Right and wrong, but it's better illustrated with a rock paper scissors.

Imagine a heads up match, GTO for rock paper scissors will be playing TRULY RANDOM 1/3 each. If you and your opponent play GTO, it WILL be 0 EV and you will both lose in that game if you guys are raked.

Now, if in the same match you play GTO and your opponent has a preference over one option (rock, paper or scissors) he will automatically lose and your winning will be based on how big his deviation are.

So basically, if all the opponents are playing GTO and are getting raked, all will lose the rake, but if one deviates, the others get some profit.

If someone plays GTO in any normal poker game, he will profit a lot since everyone plays an exploitative strategy, but that doesn't mean that GTO will be the most EV strategy for that specific game.

i'm curious how exactly this opponent will lose when you're randomizing 1/3 rock, 1/3 paper and 1/3 scissors

Rock paper scissors is kind of a bad example for people to keep using IMO because the GTO strategy is 0 EV against every other strategy, which is clearly not the case in poker.

He wont obviously

As many answers as it takes for a satisfactory one.
Already answered your second question.

i have made a lot of money playing online cash games and i don't know anything about gto and i don't need or want to learn anything about it. i just know what to do and im pretty sure i have pokerstove in my head.

Wow!!

If GTO for this game is to randomise, selecting rock 100% of the time will have the same expected value as countering GTO with GTO.

Likewise any other way to play. The point you're missing is that this GTO model performs exactly the same against 100% of strategies used against it. Break even. If one person playing a 2man version of this game plays GTO (random), then the ev will always be 0. The way the second person plays is irrelevant to the equation. Obv this doesn't translate to poker.

eg. You play random, I play rock

1/3 of the time my rock beats your scissors
1/3 of the time my rock loses to your paper
1/3 of the time we tie with rock vs rock

= 0

Are you sure about this? If this would be a GTO strategy, wouldn't something like "choose R, S, P, or LOSE with probability of 1/4" or "choose LOSE 100 % of the time" be the GTO strategy for your opponent? wouldn't that make your strategy non-optimal then?

Yes, I'm sure.

Again, the definition of optimal is "the opponent cannot change his strategy to make more EV." The strategy you suggest for my opponent is not optimal, because if he does that, I could accept his $100 when he chooses LOSE, and I'd make more than the 0EV value of this game.

Note that my strategy (1/3 of each, never accept) IS optimal, because my opponent can't do anything to increase his EV. (As mentioned several times, my strategy is also stupid. GTO doesn't mean best, or even non-dominated, it means exactly what the definition says - it will achieve at least the value of the game as it's EV, no matter what the opponent does.)

If I see one more rps analogy I'm gonna puke. Here's a better example that's less confusing to the game theory noobs like me and that some of you probably know about:

The Keynesian "beauty contest"

Sources: "The Intelligent Poker Player" by Philip Newall / Wikipedia

A group of people take part in a contest in which they are told ito pick a nr. between 0 and 100. The winner is the person whose guess is closest to 2/3 of the average guess.

Lvl 0: Picks a random number which on average is

Lvl 1: He knows this and picks the number that is 2/3 of

Lvl 2: He knows this and picks the nr. that is 2/3 of

And this goes on untill the gto answer is reached.

Does this mean that if you choose the game theory optimal answer everytime, you're going to win ?

Even when this type of game was played between people with math and / or basic game theory background the results have shown none of them went past level 2 thinking.

So continue to play exploitative poker and you'll be just fine.

no one in that thread said that an optimal strategy for poker could be understood and/or applied by a human mind
most of that thread is about defining what an optimal strategy is, and how an optimal strategy could win over any other strategy
the rest of the thread discussing about how an already existing bot, playing a near gto strategy, could beat any human, playing a HU limit holdem poker game

If you're playing HU, you always win or draw with 0.

The beauty contest is quite interesting when you are looking at bigger groups, but it is a little silly, if you look at only two players. The lower number will always win, therefore picking the lowest number is best/optimal.

If you're implyng that my post is off topic read the title of the thread. The whole durrrr vs bot is a huge threadjacking, an interesting one but still a jacking.

Instead of discussing whether some top players like Ivey, Antonius really use / study math and game theory and choose not to broadcast it or they play instinctively well everybody's all hyped up about durrrr vs a bot like it's Terminator 5.

All I did is provide a better example then rps to game theory noobs like me reading this thread.

Rock-Paper-Scissors is indeed a pretty bad example for introducing people to game theory as applied to poker, but this game isn't very good either.

One reason that "optimal" or "game theoretically optimal" is a reasonable term to use to describe equilibrium strategies in zero-sum two-player games (ZSTPG) is that they are in fact optimal against a rational opponent. Further, a strategy that is part of an optimal strategy pair in a ZSTPG provides fairly strong guarantees about game value. However, a strategy that is one component of an n-way strategy set is only guaranteed to be "optimal" against some joint set of strategies for the n-1 other players, and generally has very poor guarantees about game value in general. So taking a strategy that is a component of an equilibrium strategy set for a multiplayer games and calling it in isolation "optimal" or "GTO" is at best misleading and often flat wrong.

This is easily seen if you consider the original Keynesian beauty pageant game. N players are given six pictures of women, and asked to identify the most beautiful. Those who choose the most popular picture share a prize. This game has many equilibria; for example, "everyone chooses photo #k" for k from 1 to 6. Also "everyone chooses randomly" is an equilibrium. So it is hopefully clear that here "GTO" is a pretty meaningless term, as any pure strategy as well as a randomizing strategy are all part of equilibrium strategy sets for any one player.

