[W. Deranged]

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What about a bet out on the flop when checked to? Fold some people and increase your winning chances in this big pot.

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No one is folding. If we had a gutshot in addition to our backdoor flush and overs, I like a bet, but then it's primarily for value. The check by the pfr in front of us may be setting up a check-raise, and I don't want to put two bets in on this flop if I avoid it. Our overcards are likely to be either totally clean or reverse dominated, and in both of those cases there's no reason to try to clean up our overcard outs (because they're already clean or we won't be able to fold anyone who has hands that dirty them).

So I think checking this flop is probably the best way to go.