Again, RPS would be a simple example of how this could happen. A more sophisticated example would be river scenarios (folding bluff catchers that are 0 EV to call vs GTO strategy, not bluffing in 0 EV spots vs GTO Strategy, etc). There are exploitable plays in poker which are 0 EV vs GTO strategy (but of course not >0).

it's my understanding that any deviation from a gto strategy in one area throws the rest of the ranges off. any form of deviation is exploitation. there simply is no reason to do it imo

two gto players are rock-paper-scissoring at optimal 1/3 frequencies, each the nemesis of the other.

now player1 starts throwing nothing but rock. he still wins the maximum possible vs player2's gto strategy (EV = 0), and hence is still a nemesis. however he's obviously no longer gto himself.

ah i understand the concept now, ty.
this type of deviation doesn't net us more of a profit and opens us to massive counterexploitation though. a solid gto player will recognize the mistake and start adjusting on the margins (throwing rock 25%,scissors 25%, paper 50% or smth) ... the unbalanced nemesis deviation will quickly become -EV and the GTO player will increase his winrate at that point, no? (which is why a solid mix of GTO and marginal exploitative deviations applied correctly crushes)

But its not GTO anymore

yes ike was just making a technical observation. keep the distinction between a GTO player (the theoretical construct) and a GTO player (a human poker player who studies this stuff). ike's comment applied to the former, your comments apply to the latter. i think lots of confusion in this thread comes from a similar ambiguity.

As said above, as soon as you start exploiting you're not GTO anymore. But that's the practical value: Play GTO until you recognize a leak, then start exploiting that.

obviously, he's deviating, as are we! ^_^

thanks for the explanation guys

wow zobags, you were not misusing terms, you were not getting it. you could have just accepted what i wrote about 6748902 times, but you told me i would not get what you were saying instead. very grown up.

at least you could have apologized to me and not to ike, whose identical response you accepted on the spot.

no shame to not get it quick in some stuations.

Love how Durrrr has just disappeared from this thread

prlly nothin better to do

but i do hope he comes back to it at some point!

Ike,
Have you heard back from durrrr? Or is he just as silent as in this thread?

Anyone care to comment about how GTO button strategy would account for BB holding blockers some of the time on the river?

a GTO-strategy would account for all possible holdings.

it has no "special response" against specific situations based on any assumption about villain's range, that would be exploitable.

Eh, this is imprecisely worded, but I think the spirit of it isn't quite correct. GTO strategy does take into account another (optimal) opponent range and does do specific things with regard to blockers/card removal. This is not often seen in the toy games that are commonly discussed, because in general the toy games with card removal are too simple and the more complex toy games ignore card removal. However, I will give an example that I have mentioned before.

Consider the limit holdem game where both players have a random hand, it's the river on a board of like T8532 rainbow, and there is just one bet left. The pot is like, say, 6. If you solve for GTO strategies, you find that the first player does something interesting with his big pairs. He will (for example) bet AA, QQ, and JJ, but check KK. This seems odd until you look at the second player's strategy, where his "check behind" hands are mostly king-high. So the heuristic interpretation of this is the first player wants to check/induce a pretty good hand for balance sometimes. When he has KK, he blocks the opponent from checking behind the most, so he chooses that hand as the inducer, because the opponent will tend to bluff or value bet more often when he holds that.

So GTO does take advantage of the features of a specific distribution/strategy for the villain in the card removal domain.

^^guess you are right, and i worded it unclearly.

my point was that finding a gto-solution (nash-equilibrum) is kind of a evolutionary process, not a process of analyzing special situations and finding isolated solutions for them.

Jerrod,

Is there are article that discusses the solution to this game, or is this something you've just solved yourself?

Actually, this is not really right either. Yes, there are computer methods like fictitious play that solve using a kind of evolutionary process. However, this is just one possible method of solution. You could also arrive at the answer by solving a giant linear program (just good old linear algebra). This method uses computer memory far less efficiently, so you more quickly run into the wall of the current limits of computing power. And I'm sure there are other methods of solution too -- quite possibly methods that would involve analyzing special situations (though I'd imagine they would be inefficient too).

