Fundamental particles in universe: 10^80 - 10^85
Game-tree complexity of chess: 10^120
Literally took all of seventeen seconds to google.
Number of chess positions and molecules in the universe
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Well, it's good to see that google has plumbed the depths (and heights and widths) of the universe.
well wrong? prove it !
Aug 21, 2012
0
#25
Chess positions 10^43 (Shannon number)
Atoms in observable universe 10^81
Possible sequences of moves (legal games) 10^120 with 40 moves as a limit
The OP asked about positions, not sequences of moves. They are quite different.
Best website on the subject: http://wismuth.com/chess/chess.html
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also i will add it is a different mathematical equation if you take a single game in motion at any time and count the possible moves for say a mate than if you take the game it self in say unmoved the possibilities for the next moves could be infinite , then as with the atoms in a universe it is the opposite if you could stop them all and freeze them in time you may come up with a equation to count them but in motion it is infinite
Ziryab wrote:
Atoms in observable universe 10^81
Now if only they could find all that dark matter...
dark matter was found in the equations of the game ....go
The really hard part is how much the atoms all look alike...
@Popcorn - that´s a very interesting game ... 12.dxc5 however is a serious mistake by White, as removal of a piece will considerably lessen the number of remaining possibilities, and the Universe now has good chances on the c file.
Ben_Lui wrote:
@Popcorn - that´s a very interesting game ... 12.dxc5 however is a serious mistake by White, as removal of a piece will considerably lessen the number of remaining possibilities, and the Universe now has good chances on the c file.
Haha, very good.
especially if you include pineapple
Does the number of atoms in the observable universe includes the atoms in the chess pieces? If yes, universe wins :)
I think the really great thing about chess is not the sheer amount of "possible" meaningless positions, but rather the fact that there are so many openings/ways of playing that are equally good (especially at club level). If you think about it it's really amazing.
Popcorn179 wrote:
There are 26,830 plausible games of naughts and crosses (excluding symetrically identical games). But against a smart player you'll probably only ever see 10 or 20 different games. (All resulting in a tie).
That's the point!
Samurai-X wrote:
Okay, there is a quote I read somewhere a long time ago about how the number of molecules in the universe (or earth, something along those lines) and how that number is equvalent or less than the number of different chess moves or positions. Does anyone know? If you do please post it.
i wasn't being serious when i wrote it!
Does this mean that the X n' Y's of chess conversation will go on forever?....Oh no! The northern hemisphere is rolling into winter soon.
let's save ourselves, Stevie!!
I'm gonna revise my e4's n' .....How does the knights move again....And get a big fluffy dressing gown...
blake78613 wrote:
the number chess positions is much smaller. Each square has 15 possibilities (empty, WKing,WQqueen,WRook,Wknight,WBishop,WPawn,BKing,BQqueen,Bknight,BBishop,and BPawn) with 64 squares, that would mean that the possibilities would equal 15 to the 64th power. This number includes a lot of illegal positions (no kings, more than one king of a color, more than 8 pawns, ect.) Thus clearly the number of positions is far less than the number of atoms. Now the number of possible games might well be more than the number of atoms in the universe. I don't know, but it is clear that the number of positions is considerably less.
All right, I am going to have to revise my absolute limit on number of positons. My figure of 15^64th gave the number of possible visible positions, there are some non-visible factors that go into a position. (a). whose turn it is, so multiply the basic number by 2. (b). Both B & W either have the right to castle or have have lost it so multiply by 4 (c) the side to move either has no possibilities of en passant capture or has at most 8 possibilites, so multiply basic number by 9. So we can confidently say that at most there is at most (15^64th)x(73) possible positions. The number of legal positons is many magnitudes smaller. Some one gave Shannon's estimate which is probably close.
Still, note that that is technically a man-made imposition...in actuality a game "ending" in perpetual check could indeed be said to go on forever.