Durrrr >>> Sauce

I can tell you from knowing best friends of jungleman that he constantly thinks and talks about gto decisions and goes through tons of math to come up with basic strategies and specific player strats.

Emperor's clothes imo

While guys like ziigmund/PA/Ivey/isil might not explicitly think of certain actions and ranges via the language of game theory, distributions, bluffing ratios, their thinking most likely reflects it in an equal way.

Like, Sauce thinks "Am I shoving this river with a good balanced range and is it more profitable in the long run than c/c'ing would be?" Ilari thinks "I shove here some with nuts some with bluff some with okay hand. This is good shove I think" and the end results ends up the same. Just different neurological paths to the same action

I agree with this. Some people have natural tendencies that just so happen to be super optimal.

Now, the question is, is one particular neurological path superior to the other? Is it possible for someone's natural tendencies to be as optimal as a tendency that is carefully and consciously calculated? (Example: I bluff in this general spot 37% of the time, and it should be 45% --- Can natural tendencies really optimize situations to that extent?)

I know we've argued about this before! but ...

I think the argument that poker has a solution is very simple,
1) HU NLHE is a 2 player game
2) All 2 player games have Nash equilibria
therefore,
3) The Nash Equilibrium for HU NLHE is the solution for HU NLHE
so 3*) HU NLHE has a solution !

What is a game? From Wiki

1) In game theory, a game is defined as The games studied in game theory are well-defined mathematical objects. A game consists of a set of players, a set of moves (or strategies) available to those players, and a specification of payoffs for each combination of strategies. Most cooperative games are presented in the characteristic function form, while the extensive and the normal forms are used to define noncooperative games.
Extensive form
Main article: Extensive form game
An extensive form game

The extensive form can be used to formalize games with a time sequencing of moves. Games here are played on trees (as pictured to the left). Here each vertex (or node) represents a point of choice for a player. The player is specified by a number listed by the vertex. The lines out of the vertex represent a possible action for that player. The payoffs are specified at the bottom of the tree. The extensive form can be viewed as a multi-player generalization of a decision tree. (Fudenberg & Tirole 1991, p. 67)

...

The extensive form can also capture simultaneous-move games and games with imperfect information. To represent it, either a dotted line connects different vertices to represent them as being part of the same information set (i.e., the players do not know at which point they are), or a closed line is drawn around them. (See example in the imperfect information section.)

I should also note that even though I can solve some games using game theory, I don't have the formal mathematical training to understand Nash's proof for myself. So in no way am I an authority in this debate. Why does being a great poker player make you think you have the authority to disagree with a mathematical proof? Or, if you do have a way of disproving Nash, just publish and get super famous !!

YES...this thread just got sick.

I'm not even close to as qualified as you are in discussing this topic (obv), but if the game is solvable, why has no one come close to solving it? And I know it's a semi-flawed argument, "well, something hasn't been done yet, so therefore it can't be done", but I would think, given the mathematical, and general, intellect of some of the players out there, there would have been some progress made in "solving" the game if it were solvable, no?

Also, LOL at the guy who said "why is this a thread?". Maybe wrong forum, but this discussion is great.

Nice. Looks like this thread has a chance of becoming a durrrr, sauce, and ike threesome.

And after that's over, they could discuss GTO's significance in poker.

You should not have won. My play was perfect. The game is flawed.

Nash + poker seems like a perfect equilibrium.

there's a big difference between saying someone uses game theory and saying they believe in a gto solution for x game. even the most horrible of fish use game theory.

You are wrong durrrr. For lhe GTO strategies exist and it is measurable how far away the lhe bots play from it. NLHE is obv quite a lot more complicated and who knows how long before anything close to optimal even for a game like 100bb HUNLHE exists (long time obv, but probably not as long as you think)

Thats like saying "why hasnt chess been solved". The game tree is massive. If we had fast enough computers LHE would be solved currently I believe (the algorithm they use converges on nash equilibrium but stops short due to time/processing constraints)

How is this accomplished given that we don't have the GTO solution?

EDIT: Or are certain lines already solved, and this is what we're measuring against?

I guess I was wrong then. I was positive I heard you say it in an interview that NLHE was almost solved.

If I'm not mistaken...Chess has been solved, no?

http://en.wikipedia.org/wiki/Rybka

Also, does "solving" NLHE involve every hand being won? What does "solving" involve exactly?

Nah. Engines like Houdini might be (and probably are) unbeatable under normal time contrants when facing a human player, but that doesn't mean chess is solved...or even close to being solved (it is solved for 6-piece or fewer endgames though).

asdfasdf32:

http://webdocs.cs.ualberta.ca/~games...t_response.pdf

for a detailed explaination.

Thanks.

This post from the HSNL thread is interesting:

http://forumserver.twoplustwo.com/sh...&postcount=285

I'm not sure if it helps Durrrr's case. I don't have the math background to understand the article in detail. What I get from the more abstract stuff is that some mixed strategies might evade efficient solution. There seems to be a caveat made early on in the paper that may exempt zero sum games from their findings (reference to von Neumann). Not sure if that reflects directly on their conclusion, though.

We had a UofA guy posting in HULHE about a year ago whose comments corraborate the progress made toward a solution in that game. His first post in the relevant thread can be found here:

http://forumserver.twoplustwo.com/sh...5&postcount=62

As he continues to post, he goes into a lot of detail about computational limitations, the resulting use of abstraction and the already mentioned best response algorithm which can be used to find out the max that a given strategy can be beat for.

One quote I found in one of his later posts:

(http://forumserver.twoplustwo.com/sh...8&postcount=69)

ofc they use it, but they dont sit there with calculator while playing and calculate ****, they got it on a semi-conscious level.

Lol Sub conscious you mean?

I think a more interesting question isn't whether or not a GTo solution exists, as you have to be a fool/ignorant to think otherwise but rather, how big of an edge would the GTo solution have?

The GTo solution could hypothetically not even beat the rake/have barely a fraction of BB winrate vs non GTo play

it's weird to think that there's one GTO strategy when so many people are winning using much different strategies (isildur vs jman for example).

There could be multiple GTO strategies

It is only proven by Nash that 1 must exist