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The complexity of chess

The complexity of chess

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M

Earth

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Many will know this, but for those who don't, let me pose a question.
In a 40-move game, white plays and black responding equalling one move, how many possible different possible games are there?

For move one, there are 400 possible positions. White can advance any of 8 pawns, each to any of 2 squares. He could also move either knight to one of two squares. So white has 20 moves to choose from.

Based on this, black has 20 possible responses for each move white COULD play - i.e. 20x20 = 400 possible positions from each player playing once.

Take this forward in your mind to the 40th move. How many positions could theoretically exist by then? And for the really bright ones, how long would it take Deeper Blue, the most powerful chess computer to be tested against a World Champion, take to calculate every one of these possibilities (i.e. to think 40 moves ahead?).

K
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of Doom!

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Originally posted by Policestate
Many will know this, but for those who don't, let me pose a question.
In a 40-move game, white plays and black responding equalling one move, how many possible different possible games are there?

For move one, there are 400 possible positions. White can advance any of 8 pawns, each to any of 2 squares. He could also move either knight to one of two s ...[text shortened]... d Champion, take to calculate every one of these possibilities (i.e. to think 40 moves ahead?).
After those first two moves (one for white, one for black) the number of moves available at each node will not necessarily be 20. To work out how many positions are possible after 40 moves would require that every move be computed. So we need Deeper Blue to tell us how long it would take Deeper Blue to work this out!

e
Eye rival to Saurons

Land of 64 Squares

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

I don't know the credibility of the above link but I think it gives a good/rough/ballpark idea of how many possible games in chess there are.

I'm sure we all know the chess game with the shortest number of moves!


White Black
----------------------------
1. Draw agreed

K
Demon Duck

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Originally posted by eagleeye222001
http://en.wikipedia.org/wiki/Shannon_number

I don't know the credibility of the above link but I think it gives a good/rough/ballpark idea of how many possible games in chess there are.

I'm sure we all know the chess game with the shortest number of moves!


White Black
----------------------------
1. Draw agreed
It's a reasonable statistical calculation of a lower bound to the number of possible positions. That means there are at least that many positions, probably more. An accurate determination of the number would be impossible so the Shannon number, with all its inherent inaccuracy, will have to suffice.

M

Earth

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Originally posted by eagleeye222001
http://en.wikipedia.org/wiki/Shannon_number

I don't know the credibility of the above link but I think it gives a good/rough/ballpark idea of how many possible games in chess there are.

I'm sure we all know the chess game with the shortest number of moves!


White Black
----------------------------
1. Draw agreed
I think the link is very credible. The figure I had was 10x10 to the 115. Clearly 10x10 to the 120 is many orders of magnitude higher than this, but it illustrates the point.
There are more moves in a 40 move game than there are atoms in the universe, and it would take Deeper Blue many times the age of the Universe to calculate them all.
To be more precise there are a trillion trillion google possible positions (as an underestimate). About the same number of moves as years it takes a black hole to disappear into nothing, according to NASA calculations.
Puts Kasparovs defeat into perspective.

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