# More chess moves than atoms in universe? **URL:** \ **Category:** Factual Questions\ **Created:** [February 14, 2005, 4:59pm UTC](https://boards.straightdope.com/t/more-chess-moves-than-atoms-in-universe/290029 "2005-02-14T16:59:49Z")\ **Posts on this page:** 20\ **Page:** 1
**Author:** ![MotherBrain](https://avatars.discourse-cdn.com/v4/letter/m/b77776/32.png) [@MotherBrain](https://boards.straightdope.com/u/MotherBrain)\ **Post date:** [February 14, 2005, 4:59pm UTC](https://boards.straightdope.com/t/more-chess-moves-than-atoms-in-universe/290029/1 "2005-02-14T16:59:49Z")
Is it true that there are more possible chess moves than atoms in the universe? ---
**Author:** ![audiobottle](https://avatars.discourse-cdn.com/v4/letter/a/bc8723/32.png) [@audiobottle](https://boards.straightdope.com/u/audiobottle)\ **Post date:** [February 14, 2005, 5:29pm UTC](https://boards.straightdope.com/t/more-chess-moves-than-atoms-in-universe/290029/2 "2005-02-14T17:29:01Z")
What do you mean by possible chess moves? A game could conceivably go on forever with each player just moving their King (or knight, or queen, or whatever) around and around in a circle without doing anything. What are the restrictions on this? ---
**Author:** ![chrisk](https://avatars.discourse-cdn.com/v4/letter/c/6de8d8/32.png) [@chrisk](https://boards.straightdope.com/u/chrisk)\ **Post date:** [February 14, 2005, 5:32pm UTC](https://boards.straightdope.com/t/more-chess-moves-than-atoms-in-universe/290029/3 "2005-02-14T17:32:25Z")
> [@audiobottle](#): > > What do you mean by possible chess moves? A game could conceivably go on forever with each player just moving their King (or knight, or queen, or whatever) around and around in a circle without doing anything. What are the restrictions on this? How about making it possible DIFFERENT moves? Thus, figure out how many possible positions there are of pieces on the chess boards, and then how many uniquely different moves can be made from each? It’s going to be a pretty high number. ---
**Author:** ![Spectre\_of\_Pithecanthropus](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/spectre_of_pithecanthropus/32/12343_2.png) [@Spectre\_of\_Pithecanthropus](https://boards.straightdope.com/u/Spectre_of_Pithecanthropus)\ **Post date:** [February 14, 2005, 5:41pm UTC](https://boards.straightdope.com/t/more-chess-moves-than-atoms-in-universe/290029/4 "2005-02-14T17:41:01Z")
> [@chrisk](#): > > How about making it possible DIFFERENT moves? Thus, figure out how many possible positions there are of pieces on the chess boards, and then how many uniquely different moves can be made from each? > > It’s going to be a pretty high number. Whatever the souce is that the OP is referring to, I’m sure this must be what was meant. Further, I think there would have to be a restriction to legal positions. For instance, both bishops on a side can collectively hit all the squares, but each individual bishop is restricted to either black or white squares. ---
**Author:** ![Garfield226](https://avatars.discourse-cdn.com/v4/letter/g/9e8a1a/32.png) [@Garfield226](https://boards.straightdope.com/u/Garfield226)\ **Post date:** [February 14, 2005, 6:06pm UTC](https://boards.straightdope.com/t/more-chess-moves-than-atoms-in-universe/290029/5 "2005-02-14T18:06:47Z")
> [@Spectre of Pithecanthropus](#): > > Whatever the souce is that the OP is referring to, I’m sure this must be what was meant. Further, I think there would have to be a restriction to legal positions. For instance, both bishops on a side can collectively hit all the squares, but each individual bishop is restricted to either black or white squares. Don’t forget to take into account pawn promotion. You could conceivably have 5 black bishops and 5 white bishops. ---
**Author:** ![chrisk](https://avatars.discourse-cdn.com/v4/letter/c/6de8d8/32.png) [@chrisk](https://boards.straightdope.com/u/chrisk)\ **Post date:** [February 14, 2005, 6:11pm UTC](https://boards.straightdope.com/t/more-chess-moves-than-atoms-in-universe/290029/6 "2005-02-14T18:11:01Z")
> [@Garfield226](#): > > Don’t forget to take into account pawn promotion. You could conceivably have 5 black bishops and 5 white bishops. Or even nine white bishops, allowing for the fact that pawns move sideways one column wherever they capture, and this would affect the color of their promotion square. ---
