[Closed] Proof that Game Theory Optimal Can Be Found With Thoughts Alone

The level of leveling in this thread is too damn high !
Like, master troll level. With a chess option.

Originally posted by MyFloXyBabY
The level of leveling in this thread is too damn high !
Like, master troll level. With a chess option.

Such a wasted meme opportunity. Here you go:

Originally posted by MyFloXyBabY
The level of leveling in this thread is too damn high !
Like, master troll level. With a chess option.

It´s infinite!

Originally posted by VorpalF2F
Two profit maximizing players can use any strategy they want. As mentioned elsewhere in this thread -- and elsewhere -- GTO seeks to be unexploitable, not to maximize profits.

Two players playing against each other over a long period of time may reach an equilibrium (and thus both lose to rake), but whether that equilibrium is approximately the same as an equilibrium base on Game Theory, no-one will ever know without doing the math.

All the best,
VS

Originally posted by la55i
One can play GTO regardless of villain's strategy. If one is exploiting, he is not playing GTO. Two players playing exploitative poker can not play GTO.

If villain is playing perfect exploitative poker, and we are playing perfect exploitative poker, we will not be using GTO, we will be using exploitative strategies. GTO is when you play in a way that you can't be exploited. That also doesn't exploit the villain.

I'm not going to take part of discussion in this thread, but I think here you guys have actually misconception.

GTO is same time unexploitable and maximally exploitable strategy assuming another player plays GTO as well. If one decides to devide from GTO, another can find more profitable strategy than GTO. But if both players are playing GTO it's indeed maximally exploiting strategy. GTO is as well exploiting opponent who is not using GTO, in that case it's just not anymore maximally exploiting.

2 players exploiting each other and ending up GTO idea is actually suggested in Will Tipton's book Optimal and Exploitable Strategies https://www.amazon.com/Expert-Heads-Limit-Holdem-Exploitative/dp/1904468942 It hardly never happens tho. Normally 2 players end up switching strategies back to back. Let's take easy example from Push & fold game in HU 5bb (To simplify let's just assume rules of the game only allows us to jam or fold.) Nash range (no ante) 5bb for SB would be to shove 71,5% and BB to call 62,1%. If BB decides to fold 95s and 97o which are breakeven calls, SB can jam now 73,8% hands, this will result BB calling 64,4%. That will result SB shoving 67,4% --> BB calling 57,8%, SB shove 78,3% --> BB call 68,6% --> SB 65,6% --> BB 57,5% --> SB 80,1% and so on. (This is based on HRC calculations).

So generally by maximally exploiting our opponents we don't end up in GTO. Same you could notice from PIO solver river gametree. In situation where is actually not enough FE for bluffing, PIO is mixing some small % of bluffs to avoid exploiting even tho it's -EV in the vacuum (this is +EV for the sake of the full strategy tho). If you decide on the other hand not to bluff, your opponent can decide to fold some of the hands which he would be otherwise calling. Now you can start bluffing more, and you opponents doesn't fold anymore, which results you going back to not bluffing... So generally we don't end up in GTO or even "GTO like" strategy, but by exploiting we just end up going circles back and forth between different strategies.

Can you point out where is that misconception you mentioned?

I have, and others have too, concluded that if villain is playing GTO, then our max EV line is to play GTO.
We have also concluded that 2 players switching back and forth and trying to exploit each other might lead to something close to GTO but probably still quite far from true GTO. You also said that it almost never happens.
You used a very simple example and we all know if it goes any more complex than that (like it is in reality) then it would be impossible.

When I read your conclusions and especially your last sentence, I think we pretty much agree on these things. However, this thread is all about proving that "Game Theory Optimal Can Be Found With Thoughts Alone".

Originally posted by la55i
[...] With Thoughts Alone".

Originally posted by la55i
Can you point out where is that misconception you mentioned?

