Someone already gave you the answer above. It's captured in "the Shannon number", after Claude Shannon, the famous information theorist.
Essentially, the number is greater than the number of electrons in the universe. So it's not likely to be captured anytime soon by a chess computer !
Actually there are 10^43 positions versus 10^80 protons. So we still have a chance of capturing it, lol.
DJHeilke wrote:
Rather interesting about the number of games. But as for the number of positions, I think the sum total of information presented in these posts would give you a fairly accurate estimation. As for computability in solving chess (not just making an AI that can beat everybody on earth), chess is part of a set of problems generally refered to as "NP Complete" many real world problems in business, marketing and other areas are also in this set. What makes NP complete problems really nifty in mathematics is that there is one particularly esoteric NP complete problem that has the following unusual property: any problem that can be proven to be NP complete posesses a unique mathematical transform into the one problem, and a unique transform that can be aplied to the solution of the one problem for every problem in the set of all NP complete. So basically, if you find a way to solve just one of these guys, all the rest fall like dominos. So much attention is given to chess because it is by far the oldest NP complete problem that has been continuously worked on, it gets worked on by a lot of people, and its fun, too :) !!
Please dont say NP-complete [or NP-hard or BPP] if you don't know what you are talking about. Chess is one game, and it is a finite 2-person complete-information game. So solving chess is constant time and constant space. What NP are you talking about?
Where is the parameter n in chess so that we can say it is NP-complete or NP-hard wrt n? You're talking of nxn chess define the rules of nxn chess first.
I hate people showing off with nonsense like this. Read your Aho&Ullman or Papadimitrou properly before talking complexity theory.
Actually I figured it out yesterday with an abacus and a rubiks cube.
The answer is amazing and will blow your mind.
Send $99 to my paypal account and write 25 emails saying Oginschile is cool and I'll explain it to you.
By the way, you will need an abacus and a rubiks cube.
normajeanyates wrote:
Where is the parameter n in chess so that we can say it is NP-complete or NP-hard wrt n? You're talking of nxn chess define the rules of nxn chess first. I hate people showing off with nonsense like this. Read your Aho&Ullman or Papadimitrou properly before talking complexity theory.
I believe n is the number of moves, or plys, whichever you like. Searching a position n plys ahead is exponential in time so is considered NP-complete.
In fact there could be more than what you said in your first post, as you also have to take into account the possibility of castling (2 positions can be identical, but in one castling is illegal because the rook has moved and come back), or en-passant...
I was thinking too hard about this before. Turns out there are only three:
"Winning", "Losing" and "Drawish".
I usually sit up in a chair or something, my legs slightly apart, or sometimes crossed, depending on my mood.
My left hand is usually on my knee or holding a beverage of some kind, while my right hand deftly manouvers the mouse.
I suppose there are other chess positions, but this is the one that works for me.
LOL
Ok, now when all you clever guys are done with cakculating all this, please count all the positions where white has a forced win.....
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:
Unfathomably large is not the same as infinite.
If you stop playing all the bad variations, there is not much left, just ask Hans Berliner...
Berliner, Hans (1999), The System: A World Champion's Approach to Chess, Gambit Publications.
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:
It can't be infinite if you are confined to a 8x8 board. Even if both players have a bishop and are moving it back and forth for an infinite amount of turns (which would normally just be a draw), there is still a finite amount of places they can move..
this might sound elementary,but it seems to me the total would be infinite,a boundless space or extent , chess moves are limitless.
(I'm going for 3-fold repetition on this thread.)
This is a hard one, but I thought about it and it could be a new way to look at chess and/or chess computers. Assuming there is a perfect single move for every position, how many would have to be known to create a theoritical perfect chess computer/player?
To start, there are 7 different possiblilites that can be on a square at one time. A King, Queen, Knight, Bishop, Rook, Pawn, or an empty space. So that means the max possible number of positions would be 7^64 (number of squares) which is somewhere around 1.2 e 54, or 2.4 e54 if you count whose move it is. But then when you start taking out impossible combinations, such as more than 2 king on the board at once, pawns on the back row, more than 10 of a knight, rook, bishop, 9 of a queen, or 8 of a pawn on either side, it gets smaller. And of course there are other board impossibilites, like 8 pawns on the same side lined up vertically, a double knight check, etc.
So has anyone ever heard of someone who has calculated this number? I tried searching for it but it doesn't seem many people have thought as chess this way.
Edit: There would be 13^64 maximum possible positions, because each piece could either be black or white.
It has been said that the number of possible chess positions are greater than the number of atoms in the known universe!
I was thinking too hard about this before. Turns out there are only three:
"Winning", "Losing" and "Drawish".
Very true. Lol 
How much wood would a woodchuck chuck if a woodchuck would chuck wood?