**Author:** ![lno](https://avatars.discourse-cdn.com/v4/letter/l/a8b319/32.png) [@lno](https://boards.straightdope.com/u/lno)\ **Post date:** [February 14, 2005, 6:12pm UTC](https://boards.straightdope.com/t/more-chess-moves-than-atoms-in-universe/290029/7 "2005-02-14T18:12:22Z")
[howstuffworks.com](http://howstuffworks.com) has an [article](http://computer.howstuffworks.com/chess1.htm) on chess computing. This is the pertinent part: > [@](#): > > Let’s say you start with a chess board set up for the start of a game. Each player has 16 pieces. Let’s say that white starts. White has 20 possible moves: > > ``` > * The white player can move any pawn forward one or two positions. > * The white player can move either knight in two different ways. > > ``` > > The white player chooses one of those 20 moves and makes it. > > For the black player, the options are the same: 20 possible moves. So black chooses a move. > > Now white can move again. This next move depends on the first move that white chose to make, but there are about 20 or so moves white can make given the current board position, and then black has 20 or so moves it can make, and so on. > > This is how a computer looks at chess. It thinks about it in a world of “all possible moves,” and it makes a big tree for all of those moves, like this: > > (image not included here) > > In this tree, there are 20 possible moves for white. There are 20 \* 20 = 400 possible moves for black, depending on what white does. Then there are 400 \* 20 = 8,000 for white. Then there are 8,000 \* 20 = 160,000 for black, and so on. 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 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 thought to be only 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 that’s a whole lot of atoms. That number is dwarfed by the number of possible chess moves. Chess is a pretty intricate game! ---
**Author:** ![Garfield226](https://avatars.discourse-cdn.com/v4/letter/g/9e8a1a/32.png) [@Garfield226](https://boards.straightdope.com/u/Garfield226)\ **Post date:** [February 14, 2005, 6:12pm UTC](https://boards.straightdope.com/t/more-chess-moves-than-atoms-in-universe/290029/8 "2005-02-14T18:12:48Z")
> [@chrisk](#): > > Or even nine white bishops, allowing for the fact that pawns move sideways one column wherever they capture, and this would affect the color of their promotion square. Indeed. Hadn’t thought of that possibility. ---
**Author:** ![Exapno\_Mapcase](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/exapno_mapcase/32/1051_2.png) [@Exapno\_Mapcase](https://boards.straightdope.com/u/Exapno_Mapcase)\ **Post date:** [February 14, 2005, 6:23pm UTC](https://boards.straightdope.com/t/more-chess-moves-than-atoms-in-universe/290029/9 "2005-02-14T18:23:35Z")
> [@audiobottle](#): > > What do you mean by possible chess moves? A game could conceivably go on forever with each player just moving their King (or knight, or queen, or whatever) around and around in a circle without doing anything. What are the restrictions on this? IIRC, after 30 moves this is an automatic stalemate. The number of physical things is a relatively low number compared to almost any computation of permutations. The number of possible variations of a deck of cards is 52! or 80658175170943878571660636856403766975289505440883277824000000000000 or 10[sup]68[/sup]. It would take only a slightly larger deck to outnumber all particles in the universe. Two decks would be vastly huger even than 10[sup]100[/sup] or googol. ---
