[ QUOTE ]
Can anyone explain this quote for me?
Heads up matches are the closest thing to the many of the advanced game theoretical models of poker. Anytime you have a known bet size, you can reduce the the complexity of the linear equations substainally.
It came from this thread at Daniel Negreanu's site in
From this thread.
I don't know much about game theory, so I'd love to understand something about this.
[/ QUOTE ]
One of the most important results in game theory is that any one-on-one game with a finite decision tree can be solved. Tic-tac-toe is a trivial example of a solved game. Heads-up limit holdem with a limited number of bets per round is finite, and could theoretically be solved. However, there are so many variables in holdem, even when played heads-up with limit betting and a 4-bet cap, that the actual solution is far beyond what could reasonably be calculated. Still, even without fully solving holdem, it would be possible to create a very strong computer player by approximating a game theoretic solution.
There's a group at the University of Alberta computer science department that is working on game theory and artificial intelligence by programming computers to play and analyze games ranging from chess to go to poker. Their checkers program beat the human world champion at that game.
Their website is here:
http://www.cs.ualberta.ca/~games/poker/
(scroll down to publications)