[bozlax]

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Ok, misapplication of the value betting concept on my behalf then. Is betting here ever correct when villain checks?

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Value-betting is betting when the percentage of time you expect to win the pot > the percentage of bets you're putting in the pot if you get called. Given that you're playing the board, this cannot be a value bet. That said, you answer your own question. What needs to be true in order to consider betting, what's that called, and what's your plan if c/r'ed?