I have, and others have too, concluded that if villain is playing GTO, then our max EV line is to play GTO.
We have also concluded that 2 players switching back and forth and trying to exploit each other might lead to something close to GTO but probably still quite far from true GTO. You also said that it almost never happens.
You used a very simple example and we all know if it goes any more complex than that (like it is in reality) then it would be impossible.

When I read your conclusions and especially your last sentence, I think we pretty much agree on these things. However, this thread is all about proving that "Game Theory Optimal Can Be Found With Thoughts Alone".

I guess we understand each other then. For example what you say "If one is exploiting, he is not playing GTO." this is actually not true, because playing GTO as well exploits weaker opponents just not to the maximum level. As well Verpal says: "GTO seeks to be unexploitable, not to maximize profits. " As well not true because it maximizes profits when either 1) you play against perfect opponent who's capable of adjusting strategies and is always aware of your strategy... Or 2) When we are unware of our opponent's specific tendencies or tendencies of the the population.

As discussed the idea of two players exploiting each other and ending up in GTO is somewhat valid, but in real life it never happens as you mention. I actually think if you cut all BS, there's lot of good stuff in this thread which you can as well use in practical way. But since this thread is probably very hardly understandable for the most I was thinking to try to explain it more understandable way.

I can agree with that. Myfloxybabe said it pretty well a couple of pages ago:

Originally posted by MyFloXyBabY
The problem lies within 2 intuitive definitions of what an exploitative strategy can be : on one hand we call "exploitative" something that maximizes our profit against an opponent, on the other hand we also call "exploitative" something that simply deviates from GTO. When the strategy maximizing the profits happens to be GTO itself there seems to be a paradox.

I think we all understand each other pretty well, but the problem seems to be how we understand the term exploiting.

Now we can get all philosophical and start thinking about what the real idea behind GTO is. I do agree that GTO maximizes profits in those scenarios you mentioned, but is it the goal here, or is the max profit just a byproduct? If we are playing against perfect opponent, we have to switch to GTO because otherwise he would exploit us. So we are aiming to be unexploitable. At the same time of course it maximizes our profit (now break even), but the main goal was not to get destroyed by him?

Originally posted by la55i
I can agree with that. Myfloxybabe said it pretty well a couple of pages ago:

Originally posted by MyFloXyBabY
The problem lies within 2 intuitive definitions of what an exploitative strategy can be : on one hand we call "exploitative" something that maximizes our profit against an opponent, on the other hand we also call "exploitative" something that simply deviates from GTO. When the strategy maximizing the profits happens to be GTO itself there seems to be a paradox.

I think we all understand each other pretty well, but the problem seems to be how we understand the term exploiting.

Now we can get all philosophical and start thinking about what the real idea behind GTO is. I do agree that GTO maximizes profits in those scenarios you mentioned, but is it the goal here, or is the max profit just a byproduct? If we are playing against perfect opponent, we have to switch to GTO because otherwise he would exploit us. So we are aiming to be unexploitable. At the same time of course it maximizes our profit (now break even), but the main goal was not to get destroyed by him?

I try to make my point more on the practical side where we realize people actually cannot play GTO:

Yes I think if you "trying to play GTO" your goal is actually to win most money from all sorts of opponents whether how strong or weak they are, because when you playing without reads you actually don't have any information to rely on. This could apply for Antonymous tables or Basically any playerpool where all opponents are random to you and you don't have specific reads how average player plays on those games. Once you gain experience you start to switch from GTO --> Population Exploit and once you aware of 1 specific player tendecies you go on exploitable towards that player.

