The optimal calling frequency is the calling frequency which makes your opponent's expected value of always bluffing equal to his expected value of never bluffing. Theoretically, if you call bets with the optimal calling frequency, whether or not your opponent employs a strategy of bluffing or not shouldn't matter to you (since his expected value will be the same either way).

After reading this article on optimal calling frequencies, I am having trouble understanding why if your opponent bets B into a pot of P, your optimal calling frequency is

1 - B/(B+P)

if you think he is bluffing at a rate of B/(P+B) or higher and

0

otherwise. Here is the passage it comes from in the article:

Question 1: What justifies this? The author states this rule comes from Sklansky's Theory of Poker, but I can't find it anywhere in the book (all I can find is stuff about optimal bluffing frequencies, not optimal calling frequencies). Also, I understand the author's lengthy argument at the beginning of the article for a particular case, but then generalizing to this rule isn't justified and it just comes out of nowhere.

Question 2: Let's say you apply this formula in a particular situation and it comes out saying you should optimally call 10% of the time. Does it matter whether or not you only call with bluff catchers or not? Or could you literally call 10% of the time with any two cards (including occasionally with 23o that didn't hit), and fold 90% of the time (including occasionally AA), and still force your opponent's EV to be invariant to whether or not he bluffs?


EDIT: I understand that if our opponent is assumed to be bluffing on one particular hand, and he bets B into a pot of P, then us calling him 1 - B/(B+P) of the time with a bluff catcher makes his long-run expected value equal to 0 (in this spot only, when he is bluffing). But I don't see how this fact takes us to a generalized optimal calling frequency, where the opponent's expected value is the same whether he always bets (regardless of whether he is bluffing or not) or always only bets with made hands.

Not a full answer.

But the bluff rate is not 100%. There is an equation for optimal bluff rate from GTO (Game Theory Optimization).

Just as your opponent puts you in tough spot by bluffing. You need to turn it around and call back at an optimal call rate from GTO.

If you never call back then your opponent will stop playing GTO and play exploitative. Always bluff.

If you always call back with a bluff catcher then your opponent will play exploitative and never bluff.

I suggest you read up on GTO.

I don't agree with that bluff rate of B/(P+B) or higher. Where did you get that?

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