**Author:** ![chrisk](https://avatars.discourse-cdn.com/v4/letter/c/6de8d8/32.png) [@chrisk](https://boards.straightdope.com/u/chrisk)\ **Post date:** [February 14, 2005, 6:34pm UTC](https://boards.straightdope.com/t/more-chess-moves-than-atoms-in-universe/290029/10 "2005-02-14T18:34:38Z")
As an aside, I wonder how complicated it would be to construct some kind of computer program that would take as input a chess board, and determine whether or not there was some legal sequence of moves from a regulation start that could lead to that point. It would obviously get impractical to solve the question from a brute force angle, (as lno’s cite covers,) and could be very convoluted to solve the question deductively. Some of the simpler aspects that immediately occur to me… - if white has two pawns on the same column, but black still has all of his pieces and pawns, that’s a pretty obvious disqualifier. - either player could conceivably transpose his knight and rook on the same side without disturbing any of the pieces surrounding them, but not a knight and a bishop. I remember reading a chess puzzler in scientific american which hinged on the following succession of deductions. - The position was declared to be one reachable during the course of legal play. Black apparently had all of his pieces and pawns in their starting places, and white apparently had all of his pieces in starting places, but had no more pawns left. - However, black’s king and queen were switched, (noticeable because one of them must always start on a black square.) - the king and queen cannot transpose in their true starting places without disturbing at least one of the pawns in front of them or to the sides, which can then not return to their starting positions. Therefore… [spoiler]- No pieces were actually at their starting places - the board is upside down from the way it appears. Black’s pieces are all pinned against black’s eighth file by his pawns. Black can only resolve this situation by hopping his knights over the pawns, moving pawns in to promote them, which creates an opening in the row of pawns on seventh file. - As it happens, black does not have time. White has a mate in four by using one of his own knights to checkmate the (thoroughly trapped) black king across the layer of pawns. If black does not play defensively against this option, white can actually make the mate in three, but black cannot stop it entirely.[/spoiler] Quite a trick question, if you ask me. On preview… > [@Exapno Mapcase](#): > > IIRC, after 30 moves this is an automatic stalemate. An automatic draw, I believe. ‘Stalemate’ in chess is a particular draw condition where one player is not in check but cannot make a legal move. There is also draw by perpetual check, and the 30-move rule, whose name I do not remember offhand. Incidentally, I’ve always wondered what chess would be like if the following rule changes were adopted to alter the stalemate rule. - if player A stalemates B, (A moves such that B has no legal move,) B is considered to be constrained to ‘offer a draw’ to A, but A is not obliged to accept. He can instead play on, with B being unable to move until such time as the stalemate is lifted. In other words, if A wants to play on, he may immediately make any other legal move that he can, without a response from B other than the verbal response ‘stalemate’. - if A’s move keeps B under stalemate, he can continue to move or change his mind and accept the draw. If it lifts the stalemate and allows B one or more legal moves, B must now make one of them. - in the case of a double stalemate… (A has no further legal moves himself, which is possible although I cannot remember an example,) then the draw is final with no exceptions. ---
**Author:** ![rjk](https://avatars.discourse-cdn.com/v4/letter/r/ed655f/32.png) [@rjk](https://boards.straightdope.com/u/rjk)\ **Post date:** [February 14, 2005, 6:36pm UTC](https://boards.straightdope.com/t/more-chess-moves-than-atoms-in-universe/290029/11 "2005-02-14T18:36:13Z")
> [@audiobottle](#): > > What do you mean by possible chess moves? A game could conceivably go on forever with each player just moving their King (or knight, or queen, or whatever) around and around in a circle without doing anything. What are the restrictions on this? IIRC, three occurences of the same position make the game a draw. They might have to all occur within 40 moves, but I’m not very confident of that. ---
