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What fold equity do we have against a better hand on this board? If we have the best hand, why do we want the villain folding? If the villain has a better hand, then I'd rather find out for one bet at showdown, rather than no showdown costing us up to two bets.

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You're right. I think I phrased my thoughts wrong. What I meant to say is that I'd rather just take the pot now even if it means that there's little chance the opponent will fold.

If he just calls, we can just check behind for the same amount of bets and still get a showdown...if you don't want to invest any more money into the pot.