Allow me to reformulate the question. Is gto poker all about arriving with an óptimal bluff to value ratio and call frequency to every possible end branch of the game tree where only call or fold are possible (and is everything before that just an intermediate step in order to achieve that end)?

no

Not quite, but it's a good way to think about it tbh. Prior to solvers, primitive human GTO models essentially worked like this. The entire book Applications of NL Hold'em uses this method, working backwards from the river to solve turn and flop spots.

The truth is that GTO solvers are just algorithms that find the highest possible EV across all runouts, assuming perfect play. But not all runouts are equal. Sometimes one player just gets run over. Sometimes you get a really lucky card and the edge shifts drastically. One player may have to overfold quite a bit more than MDF, for example.

The point of GTO is to play the strongest possible strategy against a perfect opponent. Well balanced river ranges just so happen to usually accomplish this task.

You need to exchange the word “Perfect” for “GTO” to make proper sense of Tomass’ post. Many people are obsessed with GTO and think that GTO is perfect, when really, it’s never the most profitable strategy to use.

I didn't say it was the most profitable. I said it's the most profitable against a perfect opponent. Imagine a GOD that would attack every one of your weaknesses and exploit every mistake. The best possible strategy against such a player would be GTO.

From the founder of game theory himself, Ask this simple question:

"Knowing the strategies of the other players, and treating the strategies of the other players as set in stone, can I benefit by changing my strategy? If any player could answer "yes", then that set of strategies is not a Nash equilibrium."

Listen Y.J. I know the term "GTO" sets you off. And I know you're gonna start rattling on about controlling your opponents actions and influencing the metagame and levels and blah, blah, blah, but that's not the point of this thread. Please stop spreading misinformation.

I think solvers just work with a bunch of non-lineair optimization algorithms to maximize reaction functions. There maybe some markov processes involved as well.

Solvers just try to maximally exploit and get close to nash that way. So let's say OOP starts with strategy O1 then the solver will try to maximally exploit this by responding with I1 then OOP responds with O2 --> I2 --> I3 --> ... --> On --> In. An example would be: let's say O1 is that OOP x/folds everything then IP can respond to that with I1 where he just bets everything for 1BB. Then OOP can respond to that by x/r a lot in his new strategie O2 and so on.

Eventually these strategies will converge to the nash-equilibrium. At that point the reaction functions are maximized and neither player can increase their EV by switching to another strategy.

OTF and OTT solvers have to take later streets into account aswell, but that's just part of the reaction function. I'm not sure how these reaction functions actually look like, but I'm pretty you can find some papers through google scholar or something if you really want to get into it.

In layman's terms:

Imagine a bot. You input your strategy, and it will output a perfect nemesis strategy (the strategy that exploits you the most). Now get a second bot and let them play each other, back and forth, continually counter-exploiting each other. Eventually, they'll reach Nash Equilibrium.

It's funny that the culmination of two perfectly exploitative players is GTO. But don't tell that to Y.J. or he might explode.

I’m just pointing out your mistakes Tom.

This statement is wrong. If the opponent knows all your mistakes the best thing you can do is learn your mistakes yourself. This flip reverses the money you would have lost, turning a measure of it into profit for you to win. You’d also learn about yourself and become a better player. Next time it’ll be you who knows the opponents mistakes and him who must learn.

... Turns out, you didn’t have a clue what I’d say. I knew what you’d say though; When obsessed with a strategy, players always reflect their own flaws into the person trying to teach them. If you were a troll you’d call me a troll. If you rattle on about GTO all day long you’ll say that I do.

I’m getting tired of your abuse. You are all getting better though. I mean, yesterday Tom did post a 1000 word essay about me which was so insulting it’d make the devil blush. But, it’s been a while since you guys mentioned my kids! Good for you!

I’m pretty sure the op realised that GTO breaks even against GTO, but always nice to have your input.

Hmmm... I’m getting real sick of you GTO players. I’m thinking about leaving never to return. This can just be a forum where GTO = Perfect. You should add that to the forum rules. “Posters must believe that GTO is perfect or they will get emotionally abused by our community and mods”.

My statement is correct, you're just ignorant.

Yes, you can counter your opponent, turning loss into profit. And they can counter your counter. And you can counter their counter of your counter. If you continue this process forever, you reach Nash Equilibrium (GTO). I can back this up wiith sources from Mathematics of Poker, Modern Theory of Poker, and a thousand other strategy books if you like.