**Author:** ![Garfield226](https://avatars.discourse-cdn.com/v4/letter/g/9e8a1a/32.png) [@Garfield226](https://boards.straightdope.com/u/Garfield226)\ **Post date:** [February 14, 2005, 6:42pm UTC](https://boards.straightdope.com/t/more-chess-moves-than-atoms-in-universe/290029/12 "2005-02-14T18:42:08Z")
> [@chrisk](#): > > Incidentally, I’ve always wondered what chess would be like if the following rule changes were adopted to alter the stalemate rule. > > - if player A stalemates B, (A moves such that B has no legal move,) B is considered to be constrained to ‘offer a draw’ to A, but A is not obliged to accept. He can instead play on, with B being unable to move until such time as the stalemate is lifted. In other words, if A wants to play on, he may immediately make any other legal move that he can, without a response from B other than the verbal response ‘stalemate’. > - if A’s move keeps B under stalemate, he can continue to move or change his mind and accept the draw. If it lifts the stalemate and allows B one or more legal moves, B must now make one of them. > - in the case of a double stalemate… (A has no further legal moves himself, which is possible although I cannot remember an example,) then the draw is final with no exceptions. I believe in most cases, that would result in the first player mating in a few moves. Consider: If you stalemate but have a pawn left, you’d likely be able to promote that pawn and mate with it. There are exceptions of course. If you have other pieces left, you’re free to use them to capture the stalemated player’s pieces and also to take as long as you need to maneuver them to give mate. I’m pretty sure it would usually result in mate for the stalemating player. ---
**Author:** ![chrisk](https://avatars.discourse-cdn.com/v4/letter/c/6de8d8/32.png) [@chrisk](https://boards.straightdope.com/u/chrisk)\ **Post date:** [February 14, 2005, 7:05pm UTC](https://boards.straightdope.com/t/more-chess-moves-than-atoms-in-universe/290029/13 "2005-02-14T19:05:22Z")
> [@rjk](#): > > IIRC, three occurences of the same position make the game a draw. They might have to all occur within 40 moves, but I’m not very confident of that. Yeah, you might be right. I think there could ALSO be a rule along the lines of ‘if both players keep moving for 200 moves, neither of them advancing a pawn, nobody checking anyone, nobody capturing anyone, then the game is considered to be a draw.’ > [@Garfield226](#): > > I believe in most cases, that would result in the first player mating in a few moves. Consider: If you stalemate but have a pawn left, you’d likely be able to promote that pawn and mate with it. There are exceptions of course. > > If you have other pieces left, you’re free to use them to capture the stalemated player’s pieces and also to take as long as you need to maneuver them to give mate. > > I’m pretty sure it would usually result in mate for the stalemating player. Yeah, that makes sense. There would be some stalemating situations where the player who gets the stalemate advantage would not quite be able to drive a fatal attack home, but that would probably be rare. I know that there are some circumstances (king-pawn versus king for example) where the player at a disadvantage would be strongly inclined to lure his opponent into stalemating him, if that is at all possible, since a draw is the best outcome he can hope for. (if you have a king-pawn versus king, with all three pieces on the same column, the lone king on the pawn’s queening file, then the pawn one file away, and the king on the other side, with the lone king to move, that’s a stalemate correct?? The lone king cannot move to either side because he would be in check from the pawn, cannot capture the pawn or move to either side of it because of the enemy king, and yet he is not being attacked where he sits.) I love a chance for some obscure chess talk. 😉 ---
