The paper and others (mathematically inclined) have indicated that poker can be solved mathematically. However, to include a no limit aspect with variable stack sizes, multiple streets and more than 3 cards would be extremely computationally intensive that it's assumed that there's no computer that could "solve" the GTO of any situation (assuming all frequencies were known).

I did put words in Sauce's mouth and do take it back. My understanding of his argument is that he's saying that hu poker it is mathematically solvable with GTO. Durrr is saying that GTO can be exploited since frequencies ought to be changing given the circumstance, if you're a good player. I believe there's validity in both arguments. I think if frequencies were known and were constant then one could solve what the GTO decision for any set of circumstances if computational power was not a limitation. However, Durrr assumes (or implies) that we don't have the ability to calculate situations where we need to account for shifting frequencies.

I'm not saying the linked paper is the authority of GTO but I'm assuming that their explanation and logic is accurate.

Given the "stupid mistake" assumption, I think we can extrapolate it to five cards and say that we're never calling a bet on the river with 32o, we're never folding or not betting in position with the nuts. Now stupid mistake #4 makes the math interesting regarding what's the worst we can bet which will be GTO.

no he isn't. he's saying it doesn't exist for that game. how many times does that have to be repeated?

He states that since it's a game of incomplete information that it's not possible to come up with GTO. This is obviously not true but it's his underlying argument that no "bot" could ever know with certainty his frequencies so thus cannot solve/calculate what would be the GTO decision under those particular circumstances.

I agree that GTO will be >0 EV against any human today, but in the example you provided folding or calling a K 100% of the time will both have the same EV as calling 1/3 of the time. Assuming a pot-sized bet, 1/3 of Player 2's betting range should be bluffs to make calling with a K break even, so he should bet with a Q 1/2 of the time. Assuming that the pot size became 1 by both of you anteing half a unit, calling 100% of the time will have an EV of (1/3)*1.5-(2/3)*1.5=-.5. If you fold every time, you will also have an EV of -.5 because you are just losing your ante every time.

When the GTO play is a mixed strategy, by the definition of GTO all the individual strategies in the mixed strategy must have equivalent EVs.

He pretty clearly was? He's maintained that if a bot plays "GTO", that he could still find occasional ways to exploit it by using his uniquely human rationalisation; and that this proves that there is no true GTO.

not really saying he can beat a gto bot... he's saying that it can't exist.

Well, he was saying one therefore the other :P His evidence for the claim that GTO can't exist is that he could adapt to exploit any strategy that people claim is GTO.

so much signal, so much noise..

He's saying a solution exists, which sounds like a small distinction but is actually a huge one. It's a mathematical fact that a solution exists. Proving this is what John Nash is famous for. That doesn't mean computing it is practical with current technology. It's kinda counterintuitive but there are a bunch of situations in math where it's possible to prove that something, like a GTO solution to HUNL, exists without being able to actually find it.

This is definitionally not true. You're misunderstanding what at least on of the two terms "GTO" and "exploited" mean. This is why I said that what Durrrr must mean, even if it's not precisely what he actually said, is that he doesn't believe a Nash Equilibrium exists for HUNL or HUPLO.

The paper you linked shows that it is sometimes possible to improve on GTO play when the opponent's strategy is known. This is not the same thing as exploiting or winning against GTO play.

I don't mean to be dismissive or a dick because I can tell you're really trying to understand this stuff, but this paragraph is just gibberish. Computing GTO play has nothing to do with knowing anyone's frequencies. A GTO approach to decision making explicitly doesn't care what your opponent is doing.

As far as I can tell, nothing in the paper you linked is "wrong," per se. It's a pretty competent analysis of the game he's writing about, but the guy who wrote it seems not to have a very deep understanding of the material and a lot of it is kinda confusing and misleading if you try to apply it to bigger problems. I've been looking around for a better quick primer on game theory in poker but haven't found one. I'll post it if I do or if someone else knows one it would be cool if they did.

The problem is that "Stupid Mistakes" don't translate to more complicated games in this clean of a fashion. It's not a distinction I've seen made elsewhere. He doesn't really make it clear how he's defining a "Stupid Mistake," but he does eventually make this claim:

"The heart of the game is the struggle. Playing optimally erases this struggle. Playing optimally prevents your opponent from taking advantage of you, but it also prevents him from being punished for his mistakes. As such, using game theory to “optimally” bluff or o “optimally” call a bluff can only be regarded as a defense. But since it defends both you and your opponent, a better defense is to simply not play at all.

