Hi all, I have a game theory 101 question of a GTO concept I don't fully understand.

Basic question: If a GTO wager on the river is constructed in a way where the bettor is indifferent if the caller calls or folds, how does a GTO player ever make any money off someone playing non-GTO? Obviously if a GTO bet is made, and called by a GTO player at the correct frequency, both players break even in the long run. When the caller deviates from GTO, he should be losing money.



There is a fundamental concept of GTO that I don't really understand, I'm hoping someone can clarify. When I'm faced with a bet on the river by a bot playing GTO, it's supposed to be constructed in a way that makes me indifferent to calling or folding.

For simplicity, let's say I'm faced with a bet that GTO says I should call with 50% frequency. If I fold to this bet every time, I should be losing as much money as if I call this bet every time. However, if the bettor is balanced, don't we break even by calling 100%? [I know this is where my error is,
but why don't we call GTO bets 100% of the time, if the bettor is indifferent?] Something's gotta give, and I'm a little confused where my logical error is.

Not true for a few reasons:

#1) Some of your calls will beat "value betting" hands in your opponents range, so they're +EV calls. It's very rare for your river range to include only "bluff catchers" unless you're facing an overbet from a very polarized range.

#2) If your range was literally all "bluff catchers" (potential calls that never beat value hands), there would still likely be a removal effect component that made some calls better than others.

But your general point remains true. If you have a "bluff catcher" on the river and your opponent is betting a polarized range, you're pretty much screwed no matter what you do.

I think what you're missing is a common tricky point in GTO thought.

If your opponent is betting on the river with GTO frequency, then it's true that it doesn't matter what you do. Call, fold, flip a coin, whatever. That is, provided he won't change his strategy.

If he might change his strategy, then it does matter. If you fold 100% of the time, he can start betting every time. If you call 100% he can stop bluffing. So maintaining your GTO frequency is a defense.

You see this also as the reason why GTO solutions often contain mixed strategies, like calling 80% and raising 20% or something like that. It should be the case that any option in a mixed strategy should have the same EV as any other option, otherwise, you should remove it from your strategy. Then, why do mixed strategies exist? Because the notion that each partial strategy has the same EV as the other is based in the notion that your opponent is playing the other strategy in the NE pair. If you chose to call 100% instead of 80%, against a NE opponent you'd have the same EV either way. Against someone who might adjust, you have to play your mixed strategy or you'll get exploited.

Follow up question, since I am very much not a GTO expert.

Optimal frequency play on the river ultimately rewards the optimal betting player the value of the pot on the turn, before the river, correct?

Or, is that an exploit and would require unbalanced river play?

Any long term profit actually earned on the river card will come from mistakes by one or the other of the players not betting or calling correctly as to their location in range.

If we're the optimal river better, then it would have to, because we're indifferent to our opponent calling or folding, and if he folds we get the pot. One of the nice side effects of indifference is that to calculate the EV you can consider the easiest spot to calculate and do that one.

This is not true. Poker is not such a smooth mathematical game, and on rivers some bluffcatchers will be indifferent, but quite often most hands are clear folds/calls.

Only the truly indifferent hands can call 100% or fold 100%, but I haven't seen many situations where there are more than like 5 indifferent hands (fwiw there are more indifferent hands when the bet is a huge overbet jam).