**Author:** ![Walton\_Firm](https://avatars.discourse-cdn.com/v4/letter/w/45deac/32.png) [@Walton\_Firm](https://boards.straightdope.com/u/Walton_Firm)\ **Post date:** [February 14, 2005, 7:20pm UTC](https://boards.straightdope.com/t/more-chess-moves-than-atoms-in-universe/290029/14 "2005-02-14T19:20:20Z")
Nitpick: Actually, the “50 moves rule” (not 30 or 40 or 200) does not say that the game automatically ends in a draw after 50 moves with nothing interesting happening – it only says that either player can _claim_ a draw in that situation. If neither player chooses to claim a draw, then the game can theoretically go on for an infinite number of moves (assuming that no chess clock is used). [Official FIDE chess rules](http://fideonline.com/official/handbook.asp?level=EE101) ---
**Author:** ![Whack-a-Mole](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/whack-a-mole/32/141_2.png) [@Whack-a-Mole](https://boards.straightdope.com/u/Whack-a-Mole)\ **Post date:** [February 14, 2005, 10:42pm UTC](https://boards.straightdope.com/t/more-chess-moves-than-atoms-in-universe/290029/15 "2005-02-14T22:42:58Z")
As an interesting aside it should be noted that as amazing as the possibilities are in Chess the possibilites in the Chinese game Go dwarf it. It is psrtly for this reason that no one has been able to make a computer program even remotely good at playing Go (supposedly the very best out today can’t even beat a mediocre player). > [@](#): > > As a computer scientist would put it, the branching factor is much higher for Go than for chess. In chess the approximate number of possible board positions after only four moves is typically 35 times 35 times 35 times 35 equals 1,500,625. For Go, the number is 200 times 200 times 200 times 200 equals 1,600,000,000 – and far more toward the beginning of a game. Search one ply deeper and the numbers rapidly diverge: about 1.8 billion possible outcomes for chess and 64 trillion for Go. > > Looking ahead 14 moves, or seven plies, in Go creates a search tree not with a mere 35 to the 14th power leaves, as for chess, but with more than 200 to the 14th power leaves. Pruning techniques cut this down to about ten thousand trillion possibilities to consider. Still, a Go computer as fast as Deep Blue (which analyzed some 200 million chess positions per second) would take a year and a half to mull over a single move. > > SOURCE: [http://www.rci.rutgers.edu/~cfs/472\_html/Intro/NYT\_Intro/ChessMatch/ToTest.html](http://www.rci.rutgers.edu/~cfs/472_html/Intro/NYT_Intro/ChessMatch/ToTest.html) ---
**Author:** ![CynicalGabe](https://avatars.discourse-cdn.com/v4/letter/c/3e96dc/32.png) [@CynicalGabe](https://boards.straightdope.com/u/CynicalGabe)\ **Post date:** [February 14, 2005, 10:48pm UTC](https://boards.straightdope.com/t/more-chess-moves-than-atoms-in-universe/290029/16 "2005-02-14T22:48:19Z")
I’m pretty sure there are only 13,383,816 possible chess moves. ---
**Author:** ![emarkp](https://avatars.discourse-cdn.com/v4/letter/e/3be4f8/32.png) [@emarkp](https://boards.straightdope.com/u/emarkp)\ **Post date:** [February 14, 2005, 11:17pm UTC](https://boards.straightdope.com/t/more-chess-moves-than-atoms-in-universe/290029/17 "2005-02-14T23:17:55Z")
> [@Martin Wolf](#): > > Actually, the “50 moves rule” (not 30 or 40 or 200) does not say that the game automatically ends in a draw after 50 moves with nothing interesting happening – it only says that either player can _claim_ a draw in that situation. If neither player chooses to claim a draw, then the game can theoretically go on for an infinite number of moves (assuming that no chess clock is used). Also note that USCF rules might be different on that point (but probably aren’t). Additionally, it’s 50 reversible moves. Capturing a piece, advancing a pawn, etc. starts the count over. Also, some endgames are proven to require more than 50 moves to force a mate (I think K vs. K+N+B is one but don’t hold me to that), and have limits higher than 50–though I’ve never seen that matter in practice. The answer to the original question is that it’s not the number of moves, but legal games (i.e. the movelist from start to finish) that outnumber atoms in the universe. ---