Truth is that very few people consciously switch between strategies, they play "their strategy" making very few adjustments no matter how GTO or exploitable it is... That's why they might be winner in certain playerpool let's say NL200 livegame, but losers online, but when they actually learn to beat NL50 online they might end up lower €/h in NL200 live because they are not actually conscious what they are doing right or wrong... When they change from playerpool to another it takes for them too long time to adjust "their strategy" when in reality they should never have "their strategy" but they should always be adjusting it based on their opponents. (Obviously you need some Baseline to start for which GTO is very good for)

And often debates like this are more like debates "how GTO I should play" are actually more like "In which situations my opponents are capable of exploiting me if I don't have balanced strategy". You should study GTO, because higher stakes you go more difficult it is to found leaks from opponents and as well your opponents are more capable of exploiting leaks which maybe you not even realize are exist. You might for example find very good opponents defending same range from BB against 2,5x raise and 2,2x raise and based on your knowledge you should decide which openraise size makes more profit in the long run... That's why more you study GTO more you understand how much people you play against devide from it and as well you can be better at exploiting their leaks.

I agree with you.

Hey guys,

This trolling has got out of hand and as a consequence I have removed all posts since the last relevant post.

Please keep any future posts to the subject at hand.

Regards

Laz

Geez. Now we don't know where thought level we were at anymore.

Didn't come around this thread in awhile , where's the discussion at ?
What about the difference btw exploitive , exploitative , levelling and steps ahead ?
Would like to hear Yadijavadi's opinion about it ?
Also were you able to proof your concept theory threw game samples ?
If not yet wich format of poker game will you make that sample ? wich stake ?
How will you analyse the results to confirm or not your theory ?
Just asking out of curiosity and coz i've a hard time to sleep obviously.

@OldSchoolPapa

We are going in circles. Nothing new has happened here and we are nowhere.
In Yadi's opinion he has already proven everything, but in reality there has been 0 proof. No concrete examples.

One thing we all agree on, Yadi included (I believe) is that it is not practical to use some of the levels. The reason is that it is impossible for humans to do that. But in some very simple games it might hypothetically work. It works in every other game too, because Yadi says so. There is your proof. For example it works in chess with levels 1 and 2 but when you ask him how it differs from a simple phrase we all know: "thinking X steps ahead" and how it will in reality help you get better, he gets offended and tells you to fuck off, so please don't ask him that.

We have had a lot of discussion and trolling here. The claim in the thread: "Proof that Game Theory Optimal Can Be Found With Thoughts Alone" has been busted in my opinion. So now we are just continuing to debate about irrelevant things like what is the true goal in GTO strategy

There is a summary for you

@la55i Thank you for your patience and kindness , just saw plenty posts has been removed.
For a second i tought some relevant progresses were made but i guess must be the meds playing on my brain.
Also in my humble dummy micro player's opinion since GTO requires huge calculations a human being will never be able to use it live in a perfect way.
Still might be possible to get close to it in a 3-Handed game like spins and with specific betting pattern sizing , stack size ...
Now the interesting debate could be if it is better to play using GTO rather than Exploitive but still the answer might vary from a game format to another and from a stake to another. But could be interesting to develop with plenty game exemples , stakes and opponent's type ...
While i'm around i hijack a bit the thread to ask you if you know a good book or solid starting informations about poker population tendencies analysis ?
Found some informations on the net but more oriented CGs rather than Tournaments / SNGs ....

Partane, cheers man! It's really good to hear somebody speaking english.

"GTO is a maximum exploitative strategy".

This obviously means that by using a maximum exploitative thought-process you could find GTO. Simple.

Now... Is GTO the highest exploitative level?

We are almost entirely on the same page, however, it is clear that your description of how these exploitative strategies progress differs from mine. In fact, the range sequence in your first post does the exact opposite to mine. In your example each new range was further from GTO than the last.

The issue here is with the simplified game.

This simplified game has no hidden factors, which means that you cannot advance beyond Level Two when exploiting. Which means that GTO is found at Level Two in this game.

Your range sequence is not displaying how the ranges change as you advance through the Levels. Instead, you have calculated GTO in many new, progressively more unfair games.

(That was really, really hard to solve)

OldSkool papa.

Essentially, all that's happened so far is that the Mods have finally accepted that GTO is the exploitive strategy you use against someone who is using GTO.

