Game Theory - Perfect Strategy?

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josh_blackheart

"The games of chess can't last forever because of certain rules, so its a finite game. It doesn't involve chance to decide the outcome, so its a deterministic game. Its obviously a sequential and non-cooperative game, and assuming you know the entire history of the game when you go to make your move, its also a game of perfect information.

So is there a best way to play chess? If the best strategies are used, every game will end up the same way. Therefore, one of these three statements is true:

1. Chess is a guaranteed win for white - there is nothing that black can do to stop this unless white makes a mistake (white goes first).

2. Chess is a guaranteed win for black - there's nothing that white can do to stop this, unless black makes a mistake.

3. Chess is a guaranteed draw - like tic-tac-toe; neither player ever wins unless someone makes a mistake.

It seems that there are more possible strategies for chess than there are sub-atomic particles in the universe. Perhaps one of those strategies is the perfect one, one that would never lose, one that would in fact win every single game...if a winning strategy exists. Just like tic-tac-toe, unless you screw up, every game ends up with the same result. Its humbling to realize that chess, for all of its complexity...is exactly the same."

                                                      

Source: Professor Scott P. Stevens, Ph.D., The Pennsylvania State University,
James Madison University. Lecture on :

Games People Play: Game Theory in Life, Business, and Beyond

orangehonda

Strong players have agreed since at least the time of Steinitz that with best play a draw is most likely.

Evidence since then has only supported this.

josh_blackheart
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CheckersBeatsChess

Its difficult to model because there are SOOO many moves for each player.  tic tac toe has 5 moves by  player 1 and 4 moves for player 2.  in chess whats the number of moves?

This lack of definitive moves makes the most natural way of approaching this problem (SPNE=subgame perfect nash equilibrium) impossible, this uses regression.  That was my first approach.   

philidorposition

It's obviously a draw with perfect play, but how does that make it exactly the same with tic tac toe? Why the rush to reach so quick conclusions? Basketball is exactly the same as football, except that it's completely different.Smile

josh_blackheart
[COMMENT DELETED]
heinzie

You cannot jump the horsie in tic tac toe

AndTheLittleOneSaid

Can't we just ask Magnus?

rigamagician

Perhaps tic-tac-toe should be played at a time control of 40 moves in 2 and a half hours.

Shivsky

 

Approves.

JG27Pyth
orangehonda wrote:

Strong players have agreed since at least the time of Steinitz that with best play a draw is most likely.

Evidence since then has only supported this.


But "most likely" is another way of saying "unknown, unsolved" -- there are lots of composed positions that look hopelessly lost or drawn but of course turn out otherwise. Who cares about the 'evidence' supplied by a bunch of patzers? And against the enormity of chess from the first position everyone (Rybka included) is still a patzer.

Chess may be a devilishly difficult endgame study composed by God... "White is in Zugzwang! 0-1 "

Dragec
josh, have you searched for Nash equilibrium for chess? :-)
Ricardo_Morro

If chess is "solved," it will not be by "strategy." The definitive solution would have to take a tabular form, although a very vast table, with every move choice met by its possible countermoves. The table would show all possible games with all possible outcomes, with the longest that could not have been diverted into shorter paths chosen as "optimal." That is not strategy, nor is it even calculation, it is just reading. Calculation is what you employ to limit possibilities, to exclude the trivial lines from consideration, whereas the grand solution table for chess would include everything. And strategy is what you use for a guide when you cannot calculate. So by definition there cannot be a perfect strategy for chess: no set of more general ideas can always lead you to the best choice in all particular situations. This is distressingly similar to Godel's theorem, though it deals with a finite system and not an infinite one.

For my part, I reject the criterion of length for optimum. I would rather choose a line of play that might win or lose in 50 or 60 moves rather than play for the theoretically perfect 977 move draw.

loved

For me it gets a bit confusing when we start to talk about "creating imbalances". Is it a tactic to create an imbalance in the position? And then, once the imbalance has been created, one can continue to play positionally, yes?

If one chooses to not create an imbalance, is that perfect play? And if one chooses to create an imbalance, is that also perfect play?

By what criteria do we recognize perfect play? If it is defined clearly, will we be more likely to attain it?

electricpawn

To say chess is finite and deterministic, and to assert that with the correct strategy the game is a guaranteed win for white or black or a guaranted draw is logical and has a certain aesthetic appeal, but I think it is incomplete.

Chess is a very complicated game, and it is a contest between two people. This brings factors like skill, discipline and character into play. In order for a strategy to be implemented properly, a player must develop his abilities and an indominable competitive attitude.  

blake78613

A rather long drawn out tautology which in the end only says "A=A".

D-

sapientdust

There is no significant evidence yet whether chess is won, lost, or drawn for white with optimal play by both sides.

People seem to be assuming that it will be solved eventually, but that isn't necessarily the case. There are physical limits to how much computation could be performed by an optimal computer that used all the available matter in the universe (http://en.wikipedia.org/wiki/Limits_to_computation). That's probably not possible for other reasons, but even if it were, it might turn out that even with that amount of computation, it still wouldn't be sufficient to exhaustively categorize the state space of possible chess games. If that were the case, then we could be certain that we'll never know one way or another.

psyduck

Well, I'm assuming that the initial position isn't a zugschwag (sp?) so I think we can take black wins off the table. And a full calculation of every possibility isn't needed to prove that it's draw or win either. I'll tell you how this one ends. Chess is a draw from starting position. There's no autowin path. And yes, I know this. Yes I can prove. But will I? of course not. I'm am lazy and indifferent to your cries for help.

 

but seriously. Black always wins with perfect play

psyduck

ducks can't stop. That's physcially impossible. Trust me, I'm actually made of matter

Musikamole
josh_blackheart wrote:

1. Chess is a guaranteed win for white - there is nothing that black can do to stop this unless white makes a mistake (white goes first).

 

2. Chess is a guaranteed win for black - there's nothing that white can do to stop this, unless black makes a mistake.

 

3. Chess is a guaranteed draw - like tic-tac-toe; neither player ever wins unless someone makes a mistake.

 


Teacher grading paper.

1. Not correct

2. Not correct

3. Correct

33.3% correct. F ;)