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.
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.
Hi all. I believe I can make some sort of input on this area.
In a mathematical point of view, there was a mathematician called Claude Shannon who, in 1950 published a paper called "Programming a Computer for Playing Chess". This paper included game-tree combinatrial theory which can approximate the finite number of combinations that can be made in any game. This would be easy for a game such as Naughts and Crosses (Tic-tac-toe) as there is much less complexity.
With regards to chess we can use the basic combinational theory nCr (n!/r!(n-r!)), but use a slight variation due to all pieces being able to move in different directions, influenced where they can move by other pieces either blocking their path or being on their landing square. The equation is denoted as:
(8 x 8)! / (8x4)! x (8!)^2 x (2!)^6
Which comes to roghly 10^43, but doesn't include illegal positions and so the value is estimated at around 10^50 this is also close to the amount of atoms that make up Earth... so pretty fascinating really!
..to go for all the trouble of necroing a thread :P
The short answer is (btw, not only are there combinations but also permutations, re: Algebra 101) for all practical purposes infinite.
Numerically? Here, ponder this: 1/0. That's close enough.
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?