Linear Equations Complexi, wha?
 

All,

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.


Regards,

T

Re: Linear Equations Complexi, wha?
 

[ 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)

Re: Linear Equations Complexi, wha?
 

I think it can be solved. The number of possible combinations of cards heads up is not that high, the number of decisions is relatively low. You could program a computer to play optimaly, and it would never lose. I'm sure it has been done already. The only thing is, by playing optimally, you are not exploiting weak players weaknesses. You will beat a weak player, but not by as much as you could. Consider, the number of card combinations is:

52c2 * 50c2 * 48c3 * 45 * 44 =

(52*51/2)*(50*49/2)*(48*47*46/6)*45*44= 55,627,620,048,000

Thats about 1000x of dollars Bill Gates has, so it can't be that hard to count! Around 55 trillion possible combinations. A computer can take care of that in no time. lol, it would take a fair while, but it can be done.

good luck, I think if you get some butchers paper and start a decision tree, you will be finished by the year 25 billion.

Re: Linear Equations Complexi, wha?
 

Thanks, Ice. I was familiar with the Poki/Albert project, but I honestly never really understood it outside a surface understanding.

Some people have very large brains.

Regards,

T

Re: Linear Equations Complexi, wha?
 

[ QUOTE ]

good luck, I think if you get some butchers paper and start a decision tree, you will be finished by the year 25 billion.

[/ QUOTE ]

I'll take the over.

Thanks,

T