The evolutionary process method seems easier for most people to grasp, because it mirrors human beings adjusting to each other, a concept we're all familiar with. But it's really just one tool of many possible tools.

Just something solved myself. But it would be easy to replicate.

First, my apology was not directed specifically to Ike. I actually had you in mind when I wrote it. Sorry for not making that more clear.

However, you basically started yelling at me (internet style) for saying,

"I would think a GTO strat would have to assume villain is playing GTO as well."

As someone unfamiliar with the formal language of game theory, I still do not see a large difference between the statement above and the correct statement,

"The nemesis of a GTO strategy is itself a GTO strategy."

But, I now understand to someone using the formal language of game theory, the first statement is non-sensical.

To say it another way: if we (as humans) attempt to calculate a GTO strategy, we should assume villain is playing a GTO strategy as well and maximize our EV against that. I believe others have said this is also correct.

Ike took the time to read what I wrote and explain to me what I was doing to cause the confusion between us. Whereas, you saw someone not using the proper language of game theory and saw the opportunity to call them stupid. I sincerely hope you feel better about yourself after having done so. I also never said, you could not understand what I was saying, just that you did not understand it because I was being unclear. Anyway, I realize the confusion between us was entirely my fault and apologize for that.

After reading this thread, I'm convinced rake is the reason there's no money heads up, because everyone is definitely not solid.

The other point I was making is that a human, when attempting to calculate a GTO strategy for a river spot, must assign a range of hands for villain in that spot, and that range should be what a GTO villain would have in that spot.

Consider the following 2 games.

Both involve the river of a hold 'em hand where there is one pot size bet left, on a board of Qc9d8d3c2s. The BB must check and the BTN can either jam or check and the BB can either call or fold. The BTN has a range of {JT, QQ, 99, 88, Q9, Q8, 98, AA, KK, QA-QT, AdKd-Ad2d, AcKc-Ac2c, KdJd-Kd2d, KcJc-Kc2c, Jd7d-Jd4d, Jc7c-Jc4c, Td7d, Td6d, Tc7c, Tc6c, 7d6d, 7c6c, 6d5d, 6c5c}.

In game 1, the BB has a range of any two cards.

In game 2, the BB has a narrow range of QA-QT.

When I use software to solve these two games, I get different GTO strategies for the BTN. I believe this illustrates that a human attempting to calculate a GTO strategy for a river spot, must assign a range of hands for the villain. However, I am not a 100% sure of this because an overall GTO strategy for hold 'em may be completely unrelated to the GTO strategy of one specific spot. This seems counter-intuitive to me, but I know a lot of game theory is counter-intuitive, so it would not surprise me if one of the experts told me this is the case.

what software do you use?

CardRunnersEV

I want to clarify some things that you are saying here, because I want future readers of this thread (and maybe you, but I can't exactly tell) to be clear about these things.

Let X be the first player and Y the second player. Strategies played by X will use lowercase x, (eg x,x'), and the same for Y. Let g(x,y) be the value to X of playing x against y.

Definition:
Let (x,y) be a strategy pair. Then x is a nemesis of y if there exists no x' such that g(x',y) > g(x,y). We also sometimes say in this case that x maximally exploits y.

So a nemesis of y is any strategy that achieves maximum value against y. In poker, it's virtually always the case that there exist a family of nemesis strategies, since you can take two options that have the same value and mix them in any proportion you want and still have a nemesis. So it's normally not that useful to refer to "the" nemesis.

You state: "The nemesis of a GTO strategy is itself a GTO strategy."

This statement is unclear because "the nemesis" doesn't have a clear meaning, as there are many nemeses, almost all of which are not GTO. (note to Cangurino: this is true for the measure theoretic definition of 'almost all' too!)

This statement is true:
If x is a GTO strategy and y is a GTO strategy, then x is a nemesis of y (and vice versa).

This statement is not true:
If y is a GTO strategy and x is a nemesis of y, then x is a GTO strategy."

It also isn't true that if we just had GTO y, we could find GTO x by maximizing against y. All we would do is find some nemesis of y, which would almost surely not be GTO.