In Applications of NLH Janda explains that, in order to remain unexploitable, we should be betting with a balanced range on the river. So, in a hypothetical example, if we had 20 combos of he nuts pre-flop, we should bet in such a way that we are betting these 20 combos on the river, balanced with 10 river bluffs (for a pot sized bet). In order to do this, however, we need to also balance our turn and flop bets. So if we're betting the 20 combos of nuts on the river, and 10 combos of river bluffs, we need to bet an additional 15 combos of turn bluffs (aka river check backs) so that villain is getting 2:1 on the turn (the 30 river bets vs the 15 turn bluffs). The same goes for the flop. We need to balance our 45 turn bets with an additional 22.5 flop bluffs to make villain indifferent.

My question - If we have 20 combos of the nuts preflop, why not just balance these out with the 10 river bluffs and then just bet pot on each street? Why do we need these additional turn and flop bluffs? If we bet our 20 nuts combos and 10 river bluffs for a pot sized bet on each street, are we not balanced? For example, we bet the flop with our 20 nuts values and 10 river bluffs for a pot sized bet. Villian know exactly what he have and is getting 2:1 on a call (the odds he needs), why is he not indifferent? We do the same on the turn. Again, assume villain know we are bluff 33% of the time, why is he not indifferent here. Why does he need to additional turn bluffs (aka river check backs) to be indifferent?

Reverse implied odds. If Villain is getting 2:1 on 3 consecutive streets—or even 2–he will fold early on because he will not win enough showdowns to justify a flop or turn call.

To clarify, this is based on a nuts/air vs bluffcatcher toygame. Hero always barrels the nuts, and therefore villain wins the pot whenever you check.

Why would BB call flop in this case? They would just rangefold. And now you have a bunch of extra air in your check-back line that gives up.

Think about it like this - BB needs to be getting a breakeven call. That means they need to win the pot 1/3 of the time in order to call the flop. But they won't actually be winning 1/3 of the time, because you literally always triple barrel. A balanced range will give up 1/3 of the time on the turn and river (for a pot-sized bet), giving them a breakeven call.

Another way to think about it: Villain can only win (gain EV) when you give up. Whenever you bet their bluffcatchers are at most 0EV. So they need incentive to call the flop/turn, which comes from your give up range.

It's not a stupid question.

Imagine a game with no outs, draws or equity, it's just nuts, napkins, and bluff catchers.

You are holding a bluff catcher.
On the river, whenever you face this 20:10 range, the EV of your bluff catcher goes down to 0. (You are indifferent between calling and folding).

On the turn, if you faced a potbet with a 20:10 range, knowing your EV on the river is going to be always 0, the EV of calling turn would, on average, lose the entire pot bet. Therefor you would not be indifferent between calling or folding, you would always fold.

Villain needs to add bluffs until he checks back river enough for you to win the pot 1/3 of the time. This means, on turn, he needs to use a 20:25 ratio.

You can probably infer how this applies to previous streets.

"Nuts, napkins, and bluff catchers" is my new favorite way to describe this toy game

Yes okay so my problem with this - if villain calls that turn pot sized bet, he is not necessarily losing it. If he calls the river bet, he would be winning back that money he put into the pot on the turn. So the turn call is -EV for a pot size bet, but then the river call is +EV for a pot sized bet? But wait, I guess that's only when he wins on the river... When he loses the river call (which would happens 2 out of 3 times), he loses his river call, plus he loses the money he put in on the turn. And when he wins the river call, he wins the river call money, but a fraction of this is his turn call anyway. Hmmm, confusing.

You can simplify the river to 0EV facing a bet; you only gain EV when they check back with their give-ups.

So they need to check back the river often enough in order for you to justify calling the turn. Same goes for flop->turn.