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calling all mathematicians

calling all mathematicians

Only Chess

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i don't know how to properly phrase this, but has anyone ever calculated how many combinations of moves can be made on a chess board.

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Originally posted by smw6869
i don't know how to properly phrase this, but has anyone ever calculated how many combinations of moves can be made on a chess board.
Greater than or equal to 3.


But seriously, the old saw is more than the number of atoms in the known universe. (Someone was going to say this, so I thought I'd be first 😀)

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Originally posted by smw6869
i don't know how to properly phrase this, but has anyone ever calculated how many combinations of moves can be made on a chess board.
Technically, there can be an unlimited number, if two players end up with kings moving back and forth...

But some people have calulated how many possible combinations can be made within a certain move limit...what move number did you have in mind?

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Here's a good site for the info

http://mathworld.wolfram.com/Chess.html

And another
http://computer.howstuffworks.com/chess1.htm
Interesting reading.
What amazes me is the power of the human mind that can play despite these numbers.

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And from Wikipedia

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

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I've read 2 couple of things

More combinations than the atoms in the universe
more combinations than the seconds that have elapsed since the formation of the solar system

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Of course, all these are approximations. If it were possible to calculate exactly how many combinations, then it will be possible to "solve" chess completely.

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I think the branching factor is at 35.

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I think that in any position there are moves that if made will result in a forced loss or draw, so the human mind can recognize these and immediatley rule them out where as a computer tries to play out every possibility to the end in order to see if it works or not. So the reason it seems so mind boggling is because those numbers relate to the total number of possibilities, not the total # of winning possibilities which is much lower.

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Originally posted by ChessJester
I think that in any position there are moves that if made will result in a forced loss or draw, so the human mind can recognize these and immediatley rule them out where as a computer tries to play out every possibility to the end in order to see if it works or not. So the reason it seems so mind boggling is because those numbers relate to the total number of possibilities, not the total # of winning possibilities which is much lower.
Yes, it's total positions, regardless of good or bad lines. And another question...has someone actually calculated how many atoms are in the known universe? And I would like to know how.

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duh! Guess and check! 😛

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Originally posted by wittywonka
Technically, there can be an unlimited number, if two players end up with kings moving back and forth...
No, the numbr is not unlimited. It is limit amount of combinations of moves. The number is high, very high, but you can't move forever.

The reason to this is of course that every move you do is on move less from the end of the game.

You can't move kings back and forth unlimited number of times due to the 50-moves rule. It's a draw.

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i tend to use forcing moves if the position is slightly better for me, if i can't find a better way but forcing moves can help you get a better grip on the situation. on average some moves i've seen 4 different variations but very hard to calculate. maybe more.

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Originally posted by FabianFnas
You can't move kings back and forth unlimited number of times due to the 50-moves rule. It's a draw.
The 50-move rule is not automatic. One of the players must claim the draw, and if none of the players claim the draw, the game continues. Likewise for draw by three-fold repetition.

Having said that, I think the initial question assumes that this situation won't happen.

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No you can totally move forever...

1. f3 f6
2. Kf2 2. Kf7

Then just keep moving the kings around. I think you could go on forever if you like. Just would be rather pointless.

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