[holdem2000]

If we're in some situation where the villain's hand is concretely defined to be either a hand he should value bet or a hand he can either bluff with or check with (and I guess some hands in between that he just checks with), and if we also assume that there's a set of our holdings rigidly defined as bluff-catchers (hands better than all his bluffing hands and worse than all his value betting hands), then there will be some optimal amount of the time he should bluff when he has a bluffing hand. If he bluffs precisely this optimal amount, we will be indifferent to calling and folding with our bluff-catchers.

If the opponent bluffs more often than this than our correct strategy is to call with 100% of our bluff-catchers, while if he bluffs less often than this our correct strategy is to fold all of our bluff-catchers.

OP asked if we could easily calculate this indifference threshold, and I agree that we could in this artificial situation where hands may be rigidly defined as hands you bet for value or hands you bet as a bluff, and also where hands can be rigidly defined for bluff-catchers (the A, K, Q game is the most iconic game of this type, where aces are bet for value, kings are always checked, and queens are only bet as bluffs, while kings become bluff-catchers).