I still believe this is incorrect. A GTO is unbeatable, but it does not mean it is indifferent to strategies. The further we stray from GTO ourselves, the more negative our ev will be.

For example. Say GTO plays around 25% of hands. If we were to open 0% we would forfeit all blinds, but if we were to play 100% of hands we stray further from GTO and lose more.

Somewhere ITT the read on the limper was that he's fit or fold station but his open limp from MP should be enough proof.

I disagree that flatting flop and betting turn looks just as strong as raising flop. There's a pretty good chance the limper would overcall 9x hands, especially 9x with good kickers like A9/K9/Q9. I would also expect him to overcall with gutters such as A4 and A5. When we raise we blow out pretty much his entire range except for maybe 45s.

I said he was probably fit or fold because I didn't even know who it was so he obviously had no real presence at the table considering I knew 4 of the 8 other people in the game. 90% of the time he just whiffed this flop and is folding. OP says the other guy had a $250 stack, so why worry about him hopefully hitting part of this flop when I'm trying to get stacks in with the guy that has me covered and almost certainly has a much stronger hand than the limper?

I'm sorry, but the bolded is just wrong. While your example matches the bolded, correlation does not imply causation. Exploitative strategy winrate is >>>>>> than GTO winrate unless your opponent's skill level is very high and GTO becomes the only successful adjustment.

^^ I meant the further we stray from GTO when playing against a villain that is playing GTO.

Clearly exploitative is more +ev than GTO as long as we make correct adjustments.

Mayhap so, but no decent Villain is playing GTO, because he actually has reads and the ability to make exploitative adjustments. No one has a goal of playing GTO, they have a goal of maximizing winnings.

I was originally responding to a post that said playing against someone who is balanced is easy because it doesn't matter what we do.

I don't believe this is true.

I would have to say that Villain had 22 or 33 preflop. It's a hand that he would check out of turn with, yet still call the raise. Villain perceives Hero as being nitty. Being that both were deep stacks, it's an easy call from Villain.

And on the flop, villain can be raising with a set or can be bluffing. But on the turn, when villain bets $120. It's almost never a bluff imo. Villain should by turn know that Hero has a real hand. He's sizing his bet and shoving on anything that's not an Ace or King on river.

It would be a tough laydown for Hero on turn, but I would if i could, lay this one down. On flop, I would be looking to protect my hand, but on turn, i would have to lean towards protecting my stack.

It's a good chance I'm wrong, but i would play this hand exactly like villain if i had a set of 2's or 3's up against Hero.

90% is a bit extreme.

The read is that OP is competent and isn't always stacking off with an overpair. Raising also blows out his bluffs and thin value bets.

I don't want this thread to turn into me giving a math lecture, but you are mathematically wrong despite whatever you believe.

Your examples would lose money against a GTO strategy, it is true, but that is not because they are "straying from GTO"--it is because they are dominated. A dominated strategy is a strategy that is so bad that there exists a different strategy that does better against any other strategy your opponent chooses.

It is clear to see that your 2 examples are dominated strategies (and therefore would lose against a GTO strategy). Folding every hand you play is dominated by the strategy of jamming preflop with AA and folding everything else (which may, in turn, also be dominated by something else). Never folding any hand is dominated by never folding unless an opponent moves all-in when your equity against a range of any two cards doesn't justify the pot odds you're getting (which, again, might be dominated by something else).

The definition of a GTO strategy includes throwing away dominated strategies before you compute it. So your examples are totally irrelevant.

GTO is by definition indifferent to strategies. Whatever you think GTO is, if it's not indifferent to non-dominated strategies, it's not GTO. And by the way, for the record, as Kyle21 has also said, I have no idea what a GTO strategy in poker would look like. I am just talking about the math behind what GTO means.

Well just agree to disagree on this one...

Does anyone know what a gto strategy might look like for no limit multi way, or is it just too complicated a problem to solve? Presumably the machines you can play hu limit against are playing gto, or close to it, but that's a much simpler game.

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Vernon is completely correct, and no, no one has a really good idea of what GTO is multiway, in fact it's not even solved Heads-up without a lot of qualified assumptions.