Now the 2/3 game is a useful modification of the original game for purposes of behavioral economics, because it demonstrates that participants, even educated ones, are hardly rational. But the link to poker here is pretty tenuous. Is your claim that poker is a game where a) there is one equilibrium strategy, b) if you play that strategy and there is at least one bad player in the game, you lose? Those are the parameters of the 2/3 guessing game, but these are pretty strong and unsupportable statements about poker.

This is just a more complicated way of saying "there are people out there playing rock every time, so you should just play RPS exploitively."

One of the better ones is the game where both players secrectly write down the number one or the number two. They compare numbers and if they are equal, Player A wins ten bucks. If they are unequal Player B wins either five or fifteen bucks, depending on whther he wrote one or two.

i just thought a little bit about game theory and one situation came to my mind in which i dont see why gto is unexploitable, and this really bothers me so i thought i just post it here:
Lets assume player A and B are both playing gto strategies. Lets assume gto strategy for player A is betting the river full pot. Because player B is playing gto as well, he has to call 50% of his hands, which means player A has to valuebet any hand which is better than 75% of player Bs total range (because player B is calling top 50% of his range and player A has to be good >50% of the time against the calling range in order to make it a value bet).
Now lets say player A has some hands in his range which are better than 70% of player Bs hands. He cant value bet these for full pot because it would be an incorrect value bet, but he can bet it for ½ pot ( balancing it with the right frequency of bluffs obviously). Player B has to call with 66,6% of his range now, so the second range with which player A was betting ½ pot is a +ev play.
Given the fact player B is playing gto, player As strategy with just one betsizing is not the gto strategy, the strategy with the two betsizings may is, but if you continue my example ist pretty obvious that the more betsizings you have, the more ev the strategy gets, which leads me to believe that a gto strategy has a lot of different betsizings, depending on how much value your hand has, so the betsizing of a gto strategy should almost exactly tell the opponent which hands the gto player is betting for value in a certain spot, which is obviously very exploitable.
In reverse, if you are playing this gto strategy with the many different betsizings, your opponent, if he is playing gto, cant take advantage of that, because hes not reading hands or interpret something in your betsizing.
That means you can make money in these situations and its reverse if you know your opponent is playing gto, which obviously shouldnt be the case in theory.
i thought about this quite a bit but didnt see my mistake so i hope you guys can help me out, it really blows my mind

I'm not going to nitpick through your original post for minor inaccuracies, because you seem to have the right idea in the end. I'd like to focus your attention on the above claim. You say that this is "obvious", but I don't agree. In fact, I think it is totally non-obvious and quite possibly false.

(Socratic method ON)
Would you care to argue for this claim?

Jerrod, how big of a monkey wrench does playing vs more than 1 opponent(6 max, multiway spots) throw into the mix when looking for GTO plays in certain situations.

Well, in theory, it renders the concepts of "game theory optimal" meaningless, and creates a complex network of opportunities to form implicit alliances.

In practice, the same thought processes that are strong in headsup games (ie the ones that move you toward optimality) are likewise strong in multiway games; aggressiveness so that you are "getting your value," so to speak, and balance so that your opponent(s) can't exploit you.

Wow, this 's gotta be the best NVG thread ever! So much gems (and craps also ). I think this should get 5 stars or stickie sumthing.

well if you play against a gto calling strategy and have the nuts, betting very big shows the most profit. if you have a hand which is better than lets say 75% of your opponents total range, a much smaller sizing has the highest ev(probably something between betting 1/3 and 1/2 pot). you can do this for all different kinds of hands and i think the most +ev value betting sizing is different every time, depending on how strong your hand actually is.
given that, a gto strategy should contain a lot of different betsizings.
Now, if you know your opponent is playing gto and you know everything about how this strategy looks like, you can make fairly well assumptions on what your opponent has. e.g. if your opponent is betting 43,21% of the pot, you know for which hand in your opponents range it is optimal to bet this exact amount. now you can valueraise every hand which is better than this hand (and bluffing with the right frequency as well). so you can extract value with hands you usually wouldnt even consider raising for value with, just because your opponents range is capped to this assumed hand.
in reverse, if you play this strategy and your opponent still plays gto, he cant go for value this thin, because he doesnt make any assumptions on what your range looks like based on betsizing.

curious what makes you think you have any idea how durrrr thinks about poker and for that how 95% of winning HSNL players think about poker?

Even if it were true that each value hand had a distinct bet size (seems doubtful but I guess no one knows at this point; to my mind assigning even two (fairly widely spaced) value hands to each bet size would do better), it doesn't really matter. If it's GTO then we can be sure that no other strategy has higher value while also remaining unexploitable. Maybe it's only marginally +EV. Doesn't matter; everything else is even less +EV. By definition. And that's all that matters.

Right, so the conclusion would be that even if there are alot of different bet sizings, within each size there are a mix of possible hands. (The answer to "Given my opponent just bet 48.1% of pot what hand does he have?" will be "25% chance of X or better, 25% chance bluff etc" Rather than "Exactly top 2 pair".....the latter as you pointed out is very exploitable)

Why can't GTO take into account bet sizing?

Lol u mad