That being said, it should be pointed out that there are times when the optimal strategy will be profitable; namely, when your opponent makes Stupid Mistakes. In that case, you can play optimally and be a long term winner. By playing optimally, you ensure that changes in his bluffing and calling frequencies will not affect his EV. Since his EV will be intrinsically
negative due to his Stupid Mistakes, you will have a positive expectation. (On the other hand, if he is making Stupid Mistakes, then you can probably outwit him without game theory.)"

In games like One Card Poker or Rock Paper Scissors that are often used as introductions to game theory, this seems like a reasonable claim. However, as far as I can tell, it's only true in a more general sense if you define "Stupid Mistakes" as those mistakes which are worse than, rather than equal to, their alternatives against GTO play. This is a circular and essentially useless definition when you're talking about a full scale poker game. It will include lots of mistakes that don't seem "Stupid" in the same way the "Stupid Mistakes" in One Card Poker do.

I think Durrrr solved HUNL and he's just trying to convince other people to stop looking

They are two different claims. One of them is wrong while the other is nonsense.

There is no GTO solution to HUNL. = There is no tallest man in the world.

I can beat the GTO solution to HUNL. = I am taller than the tallest man in the world.

I only skimmed what he was saying (because it was wrong for trivial reasons) but my interpretation was if you give him the code to any bot in NL he can make slight changes and have it beat that bot.

There are situations where something like that is possible.... like if somebody gave you a number from the interval [0,1) you can always name a larger one because the largest number on that interval doesn't exist. It's actually possible in real game as well....it's called epsilon-equilibrium but poker is not one of those gmes.

tbf if a woman or a really tall robot said that it could be true.

I agree with you that they're wrong/nonsense, I'm just not sure why you're saying durrr hasn't claimed this. He literally claimed that there is no GTO, and that he could beat any strategy employable by a bot simply by adapting with human rationalisation.

Yeah, he claimed both of those things. He didn't claim he could beat a bot that did play GTO, because that would be nonsense. That's all I'm saying.

Guess I just interpret this differently heh.

Computers assume that their opponent will spot a 15 move forced checkmate against them. And they won't make a move that will put them in this position even if there is only a miniscule chance it would be spotted. Not if an alternative guarantees a win in say fifty more moves.

too bad he isn't just claiming that one won't exist instead of can't exist(a hunl gto bot i mean). because then i would be inclined to agree with him.

some regurgitation from other sites regarding definition nash equilibrium and nash equilibrium with incomplete information -

nash equilibrium - "In game theory, the Nash equilibrium is a solution concept of a non-cooperative game involving two or more players, in which each player is assumed to know the equilibrium strategies of the other players, and no player has anything to gain by changing only his own strategy unilaterally. If each player has chosen a strategy and no player can benefit by changing his or her strategy while the other players keep theirs unchanged, then the current set of strategy choices and the corresponding payoffs constitute a Nash equilibrium." (wiki)

does nash equilibrium exist under circumstances with incomplete information? - "In economics and game theory, global games are games of incomplete information where players receive possibly-correlated signals of the underlying state of the world...Stephen Morris and Hyun Song Shin (1998) considered a stylized currency crises model, in which traders observe the relevant fundamentals with small noise, and show that this leads to the selection of a unique equilibrium. This result overturns the result in models of complete information, which feature multiple equilibria." (wiki)

This.

I feel like durrrr is wrong about exploiting gto. But he does stand a very good chance against a top lhe bot, considering it won't be anywhere near gto and won't adjust it's strategy at all vs him

This is a rare nvg thread with signal>noise

The original statement barely means anything because we haven't defined the nature of durrr's knowledge, nor likely could we, which can exist on a wide spectrum right up to an omniscient nemesis-like ability to perfectly respond with accuracy of a millionth of a big blind to the slightest variation however imperceptible, and the second part implies that he would have perfect insight into the nature of his own knowledge because this is what the strategy will be based on and thus so must his counter strategy.

i just play poker and try to adjust to my opponents, i do pretty well and dont know anything about GTO

I looked around for one a while ago and didn't really find one....the best relatively short ones I found were this by jesus

and a masters thesis

there is also a nice matheoverflow discussion with 2+2er Doug Zare.

All of these are toy games of course....which is what you have to restrict yourself to if you want to give a constructive proof. But if you understand those papers and have a just a vague idea of Nash's proof works you should see why a GTO solution exists for NL.