I wonder how many possible combinations there is in a game of chess. Is it at all possible for man to calculate or program a computer if there were infinite time? There MUST be a finite number...but the question is: can man find it?

Qrazy question but a guy told me that bridge was the game with the highest number of possible combinations. I did not agree with him. How about you?

Have you an idea or comment?

1) "The number of legal positions in chess is estimated to be between 10^43 and 10^50, with a game-tree complexity of approximately 10^123. The game-tree complexity of chess was first calculated by Claude Shannon as 10^120, a number known as the Shannon number. Typically an average position has thirty to forty possible moves, but there may be as few as zero (in the case of checkmate or stalemate) or as many as 218."
Source and further information:
http://en.wikipedia.org/wiki/Chess


2) "Chess is infinite: There are 400 different positions after each player makes one move apiece. There are 72,084 positions after two moves apiece. There are 9+ million positions after three moves apiece. There are 288+ billion different possible positions after four moves apiece. There are more 40-move games on Level-1 than the number of electrons in our universe. There are more game-trees of Chess than the number of galaxies (100+ billion), and more openings, defences, gambits, etc. than the number of quarks in our universe! --Chesmayne"
Source and further information:
http://www.chess-poster.com/.../did_you_know.htm

Thats what I like to read. Thank you very much eainca. I must say I laughed when I read it. The numbers are growing so fast after each move. An interesting point i think is that the brain can play strongly in spite of all the theoretical possibilities.

Like math and chess.

I don't think the brain is playing strongly in spite of all the theoretical possibilities because I don't think the vastness of the theoretical possibilities has anything to do with the way an individual position is calculated by someone.

The brain aligns itself with the current position; understands the intricacies of it and then begins to think through it in a visual and logical way, it doesn't need to know what has happened previously or what might happen in 20 moves to make a good move now. This is where humans and computers differ slightly because humans are more intuitive than computers but computers are number crunchers. Humans put a piece in a particular place because it 'looks' good (strategically) even if the reasons why are not immediately obvious; whereas computers put a particular piece in a position because it serves a purely tactical goal at some stage within its thought process (which is far deeper than human ability). The second is the safer option and theoretically much more logical; which explains why computers > man at Chess.

On the issue of the number of combinations in Chess it's still beyond any computer to work through and probably will be for a long number of years to come.  It is an interesting topic though and always opens up some very interesting debates.

A

Thank you AMcHarg. I agree that we don't play only in spite of the number of positions but my thought is that not only the brain is without comparison - the chessgame is really an extreme game. No wonder some people study it all their lives. I do it myself, not fulltime though.

Another interesting question is exactly as you wrote: intuition. But we also play by recognition. Forexample:

Try to -as Bobby Fisher has recommended, to place all the pieces on the board in another order (random order but in the same rows). This should take away the old and learned thinking and provoke the intuition and creativeness.

By the way: In  terms of mathematical statistics it has ben stated that when a number is about 10^400 it can be accepted as infinite.

So chess is in a 'infinite' game in practical life.

I have just noticed that chess960 on this site actually uses the Fisher suggestion to put the pieces randomly. Looks like fun. Have any of you some experience with that. What do you think about it. Must be fun but not the real stuff  

Chess960 gets rid of opening preparations. It's pure chess play, not memorization.