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Proving that GTO is Level Infinity

    • yadijavadi
      yadijavadi
      Basic
      Joined: 31.01.2018 Posts: 83
      Imagine the villain opens on the button, and we somehow know that he plays with a real tight range. Something like;

      88+
      ATs+
      KJs+
      AQo+

      SB folds and we are on the BB.
      If we are a Level Two player, who can only take into consideration the strength of the opponents range in comparison to our hand, we’d design our continuing range to be stronger than the villains. It would look something like this;

      TT+
      AJs+
      KQs
      AKo

      If we were a Level Three player, who could also consider how the opponent perceives our range, we would be able to mislead him regarding our strength and so would start to bluff. We know that when we continue it looks like we hold the above range and so; We can REMOVE the weaker portion of said range as we will get almost no value from these hands on later streets. We can ADD to our range the best the hands that the opponent will not expect. Our new range would look something like this;

      JJ+, 99, 88
      AQs+, A5s – ATs
      89s - TJs
      AK

      If we are a Level Four player, and realize that the opponent knows we’re deceiving him, we need to skim off the bottom portion of our range again, and replace them with the best of the cards the opponent will not expect;

      JJ+, 99
      AJs+, A8s – ATs
      TJs
      AK

      If you look to the ranges that we would use at the different skill levels, you can see that they gradually get closer and closer to Equilibrium. The first is purely value, the second is bluff heavy, and the third is starting to look like a Nash solution.

      If you don’t like my ranges, try it yourself. Choose any situation, consider the ranges that a player from each skill level would use in that situation, and see for yourself how they get closer and closer to Nash as the player advances through the Levels.

      Before I came along, everyone in the poker world taught that these Levels are circular, but everyone in the poker world is wrong. GTO is Level Infinity. (Quite a simple mistake for everyone to make, don’t you think? I wonder what makes them all misunderstand these Levels…)
  • 24 replies
    • la55i
      la55i
      Moderator
      Moderator
      Joined: 27.01.2013 Posts: 8,350
      I don't see how this proves anything.
      Beginner players usually have some set of ranges available that they haven't designed themselves. They all include both bluff and value raises. And when they get raised they all know that villain can bluff. Doesn't need a level 4 player to know that. And using both bluffs and value is because we want to balance our range. Balancing is probably the first fancy theory concept that beginners are interested in. They want to balance their own ranges even if they 1) shouldn't even do that or 2) don't know what it really means. It doesn't have anything to do with deceiving.

      Villain will often not perceive our range as super strong in the first place when we re-raise him.

      ----

      What I think is happening here, is that you try to describe levels of thought that we discussed many times before, but you also try to put some strategy inside those levels. And it doesn't work.
      What you have described is how we change our range based on what we know villain knows we know and so on. You can continue that I know you know I know thing infinitely. And then at some point, maybe you will reach "equilibrium" where both guys play only AA or something like that.
      But designing ranges can be done with math. GTO is a mathematical concept, as I explained before. We can take villain's range and find a mathematically perfect way to react to that. GTO has nothing to do with how we think or how villain thinks. So, you can't say that different thought processes ultimately lead to GTO.

      Back to the drawing board then :f_thumbsup:
    • yadijavadi
      yadijavadi
      Basic
      Joined: 31.01.2018 Posts: 83
      Originally posted by la55i
      I don't see how this proves anything.
      Beginner players usually have some set of ranges available that they haven't designed themselves. They all include both bluff and value raises. And when they get raised they all know that villain can bluff. Doesn't need a level 4 player to know that. And using both bluffs and value is because we want to balance our range. Balancing is probably the first fancy theory concept that beginners are interested in. They want to balance their own ranges even if they 1) shouldn't even do that or 2) don't know what it really means. It doesn't have anything to do with deceiving.
      I didn’t say that beginners don’t use the higher Levels. This is another thing they have wrong. The way we advance through these Levels is massively misunderstood.

      Originally posted by la55i
      Villain will often not perceive our range as super strong in the first place when we re-raise him.
      A Level Two villain would.

      Originally posted by la55i
      And then at some point, maybe you will reach "equilibrium" where both guys play only AA or something like that.

