush, bet, if not c/f. Never c/c in this spot with an overpair.
What do you think his calling range PF is? would it include 97, J9 or J7? If it is that wide, I probably c/f turn, since I expect him to check behind most of the time. A small bet on turn would be hard to fold to because your nut flush outs, but the reverse implied odds make it easier. I don't think betting the turn is good because you might scare too many worse hands (jacks, flush draws) and only get better hands calling you.
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