People are making educated investigations to try to estimate something approaching GTO in some certain circumstances multiway, but a complete strategy is not even close to being solved.

And yes, there is a lot of misunderstanding of what GTO is from a conceptual level, maybe we need a GTO sticky somewhere, or does that already exist?

no, he is not completely correct. gto is not indifferent to strategies as a general matter, although there are instances is which a person employing a gto strategy will be indifferent to what his opponent does (like in the example he gave). this does not hold true to every decision point across multi street play, however. the fact that a strategy is not dominated does not mean that it will have an equal expectation to every other non-dominated strategy against a gto strategy. we do know that if two players are using gto strategies against each other, this means that they will not be able to improve their expectation by changing strategy, but it does not follow that they are indifferent to their opponent choosing a strategy that performs worse, yet is not dominated.

I thought the idea of gto was that it was minimax ie if I play a gto mixed strategy then I achieve a payoff X regardless of what my opponent does in a two person zero sum game. This assumes he never chooses a dominated strategy as then I get more than x.

Does this cease to hold in a multiplayer zero sum game? Does maximin no longer equal minimax, like in non zero sum games?

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If you think about it, in a zero sum game, X has to be 0.

No. My expectation can be x and his -x. Zero sum doesn't mean fair! Eg look at me minimax article on wiki. They only show a two player game though

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the real point of confusion here is that the indifference principle is very limited in application. a gto strategy will choose a river betsize with {nuts, air} so as to make certain bluffcatchers indifferent, this is true. this does mean that all of the bluffcatchers are indifferent even in this specific scenario. card removal effects could make one bluffcatcher have a positive expectation from calling, while others are indifferent. the important point, especially when looking at other situations, is that while some hands an opponent will hold are indifferent (and we are therefore indifferent as well), many others will not be. especially as we expand the view to situations in which our opponent holds hands that beat some of our value bets, we should see that we are overall not indifferent to strategies he will choose with his entire range. the definition of dominated strategies is specific/limited enough that it does not disturb this principle. since a dominated strategy is only one that could be improved upon no matter what strategy our opponent chooses, folding a profitable bluffcatcher against a gto betsize/range is not dominated because calling would not be better against all other betsizes/ranges (specifically all-in/only nuts).

basically a person playing gto can have different expectations based on the other persons strategy, and as the other strategy improves towards gto the expectation will approach 0 (assuming no rake).

Is the complexity coming from the fact that I and my opponent have different amounts of incomplete information? So you are saying it is more complicated when we have overlapping ranges? Eg if I have nuts or air v bluff catcher its easy as I know if I am winning a showdown. But if I do not know if I actually win a showdown then things are more complex?

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You are welcome to prove this statement by giving us one example of a game for which one player has a known GTO strategy, and the other player has a strategy that is not dominated (in an iterative sense, meaning it is not dominated after throwing out all players' dominated strategies) but that has a different EV than some other non-dominated strategy.

Spoiler for everyone else reading the thread: don't hold your breath.

The fact that "the indifference principle is very limited in application" doesn't contradict anything I've said; it really just speaks to how ridiculously complicated it is to imagine a GTO strategy for poker.

Not that I'm a believer in "appeal to authority," but you should realize that CMV holds a terminal degree in mathematics. He should know what he's talking about here.

My understanding of game-theory is limited to Prisoner's Dilemma, which is a very simple HU game, but everything CMV is saying here matches what I learned in Grad School.

Poker isn't like the normal game theory examples. Let's say I bet on the river so my opponent has three options call raise fold (assume only one possible raise size) when I raised I didn't know my payoff for the opponent's raise and call options because I don't know his cards. Potentially he doesn't know the payoff of raising or calling for the same reasons. So one of his strategies might be dominated without him knowing it. Does this change the analysis, or does all the classic game theory stuff on zero sum game still hold ? put simply, the payoff of any pair of actions by the two players is unknown until the cards are turned over.

CMV is claiming, I think that there is nothing really special about all this?

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You just hit one of the major reasons why no one knows a GTO strategy for poker: since the individual strategies themselves are so numerous and because there are multiple decision points, it's often hard to tell when a strategy is even allowed to be part of a GTO strategy. (Of course, there are other reasons too.)