      But designing ranges can be done with math. GTO is a mathematical concept
      You reach the same equilibrium as usual lol. This equilibrium strategy would be GTO if it wernt for the information we have on the villain. In this example you would reach GTO if the opponent were using GTO*

      GTO can be found using math but it can also be found using the Levels of the mind.

      As you say, GTO does exist separately to any thought-process. Our thought-process doesn’t start at Level One. We only start making decisions at Level Two. Level One contains all the rules to the game along with our actual physical self, Level One relates to the physical world. The mind only kicks in at Level Two. Now, I explained how GTO is Level Infinity, but it can also be found without Level Two +. All you need to know is the rules to the game etc, the Level One factors, then, with a bit of genius math, you can calculate GTO. In actual fact, GTO it is the only valid strategy someone incapable of Level 2+ would use. GTO as a mathematical equation as you describe it, is how GTO exists at Level One. GTO is both Level Infinity and Level One.

      *In the highly unlikely event that our opponent is using GTO via the Level One route, we would reach equilibrium at Level Two. By “Level Infinity” I mean the unspecified highest Level. GTO stops us from taking an advantage through exploitation by removing our ability to mislead the opponent regarding our percieved range, GTO stops us from being able to use Level Three. If the opponent is using GTO via math at Level One, Level Two is the highest Level we would use and if we used it perfectly we would reach equilibrium... It would be like DragonballZ, with a possessed mathematician firing out a black beam of evil bad shit as a slick smooth English exploiter defends with glowing golden beam of brilliantness. The beams would collide in the air, hanging in perfect balance, until I Leveled up one last time, reached enlightenment, and destroyed all things GTO.
    • yadijavadi
      yadijavadi
      Basic
      Joined: 31.01.2018 Posts: 83
      Originally posted by la55i
      What I think is happening here, is that you try to describe levels of thought that we discussed many times before, but you also try to put some strategy inside those levels. And it doesn't work.
      What I did was arrange all Poker theory into the Levels of Thought. And it works perfectly. Beautifully.

      Lets take one small factor if you like; Bluffing. You dont seem to think it's a Level Three factor - Without any knowledge of how we are percieved by the opponent, how could we mislead him with a bluff?? We cannot. Bluffing only becomes possible when we can use Level Three.

      ... I see where this is going, and so let me be clear; When I say bluff, I mean a play that is some way deceptive. Funnily enough, the mathematical GTO players have recently changed the definition of a bluff ever-so slightly, nowadays they say that bluffing is not in any way deceptive lol! They say that it is just a bet with a weak hand to balance against the strength. (Bloody GTO trying to cover its tracks. It's the devil I'm tellin ya!! I've been stood outside church for the last 5 years holding up a sign trying to explain this to everyone but none of them get it, they all crazy :f_ugly: :f_tongue: :f_tongue:
    • Constantin11
      Constantin11
      Platinum
      Joined: 16.08.2012 Posts: 491
      While ya'll been foolish enough to discredit this man's genius work I've been voraciously studying it and now I'm proud to say that I am starting to play at levels that you mortals can't even comprehend. Here is a hand that I post as a proof, where I took the inducing line OTT to call the river bluff on a blank, and Ace is obviously the perfect blank to make the call for that sweet $120.

      PokerStars - 20/40 NL (3 max) - Holdem - 2 players
      Hand converted by PokerTracker 4

      BB: 15.2 BB
      Hero (SB): 22.3 BB

      Hero posts SB 0.5 BB, BB posts BB 1 BB

      Pre Flop: (pot: 1.5 BB) Hero has 7:heart: Q:heart:

      Hero calls 0.5 BB, BB raises to 2.5 BB, Hero calls 1.5 BB

      Flop: (5 BB, 2 players) K:diamond: T:spade: T:diamond:
      BB bets 2 BB, Hero calls 2 BB

      Turn: (9 BB, 2 players) 9:diamond:
      BB checks, Hero checks

      River: (9 BB, 2 players) A:spade:
      BB bets 10.7 BB and is all-in, Hero calls 10.7 BB

      BB shows 4:club: 2:diamond: (One Pair, Tens)
      (Pre 33%, Flop 27%, Turn 35%)
      Hero shows 7:heart: Q:heart: (One Pair, Tens)
      (Pre 67%, Flop 73%, Turn 65%)
      Hero wins 30.4 BB


      At this point this is just standard play thanks to this great man's work. But you all have cognitive dissonance, as he would say, so I'm not even sure why I bother trying to explain things and show proof.

