In applications of NLH, Janda explains that, for a pot sized bet, we should have 33% bluffs on each street. That is, if we have 20 value hands by the river, we should have 10 river bluffs to balance - this makes villain indifferent (EV=0). Likewise, we should have 15 turn bluffs to balance the 30 river bets (20v + 10rb), and a further 22.5 flop bluffs to balance the 45 turn bets (20v + 10rb + 15tb). So, in total:

- 20 value bets
- 10 river bluffs
- 15 turn bluffs
- 23(ish) flop bluffs

In this toy game, Janda assumes that when we check back our flop or turn bluffs, villain wins the pot. So we bet the flop with one of our flop bluffs and check back the turn, villain will check down and win the pot at showdown with his bluff catcher.

In a real game, however, it does not seem so simple. If we check the turn with one of our flop bluffs and villain checks down, he will not necessarily win at showdown because our bluffs still have some equity.

So my question - Should villain even call with a bluff catcher if he knows we are bluffing at the above frequencies? The above frequencies make villain indifferent in the toy game example, however, in a real game bluffs carry equity so surely we would need to be bluffing more than in this toy game example for his calls to break even - because some of the time he will just lose to the bluffs?

A lot of bluff catchers also have significant equity versus the value range (trips or 2pair outs)

Janda's toygame assumes bc always lose to value

^ also many bluff catchers have BLOCKERS which reduce the value combos and change the ratio of bluff to value making them +EV calls

Yeah I was actually thinking about this too. So, does this mean that they balance out? Does the equity lost to the fact that heros bluffs have equity against villains bluff catchers balance out the equity gained by the fact that some of villains bluff catchers have equity against heros value range?

Also, does this mean that villain should bluff catch with hands that have the most equity against heros value range? For example, MP vs BB on Q72r heros value range consists of a lot of Qx. Should villain bluff catch with his Ax opposed to other hands with more absolute strength - like small pocket pairs - since these would have greater equity against heros value range?

it is a big factor, yes. on some board and line you would prefer something like AQ high rather than pocket 44