Hello,

let's discuss the following game. You're on the river OOP with the range:

33% - nuts

33% - middle range

33% - air

Villain has

50% - bluff-catcher

50% - air

Your middle range has 50% equity versus his bluff-catcher. Stacks = 1 pot. Either player can only check or bet the pot.

Would you bet your middle part or check? Checking makes sense to pick off his bluffs. Betting makes sense because your range is stronger and forces him to fold some of his BCs therefore giving you fold equity with your middle part.