    • la55i
      la55i
      Moderator
      Moderator
      Joined: 27.01.2013 Posts: 8,350
      You playing 3max with 2 players? What level is that? It is genius...

      For me GTO is still game theory optimal which is a strategy that let's us calculate moves that villain can not profitably counter and has nothing to do with out thought process but that is probably because I have read too many books from those track covering bastards and it has fried my brain :f_rolleyes:

      Btw,
      (Bloody GTO trying to cover its tracks. It's the devil I'm tellin ya!! I've been stood outside church for the last 5 years holding up a sign trying to explain this to everyone but none of them get it, they all crazy :f_ugly: :f_tongue: :f_tongue:
      I start to like you more. Funny jokes :) Except if that wasn't a joke :pcuser:
    • Constantin11
      Constantin11
      Platinum
      Joined: 16.08.2012 Posts: 491
      Originally posted by la55i
      You playing 3max with 2 players? What level is that? It is genius...
      Oh man, the last level is when you play 3 max but by yourself and the highest mutliplier comes (spins) and you win all three places. I hope to learn this in volume 2, if It'll ever come out.

      BTW,

      It actually now all makes sense to me. If the Bloody GTO is level infinity, and the Devil is all the evil that there is, and because the universe is infinite and in constant expasion, which means that there is infinite evil in the Universe. we can connect the dots and conclude that GTO is actually the Devil.

      Now I understand the assertion that the GTO lies at the core of every evil in this world that was so eloquently put into words in a previous thread by yadijavadi.

      Wow, no wonder the guy tried to share this knowledge with the ignorant priests, parishioners and everyone else while they, blinded by their cognitive dissonance, couldn't see past the lies that their mind has been drowning in for ages.

      It's sad really. Imho professional help is needed.
      I am an as*hole with my jokes here regarding these poor fellas but at the same I realize the gravity of the situation and what it implies...
    • VorpalF2F
      VorpalF2F
      Super Moderator
      Super Moderator
      Joined: 02.09.2010 Posts: 11,263
      Originally posted by yadijavadi
      Before I came along, everyone in the poker world taught that these Levels are circular, but everyone in the poker world is wrong. GTO is Level Infinity. (Quite a simple mistake for everyone to make, don’t you think? I wonder what makes them all misunderstand these Levels…)
      Hi, yadijavadi,
      I've been studying poker for 9 years. Nowhere -- ever -- have I read anything suggesting that the levels are circular.

      Note that infinity does not exist -- it is a mathematical abstraction.

      Finally, in this thread you were challenged to post proof of your conjectures.

      The challenge (in the last post of the linked thread) read as follows:
      If you really do have something new to offer, I challenge you to offer it. clearly, and succinctly in a new thread.
      I suggest that the title of the thread should be similar to:
      Describing the levels of thought from a poker perspective
      In that thread, start by outlining clearly what you are going to demonstrate.
      Then present evidence for each point you make, taking care to keep the paragraphs respectful, on-topic and brief.
      This thread does not meet those criteria -- it is merely yet another incoherent re-statement of your original conjectures, with no proof, no methodology, and certainly not brief.

      Your "original" conjecture is merely a re-hash of old concepts.

      Please provide what was requested:
      A clear and concise statement outlining your premise, followed by clear proof that this is new and different.

      I look forward to your next post.

      Thanks
      VS

      If your next post does not provide this, then this thread too will be closed, and all future posts of yours that are mere ramblings will also be closed.

      You will always be free to discuss poker and poker related topics.
    • la55i
      la55i
      Moderator
      Moderator
      Joined: 27.01.2013 Posts: 8,350
      You have explained a situation where we try to exploit villain, he adapts and starts exploiting us and we have to adapt again. That could go on for along time. Then we decide to start using a strategy where villain can not profitably counter our moves (GTO). But that we can't do with our minds. Sometimes it takes my computer minutes to solve a tree. So I must strongly disagree with the statement that "GTO can be found using math but it can also be found using the Levels of the mind."