We are getting into some real impressive stuff here now though. If La can keep a lid on his degrading comments we might get somewhere.

Originally posted by OldSchoolPapa
While i'm around i hijack a bit the thread to ask you if you know a good book or solid starting informations about poker population tendencies analysis ?
Found some informations on the net but more oriented CGs rather than Tournaments / SNGs ....

I'm not aware of any good books that talk about that. Population analysis is basically using software like Hand2Note, creating a lot of custom stats and running the reports. From that you get the info what your player pool does in every situation. To get started you need millions of hands and some kind of an idea what stats you could look at and how to interpret them.

Originally posted by yadijavadi
Essentially, all that's happened so far is that the Mods have finally accepted that GTO is the exploitive strategy you use against someone who is using GTO.

I'm not sure why you say we have "finally accepted".. That is something we already know. If villain is using GTO, we use it too. But there has been some good discussion about this topic. Vorpal did say that GTO seeks to be unexploitable.
Now, if your villain is playing GTO, how do we exploit him? The answer is that we don't. Our best strategy is to play GTO too, and as concluded earlier that would lead to equilibrium and we would be break even. Can we call that exploiting? It is probably the most profitable line we can take, but we don't exploit him.
I agree with what Partane said earlier. GTO has its own uses and sometimes it could be the most profitable line. So we are on the same page with him but I would interpret the term exploiting a bit differently. For me exploiting and exploitable strategy mean that we are really exploiting weaknesses, leading to higher profit than balanced GTO strategy would. Now if villain is playing GTO, then us playing GTO could be max profit, but because villain can not be exploited, it is not max exploit/exploitative strategy.

Even if it would be, we have already long time ago agreed that in normal NL games with all bet sizings and so on, we can not reach GTO just by using our minds. So I don't know how this is relevant for the sake of the claims you have presented here. We have never disagreed about that using GTO would be the best option in some cases. So I really much doubt that this discussion is going to get somewhere

Ooooh, was expecting this already thought so that mods patience is not infinitie

La, I didn't actually see your query regarding Chess.

You asked if you will crush chess once you understand level one and two. The answer is, yes, you will be the perfect player if you crack level one and two In chess.

All we really have in chess is Level One and Two.

At Level One in Chess we look to our pieces, and all the different moves we can make with them.

At Level Two in Chess. We consider the opponents pieces, and all the different things he can do with them.

In chess, to make a level two decision we consider moving one of our pieces, then consider all the things the opponent could do, then all our moves, then all the opponents, etc etc. Eventually we will be able to see the GTO strategy for chess. All the factors involved in a Chess decision are level one and two factors.

In poker there is nothing taken from this Level two decision making process. In poker we obviously have cards instead of pieces. Our goal is to earn chips rather than capture the king. We share with our opponents flops rather than tiles. But, at level two we do still consider the opponents attributes and possible manoeuvres to select the best play. A Chess player trawls through all the different future situations to see if his action will give him an advantage over his opponent, a poker player considers his odds of remaining ahead of the opponent, and considers his implied odds after future bets. In Poker, using only the Level Two factors, you can also calculate GTO.

The GTO play in chess will always be the best play. For each individual chess decision, you can calculate the best play by considering Level One and Two factors. But to make the most profitable play in Poker you also need to consider Level Three and up. (Unless the opponent is attempting to use GTO)

At level three we deceive the opponent to gain control over his future actions. This brings in all kinds of additional factors that we need to consider in order to maximise our profit. All of these things are based on deception.

One of the things that comes into it (At Level Five) is the power of randomness. We have to always keep our opponent guessing what we hold so that we can deceive him in the most efficient way. What this means practically, is that, provided the opponent isn't trying to use GTO, we will benefit by playing 72o some tiny percentage of the time, and we will also benefit from using all the different betsizes available to us. There is a bot that seems to do this. It whooped a loads of famous regs. I'm sure the name begins with an L.