Game Theory - Perfect Strategy? - Chess Forums - Page 3

Dragec

Dec 11, 2010

0

#41

Barefoot_Player wrote:

...

number of possible games in chess is at least a google (10 to the power of 100), and possibly larger than a googleplex (10 to the power of 100 to the power of 100). We may very well go the way of the dinosaurs before chess is played out.

Barefoot_Player

not google, but googol:

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

Google was an obvious ripoff name such as fake "Adadis" sneakers:

Elroch

Dec 11, 2010

0

#42

Barefoot_Player wrote:

Josh, you said, "The games of chess can't last forever because of certain rules, so its a finite game".

The 50 move rule and the 3-fold repetition rule are not of fundamental importance to the theory of chess (although the former does make a crucial difference to the evaluation of positions. Some endings that would be drawn without it are classed as draws because of it. One example is some positions with QP v Q). The key thing is that there are only a finite number of positions. You can categorise a position as winning for one side or the other if they have a forced checkmate, and drawn if neither does. If there is no forced win for one side or the other, any attempt to force a win would run up against a 3-fold repetition eventually because of the finite number of legal positions (and often a breach of the 50 move rule before this).

Musikamole

Dec 11, 2010

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#43

With best play, chess is drawish. Get over it.

Barefoot_Player

Dec 11, 2010

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#44

"not google, but googol"

Thanks Dragec!

Barefoot_Player

Elroch

Dec 11, 2010

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#45

Are you sure it's not Gogol?

JG27Pyth

Dec 11, 2010

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#46

blake78613

Dec 11, 2010

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#47

There is always a googolplex which is 10 to the googolth power. Of couse if your talking about geese its a gaggle.

rigamagician

Dec 11, 2010

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#48

If you google "Gogol," you get like a googol of pages about him. I think I read somewhere that he used to wear goggles to hide his googly eyes. If you google "googolth" though, you get diddly-squat.

Vance917

Dec 25, 2010

0

#49

Vance917 wrote:

I wonder how close we might come to perfect play if we had teams of masters playing vote chess, as we do here on this site, only with the provision that moves can be taken back as far back as they want to go. In other words, if, after the 26th move, it becomes clear that the 14th move was not ideal and a better one was available, then that "team" may go back to the 14th move and now play the better move. Obviously, the intent of such an exercise would not be to see who wins or loses; indeed, masters could even play on both sides, black and white. The goal is to try to identify the best moves possible, play it out until one side or the other wins (or there is a draw), and then go back and ask if at any point during the game a better move might have been available. In theory, such a game could last forever, like an eternal flame, and accept input from any and all interested parties (even computers).

This approach is not limited to the start of a game. It could be applied to any position, in a search for a winning strategy for one player or the other. It might be interesting to know, for example, if white has a winning strategy given the advantage of black starting the game with no queen. If, as one would expect, the answer is yes, then what about if instead of a queen handicap we use only a rook handicap? A bishop? Two bishops? And if starting a queen up is not enough to ensure the victory, then a queen plus a bishop? So many questions that could be asked along these lines.

szammie

Dec 26, 2010

0

#50

josh_blackheart wrote:

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.

This is the type of conversation that went on n the post 'is intelligence the enemy of chess. I agree with that last part; I stated that intelligence is your enemy & greatest weapon, & that the most intelligent player always wins. This winning also has everything 2 do with your will 2 win, which can't b theorized.

LastImpression

Dec 26, 2010

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#51

We need a precise definition of draw. Draw by agreement isn't cutting it either.

NoPlagarism

Jan 11, 2011

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#52

josh_blackheart wrote:

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.

I'd suggest an F for plagiarism.

This is quoted verbatim from a lecture by Professor Scott P. Stevens of James Madison University. I watched his lecture this evening on the "Great Courses" DVD series. The title of the series is "Games People Play: Game Theory in Life, Business, and Beyond" and it is the third lecture of the series.

After watching Dr. Stevens lecture, I searched for "perfect chess game" and found this rip-off. Sad.

Elroch

Jan 14, 2011

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#53

It's also an utterly trivial observation.

Vance917

Jan 14, 2011

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#54

It is conceivable that the poster did not intend to represent this as his own idea. I mean, how many Face Book members post song lyrics as their status? And how many of those cite the original source?

Atos

Jan 14, 2011

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#55

[COMMENT DELETED]

beardogjones

Jan 14, 2011

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#56

He is also incorrect in saying that perfect information requires knowing the

whole history of the game: it involves counts for all positions reached that

are still reachable

some castling and enpassant flags and the current position- this is not

the whole history!!

Atos

Jan 14, 2011

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#57

Nop, the history of the position is not relevant to evaluating the position, other than knowing whether en passant and castling are possible in some (rare) cases.

Dragec

Jan 14, 2011

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#58

Not "is draw", but "may be draw". :-)

Dragec

Jan 15, 2011

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#59

Also, since 3-fold repetion is rare(especcialy in early phasess of the game) an engineer's approach could be to discard it.The evaluation would probably be the same anyhow. And if you want additional precision, you might have a flag if some position has appeared twice.

Atos

Jan 15, 2011

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#60

Fezzik wrote:

Atos, I disagree. It's impossible to claim a 3-fold repetition or draw by 50 move rule if we don't know the history of the position. A third repetition of the position is a draw, and so is very relevant to the evaluation of the position!

Hm...yes, but if the threefold repetition is forced, the evaluation is essentially the same whether or not the repetition had already occured. The things are less clear with 50 moves because there are pawnless endgames where a win can be forced but requires a large number of moves so yes, here one would need to know the history.