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Why not check behind on the turn? I think this is one of those cases where you only get called by a better hand (flush).
If you check behind and he is not holding a diamond, and a non diamond falls on the river, he's going to check again fearing you have a diamond in your hand, you show down your two pair for free and take down a small pot.
If you check behind and he IS holding a diamond, he is going to bet the river and you are going to fold, you lost all the money you put in the pot on the flop and pre flop. But you didnt lose any on the turn or river.
If you bet the turn and he isnt holding a diamond, he folds and you take down the same small pot you would have taken down had you checked behind.
If you bet the turn and he is holding a diamond, he is going to raise you or smooth call then bet out the river and you are gonig to fold. You lose more money than you would have if you checked the turn then folded the river.
Checking behind on the turn on a 3 suited board when you hold 2 pair is +EV in the long run I believe. The river might bring you a boat once in a while that villains with a big flush will pay off a fair amount of the time.
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