      We all already know these things. "What I did was arrange all Poker theory into the Levels of Thought. And it works perfectly." That is like putting a solid block of iron to a fish soup and saying it is tasty. You have just mixed up concepts that everyone already knows and described them in an incredibly complex way. It adds no value to us.

      I think this is so hard for you to prove to us because this basically is a product of your imagination. If there are this kind of levels, we can't see them or feel them or examine them in any other way. It is just in our heads and how we want to think about things. Poker has been played for decades and what you describe here hasn't been needed nor will be needed in the future.
      What you could do is ask us "guys do you think we could think like this, would this make sense and be logical". What you can not do is say you are going to prove something because that can not be done.

      Now I was going to talk about something that has been already said in the previous threads but I will not go there this time. This thread will not be another 5 page long debate. If your next post is nothing significant, I will leave it at this.
    • UPAY4DINNER
      UPAY4DINNER
      Bronze
      Joined: 27.09.2009 Posts: 22,204
      Jesus titty-fucking Christ give it up already!
    • yadijavadi
      yadijavadi
      Basic
      Joined: 31.01.2018 Posts: 83
      Originally posted by VorpalF2F
      Originally posted by yadijavadi
      Before I came along, everyone in the poker world taught that these Levels are circular, but everyone in the poker world is wrong. GTO is Level Infinity. (Quite a simple mistake for everyone to make, don’t you think? I wonder what makes them all misunderstand these Levels…)
      Hi, yadijavadi,
      I've been studying poker for 9 years. Nowhere -- ever -- have I read anything suggesting that the levels are circular.

      Note that infinity does not exist -- it is a mathematical abstraction.

      Finally, in this thread you were challenged to post proof of your conjectures.

      The challenge (in the last post of the linked thread) read as follows:
      If you really do have something new to offer, I challenge you to offer it. clearly, and succinctly in a new thread.
      I suggest that the title of the thread should be similar to:
      Describing the levels of thought from a poker perspective
      In that thread, start by outlining clearly what you are going to demonstrate.
      Then present evidence for each point you make, taking care to keep the paragraphs respectful, on-topic and brief.
      This thread does not meet those criteria -- it is merely yet another incoherent re-statement of your original conjectures, with no proof, no methodology, and certainly not brief.

      Your "original" conjecture is merely a re-hash of old concepts.

      Please provide what was requested:
      A clear and concise statement outlining your premise, followed by clear proof that this is new and different.

      I look forward to your next post.

      Thanks
      https://www.pokerstrategy.com/image/ranks/mini/moderator.pngVS

      If your next post does not provide this, then this thread too will be closed, and all future posts of yours that are mere ramblings will also be closed.

      You will always be free to discuss poker and poker related topics.
      Premise = GTO is Level Infinity

      Evidence = I showed that as we advance through the Levels, the ranges we’d use become more balanced. I gave a very clear example.

      Something new = I bet you haven’t read anywhere that Level Infinity is GTO before.

      Although you are being very rude, and can’t even see the clear and precise argument I am putting forward, I do still harbor some hope for you. I asked that a reader would perform the same task that provided me with my evidence, and I’ll specially ask you to do the same thing now. Are you capable of it? Can you choose a situation and write the range a player operating at each Level would use in that situation?

      I do harbor some hope for you, but please do be aware that I am certain you are suffering badly from this psychological problem (Like Cognitive Dissonance, I’ve mentioned it before). You seem like a nice bloke usually, and you seem to know your poker logic, so benefitting all your readers by completing the simple task I put forward shouldn’t be hard for you… right?

      I’d much prefer to discuss this with that coach from the other thread. He accepted that everything I was saying was correct, and seemed more annoyed with all these crazy prolonging hoops I am having to jump through. Are you here LemOn36 ?? Do you see my evidence and realise that GTO is Level Infinity?
    • yadijavadi
      yadijavadi
      Basic
      Joined: 31.01.2018 Posts: 83
      Originally posted by UPAY4DINNER
      Jesus titty-fucking Christ give it up already!
      Please, just call me Yadi.

