Quote:
Originally Posted by venice10
I'll admit I have only very rudimentary understanding of how GTO play impacts NLHE poker. Maybe someone can explain how I'm not "getting" a basic premise through this question.
I thought (and if the question is not applicable to GTO, let me know) that an example of GTO play is a situation on the river where Hero makes a PSB. The villain is offered essentially 2:1 odds to call and Hero is bluffing 1/3 of the time. Therefore, the villain will win 2 bets 1/3 of the time and lose 1 bet 2/3 of the time. For the villain it doesn't matter whether he calls all the time or folds all the time. He's going to break even.
What I don't get is while the villain doesn't know the Hero's range, the villain knows exactly what he has. If he has the nuts, he isn't "indifferent" to the decision. He's going to raise 100% of the time. If he has 6 high, he can't even beat a lot of Hero's bluffs. He should fold.
It just seems to me GTO is a digital binary solution to an analog problem. To take the classic Prisoner's Dilemma example, the working assumption is that they have no other options. However, if one of them knew they had the nuts (let me go free and I'll give you evidence that the other guy did a crime that you want desperately to be solved), then the NE solution collapses.
I'm sure I've misunderstood a lot, so if somebody can pick this apart, I'd appreciate it.
The problem here is that if P2 is playing his frequencies correctly his EV of bluffing is already $0 (ie. no different to if he folds), but he
forces P1 to sometimes call his raises when he has the nuts.
If he only moves all in with the nuts and calls or folds with everything else, then P1 will have the same EV even if he doesn't adjust how he plays, but more importantly P1 can now exploit P2 by always folding to a raise. Eventually both players should reach the equilibrium if they keep adjusting to each other.
For a simple example of this let's look at a situation where P2 has a range of nuts + air only, and P1 has medium strength hands only. The pot is $100 and the effective stack is $100 as well.
As P2 we can move all in every time we have the nuts and check everything else, but if we do this then P1 will never call us and we make no extra money.
Instead, we can actually force P1 to call us 50% of the time (because if he calls us any less then he knows we could move in with anything and automatically make money off him). We want to force P1 into a situation where he calls us 50% of the time (because if he doesn't we will exploit him by overbluffing in the future), but we want to make sure our bluffs are still EV neutral.
Thus we move all in 50% of the time since we are getting 1-1 on a bluff, and we do that with a range of {66.67% value, 33.33% air).
P1 is forced to call us 50% of the time, so the EV of our value hands becomes:
P(nuts) * P(call) * (current pot + P1's call) + P(nuts) * P(fold) * (current pot) = 66.67% * 50% * $200 + 66.67% * 50% * $100 = $100 ie. the whole pot
and the value of our bluffs becomes P(air) * P(fold) * (current pot) + P(air) * P(fold) * (lost bet when called) = 33.33% * 50% * $100 + 33.33% * 50% * $-100 = $0
So we lose nothing when we bluff because the times our bluffs successfully win us the pot net out the lost bets when we are called and lose (but by forcing P1 to make these calls we eke out extra value when we have strong hands and there is nothing P1 can do about this)
If P2 only moves all in with the nuts and never bluffs, and P1 is playing GTO then P1 still won't care because his EV is the exact same (because he is never losing the pot to a bluff). However P1 can now adjust and exploit P2 by simply folding every time P2 bets, thus reducing P2's EV.