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Turn is the 8[img]/images/graemlins/heart.gif[/img] and my opponent checks. Should I check behind, or push? And did I make a mistake on the flop?

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Tough turn card. There is probably a heart out there, even if only a small one. Probably only a poor to fair chance that your set is good. If there was a side pot, then maybe I try to pick it up on the turn. But in this case I probably check and hope to catch one of my 12 outs and pick up the boat, which would be hard for the opponent to pick up if he has the flush.

The only alternative is to push. However, the push doesn't have any value at this point. It only allows you a chance to get headup with the allin.

Three way doesn't look too bad here, especially if you riverboat. The opponent may even check the river with a smallish heart anyway. Maybe you can pick up a bet on the river if you catch.