Quit spewing misinformation, please.

Oh stop painting yourself as the victim. You insulted mine and everyone elses intelligence. You act like some arrogant god, talking down to everyone who doesn't agree with you. You're so desperate to prove GTO is bad but you don't even understand the core elements of game theory. Do us all a favor and leave.

Oh and FWIW Y.J., I actually prefer exploitative poker. But I've studied enough game theory to understand that explo and GTO are linked.

Solvers don't actually exploit to the maximum, but change their strategy slowly in that direction by increasing the frequency of moves that have a higher EV.

For example in nut and air vs bluff catch type of spot if polarized range bluffs too much then bluff catching range calls all the time. In next iteration polarized range would stop all the bluffs to max exploit, then bluff catching range folds all the time and so on. So in that case you cant reach GTO solution by max exploitative stra.

Page 66, Modern Theory of Poker:

"If this process of both players counter-adjusting continues for a large
enough number of iterations, eventually the players will reach an equilibrium
point where neither can improve upon the strategy they are already
playing. At this point it can be said that both players are maximally exploiting each other. This situation is called Nash Equilibrium.

It may also occur that the players’ strategies alternate back and forth and never converge to an equilibrium. In this case, the equilibrium can still be found by making slight changes in the players’ response. Instead of switching all the way to the best response on each iteration, each player can adjust their strategy one step at the time in that direction."

So what you're describing is the second scenario where counter-exploits get stuck in a loop.

Yes. Btw what is your opinion on that book? I think about reading it at some point.

10/10 would recommend

For the record, I’m fully aware that the highest exploitative level of thought gives you the GTO strategy. I also understand how the range becomes more balanced as the levels progress, I understand how the ranges converge to GTO, which none of you understand. Once you understand that, you can roughly see the GTO strategy for any situation by using exploitative theory alone. You also see many flaws in what is commonly understood to be the GTO strategy (the strategy is far more mixed than is generally accepted).

I’d guess that none of you realise that the first level of thought also gives you the GTO strategy. It was me who solved that piece of theory. I cracked loads of stuff. If it wasn’t for all you GTO lovers my findings would be known around the strategic world.

Damn what happened?

Is it safe to say that

The solution is one aspect and how/when you apply it is the actual GTO aspect of it. The fact that one line has higher EV etc is totally dependent on various factors and of course the balancing aspect is where we start to involve GTO strategies. Is taking the strongest EV line the best way to play GTO?

Is it safe to say that

The solution is one aspect and how/when you apply it is the actual GTO aspect of it. The fact that one line has higher EV etc is totally dependent on various factors and of course the balancing aspect is where we start to involve GTO strategies. Is taking the strongest EV line the best way to play GTO?

I don't really understand what you're trying to say.

"The solution is one aspect and how/when you apply it is the actual GTO aspect of it"

The solution contains all the information about how and when to apply it. I don't see how you can separate those concepts.

--

Let me put it this way. You're playing some spot heads up. You are allowed to pick a fixed (unchanging) set of strategies for some spot. Your opponent is allowed to review your strategy and adjust their strategy as they see fit. GTO is the strongest possible set of fixed strategies against all possible counter-strategies.

GTO is not necessarily about "achieving balance", it's about maximizing expectation against a perfect opponent. It just so happens that well-balanced ranges generally accomplish this task.


Let's put the delusions of grandeur aside for a moment. Can you elaborate how the "first level", as you call it, gives the GTO strategy?

You must all already know... You’re just testing me, right?

I did think that I knew more about these levels than anyone. I mean, I am the guy who wrote the book on the them. But it turns out I just have delusions of grandeur. If a bunch of microstakes regs know that I’m wrong I must be wrong.

Why don’t you tell us, how could a LEVEL ONE villain use GTO? Doesn’t that mess with the common understanding of these Levels? I thought Level One was for beginners?

Please do teach us Tomos!?

Anyone?

I'll ask this question again since all I got as a response last time was word diarrhea.

Work it out yourself! Or apologise for being a dick. As things stand, I ain’t teaching you nothing lol.

You made a claim:

I asked you to back up that claim. Either with logic or references.

Since you cannot do that, I'm gonna have to assume you were just talking out your ass.

You keep thinking that Tom, I really don’t care