Quote:
Originally Posted by durrrr
GTO (game theory optimal) implies there is a solution for poker... like chess or backgammon etc. there isn't for hunlhe (or plo etc), and I'm very confident (but can't be sure b/c simpler game and I'm worse at it) there isn't for lhe etc. just about every good nlhe specialist disagrees with me on this... except jungle/galfond/few others who r actually good. altho i think galfond wasn't sure iirc or something like that (limit games probably ruined his brain).
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 !!