      It's a Persian word that means "Hands of God". Funnily enough, someone with my name did actually try to pass himself off as the messiah once as the name fulfills both Muslim and Buddhist prophecies. But, this dude didnt even try to map out the mind like Buddha (which I did accidentally), nor did he find a cure for a madness that plagues society. I win.
    • MyFloXyBabY
      MyFloXyBabY
      Gold
      Joined: 15.02.2010 Posts: 2,995
      :pcuser:

      The ravages of drugs... it's so sad.
    • la55i
      la55i
      Moderator
      Moderator
      Joined: 27.01.2013 Posts: 8,350
      Evidence I showed that as we advance through the Levels, the ranges we’d use become more balanced. I gave a very clear example.

      You showed what I explained before. What we all know. That we adjust and villain adjusts and so on and then we switch to GTO which is a math thing and has nothing to do with thinking. If you want to use your imagination and think about a new name for GTO then go ahead but I'm not interested in that.

      You trying to prove something by demanding us to prove you are wrong by using your own insane methods is crazy.

      I said in my first post that you should go back to the drawing board. And now I think it is time to close this thread too. I will leave it open for a while, in case dear super moderator VorpAl has something to add.
    • yadijavadi
      yadijavadi
      Basic
      Joined: 31.01.2018 Posts: 83
      Sorry mate, but why'd you say we make some sudden switch to GTO???

      This is very simple. As the ranges advance, we get closer to equilibrium. If we follow only the Levels, with no attempt to calculate GTO, the last range we would use, would be an equilibrium strategy.

      There is no random switch over to a mathematical equation which has nothing to do with the Levels. As the levels advance, they get closer to Equilibrium!!! lol.

      Lemon man please hurry up and save me!! Mods, please let this dude post before you end the thread. I'm pretty sure he will agree with me, (we might need to discuss it very quickly), and I suspect he will be moderately interested in realising that at the highest Level of thought we reach equilibrium
    • TyCobb
      TyCobb
      Bronze
      Joined: 30.03.2006 Posts: 4,085
      We all know how this thread ends :f_rolleyes:
    • la55i
      la55i
      Moderator
      Moderator
      Joined: 27.01.2013 Posts: 8,350
      We are on the river. We decide to bet half pot.
      Villain folds every time, so it makes sense for us to bet our whole range, right? Then villain notices this and starts to call every time, so we decide to bet only for value. This goes on and on until you figure out that you can bet 50% as bluff and 50% as value. Villain won't know which one you have.

      Are we now in equilibrium because we have adjusted so many times that our range is 50/50 and villain really can't never know which we have, value or bluff?
    • yadijavadi
      yadijavadi
      Basic
      Joined: 31.01.2018 Posts: 83
      No were not, because you only bet half pot. The villains getting 3:1 on the call but our value to bluff ratio is 1:1. These ratios need to match for it to be equilibrium.

      I left things like this out of my example to make it clearer, easier to read, and to make it match the common understanding of these Levels (commonly people dont include chips when they speak of the Levels. Our chips do actually come in at Level One, along with our cards and our seat).
    • yadijavadi
      yadijavadi
      Basic
      Joined: 31.01.2018 Posts: 83
      It doesnt really make sense to bet our whole range either, as it will be easy for the opponent to notice and adjust.

      I dont buy into maximum exploitation as an effective strategy because it doesnt do what it says on the tin. I mean, to maximise the profit from our exploitation we need to keep the villain from knowing that he is being exploited for as long as possible. If we are using a maximum exploitative strategy we are standing up and telling the villain he is being exploited, which will take us to equilibrium very quickly.
    • la55i
      la55i
      Moderator
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      Joined: 27.01.2013 Posts: 8,350
      I thought this simple river bet thing was easier than the preflop range construction thing.

      But when you think what villain thinks you think and so on, you don't know those rations and frequencies?

      And actually those ratios don't need to match? If we bet 50% of the flop, our bluff frequency should be 33.3% of our betting range and villain should defend 66.6% of his range and he gets 25% pot odds.

      But see, you started using math. If we just think "what I have, what villain has, what villain thinks I have" and so on, math is not involved. Now in this case you adjusted and re-adjusted and then you decided that "fuck this, not gonna work, I must find a play that can't be exploited" and we started talking about ratios and pot odds and frequencies and so on. This is what we could call GTO. This is something we all know.

      As I said earlier GTO is a math thing, it has nothing to do with thinking, we all already know about this stuff, starting to apply math and finding the "perfect" strategy will not come automatically from any mind games, back to the drawing board, I'm out, thanks.
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