# chess mathmatics **URL:** \ **Category:** Cafe Society\ **Created:** [November 24, 2001, 6:21pm UTC](https://boards.straightdope.com/t/chess-mathmatics/95045 "2001-11-24T18:21:29Z")\ **Posts on this page:** 9\ **Page:** 1
**Author:** ![clayton\_e](https://avatars.discourse-cdn.com/v4/letter/c/c57346/32.png) [@clayton\_e](https://boards.straightdope.com/u/clayton_e)\ **Post date:** [November 24, 2001, 6:21pm UTC](https://boards.straightdope.com/t/chess-mathmatics/95045/1 "2001-11-24T18:21:29Z")
I’ve heard some debate on how many possible games of chess can be played. After the first couple moves the number is huge on the possible moves. That was a few years ago. Since then has anybody designed a program to figure out how many possible games of chess there are? (this is, of course not including someone killing time by moving a piece back and forth) ---
**Author:** ![mighty\_maxx](https://avatars.discourse-cdn.com/v4/letter/m/2acd7d/32.png) [@mighty\_maxx](https://boards.straightdope.com/u/mighty_maxx)\ **Post date:** [November 24, 2001, 8:08pm UTC](https://boards.straightdope.com/t/chess-mathmatics/95045/2 "2001-11-24T20:08:48Z")
> [@](#): > > If you were to fully develop the entire tree for all possible chess moves, the total number of board positions is about 1,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000, or (10120), give or take a few. I pulled that from this [link.](http://www.howstuffworks.com/chess1.htm) ---
**Author:** ![mighty\_maxx](https://avatars.discourse-cdn.com/v4/letter/m/2acd7d/32.png) [@mighty\_maxx](https://boards.straightdope.com/u/mighty_maxx)\ **Post date:** [November 24, 2001, 8:14pm UTC](https://boards.straightdope.com/t/chess-mathmatics/95045/3 "2001-11-24T20:14:52Z")
I forgot to mention that calculating that total is still up for debate as the OP said. I just thought that even a good guess at the number was a unbelievable amount, and should be shared. I’ve not been able to find any information on program that is in the works that can actually calculate the exact total. ---
**Author:** ![Bill\_H](https://avatars.discourse-cdn.com/v4/letter/b/a5b964/32.png) [@Bill\_H](https://boards.straightdope.com/u/Bill_H)\ **Post date:** [November 25, 2001, 9:04am UTC](https://boards.straightdope.com/t/chess-mathmatics/95045/4 "2001-11-25T09:04:08Z")
I particularly liked the other numbers mentioned in that cite for comparison: > [@](#): > > The total number of board positions is about 10[sup]120[/sup], give or take a few. That’s a very big number. For example, there have only been 10[sup]26[/sup] nanoseconds since the big bang. There are only thought to be 10[sup]75[/sup] atoms in the entire universe. When you consider that the Milky Way galaxy contains billions of suns and there are billions of galaxies, you can see that’s a lot of atoms - chess is a pretty intricate game! ---
**Author:** ![kniz](https://avatars.discourse-cdn.com/v4/letter/k/c37758/32.png) [@kniz](https://boards.straightdope.com/u/kniz)\ **Post date:** [November 25, 2001, 3:50pm UTC](https://boards.straightdope.com/t/chess-mathmatics/95045/5 "2001-11-25T15:50:26Z")
I do not believe there could be a mathematical way of figuring the number of moves, since the pieces can make such different moves, which is then effected by the order in which the pieces are taken. Then you speak of chess moves and therefore hopefully are eliminating some of the possible moves because they are stupid moves. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [November 25, 2001, 11:29pm UTC](https://boards.straightdope.com/t/chess-mathmatics/95045/6 "2001-11-25T23:29:00Z")
Well, a typical game lasts in the neighborhood of 60 moves per side, and I recall hearing that in a typical game position, there’s usually about 30 legal moves available, which would give us 30[sup]120[/sup] (about 1.8\*10[sup]177[/sup]) possible games (more than the number of positions, since a game consists of many positions, in a particular order). Of course, that’s assuming typical games. There’s no reason at all that a theoretical chess game couldn’t last much longer, increasing the number immensely. In fact, there’s no theoretical upper limit on the length of a game (nothing obligates either player to declare draw in a threefold repetition, or an “insufficient power to mate” situation), so we’d necessarily have to say that there’s an infinite number of possible chess games, most of which are incredibly boring. For instance, one possible game is for White and Black to move their knights back and forth 9,283,761 times each, before proceeding with the Fool’s Mate. In another possible game, they do the same, but with 9,283,762 sets of knight moves. You get the point. ---
**Author:** ![The\_Controvert](https://avatars.discourse-cdn.com/v4/letter/t/dec6dc/32.png) [@The\_Controvert](https://boards.straightdope.com/u/The_Controvert)\ **Post date:** [November 26, 2001, 12:02am UTC](https://boards.straightdope.com/t/chess-mathmatics/95045/7 "2001-11-26T00:02:06Z")
> [@](#): > > The total number of board positions is about 10^120, give or take a few. That’s a very big number… chess is a pretty intricate game! Heh, this isn’t really much of an argument, since there are also an infinite number of possible “games” of Pong. ---
**Author:** ![pulykamell](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/pulykamell/32/3166_2.png) [@pulykamell](https://boards.straightdope.com/u/pulykamell)\ **Post date:** [November 26, 2001, 1:50pm UTC](https://boards.straightdope.com/t/chess-mathmatics/95045/8 "2001-11-26T13:50:21Z")
wow! this may be the first time i’ve seen a context in which the word “google” has meaning. for me the more interesting question is how many possible grandmaster level games of chess there are. there’s probably no scientific way of determining this, but my thought comes from a comment in which bobby fischer stated that chess was in danger of being played-out at the grandmaster level. hence his development of [FischerRandomchess](http://www.zillions-of-games.com/games/fischerrandomchess.html). ---
**Author:** ![pulykamell](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/pulykamell/32/3166_2.png) [@pulykamell](https://boards.straightdope.com/u/pulykamell)\ **Post date:** [November 26, 2001, 2:00pm UTC](https://boards.straightdope.com/t/chess-mathmatics/95045/9 "2001-11-26T14:00:56Z")
This[site](http://visualbasic.about.com/library/weekly/aa040201c.htm) states there are 30^100 possible states for a 50-move game. I actually happened upon this site looking for tic-tac-toe statistics. Even tic-tac-toe has over 350,000 possible games. However, given a perfect strategy, you really have only about 100 games (my guess) or so, all ending in a tie. So I think it’s relatively meaningless to talk of possible combinations in this context, other than for reasons of sheer curiosity. To which effect, I will offer you a game with over 10^750 possible games, by [this site’s](http://www.specbench.org/osg/cpu95/news/099go.html) estimate: Go.