If we get checked to HU and our villain has more than 33% equity, they are making an error by folding if we make a pot size bet on the turn. Therefore, when we make the bet half pot, they are making a mistake when they have more than 25% equity. *This assumes that all stacks are going in on the current street as implied odds etc. influence the true equity %, especially as villain is out of position as they need to play a guessing game.
This is why check calling is horrible out of position with a marginal hand!
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