**Author:** ![rjk](https://avatars.discourse-cdn.com/v4/letter/r/ed655f/32.png) [@rjk](https://boards.straightdope.com/u/rjk)\ **Post date:** [February 14, 2005, 11:27pm UTC](https://boards.straightdope.com/t/more-chess-moves-than-atoms-in-universe/290029/18 "2005-02-14T23:27:13Z")
> [@Martin Wolf](#): > > Nitpick: > > Actually, the “50 moves rule” (not 30 or 40 or 200) does not say that the game automatically ends in a draw after 50 moves with nothing interesting happening – it only says that either player can _claim_ a draw in that situation. If neither player chooses to claim a draw, then the game can theoretically go on for an infinite number of moves (assuming that no chess clock is used). > > [Official FIDE chess rules](http://fideonline.com/official/handbook.asp?level=EE101) Of course I know I should have looked up the rules, but where’s the fun in that? Thanks! ---
**Author:** ![Meeko](https://avatars.discourse-cdn.com/v4/letter/m/e495f1/32.png) [@Meeko](https://boards.straightdope.com/u/Meeko)\ **Post date:** [February 15, 2005, 12:37am UTC](https://boards.straightdope.com/t/more-chess-moves-than-atoms-in-universe/290029/19 "2005-02-15T00:37:27Z")
No no, You can promote Pawns to Queens right? Maybe we mean “fairy chess pieces” :eek: Squirels, KnightRiders, Windmills, Jokers, Wafils, Edgehogs… ---
**Author:** ![Meeko](https://avatars.discourse-cdn.com/v4/letter/m/e495f1/32.png) [@Meeko](https://boards.straightdope.com/u/Meeko)\ **Post date:** [February 15, 2005, 12:40am UTC](https://boards.straightdope.com/t/more-chess-moves-than-atoms-in-universe/290029/20 "2005-02-15T00:40:57Z")
> [@chrisk](#): > > As an aside, I wonder how complicated it would be to construct some kind of computer program that would take as input a chess board, and determine whether or not there was some legal sequence of moves from a regulation start that could lead to that point. > > It would obviously get impractical to solve the question from a brute force angle, (as lno’s cite covers,) and could be very convoluted to solve the question deductively. Some of the simpler aspects that immediately occur to me… > > - if white has two pawns on the same column, but black still has all of his pieces and pawns, that’s a pretty obvious disqualifier. > - either player could conceivably transpose his knight and rook on the same side without disturbing any of the pieces surrounding them, but not a knight and a bishop. > I remember reading a chess puzzler in scientific american which hinged on the following succession of deductions. > - The position was declared to be one reachable during the course of legal play. Black apparently had all of his pieces and pawns in their starting places, and white apparently had all of his pieces in starting places, but had no more pawns left. > - However, black’s king and queen were switched, (noticeable because one of them must always start on a black square.) > - the king and queen cannot transpose in their true starting places without disturbing at least one of the pawns in front of them or to the sides, which can then not return to their starting positions. Therefore… > > [spoiler]- No pieces were actually at their starting places - the board is upside down from the way it appears. Black’s pieces are all pinned against black’s eighth file by his pawns. Black can only resolve this situation by hopping his knights over the pawns, moving pawns in to promote them, which creates an opening in the row of pawns on seventh file. > > - As it happens, black does not have time. White has a mate in four by using one of his own knights to checkmate the (thoroughly trapped) black king across the layer of pawns. If black does not play defensively against this option, white can actually make the mate in three, but black cannot stop it entirely.[/spoiler] > > Quite a trick question, if you ask me. > > On preview… > An automatic draw, I believe. ‘Stalemate’ in chess is a particular draw condition where one player is not in check but cannot make a legal move. There is also draw by perpetual check, and the 30-move rule, whose name I do not remember offhand. > Incidentally, I’ve always wondered what chess would be like if the following rule changes were adopted to alter the stalemate rule. > > - if player A stalemates B, (A moves such that B has no legal move,) B is considered to be constrained to ‘offer a draw’ to A, but A is not obliged to accept. He can instead play on, with B being unable to move until such time as the stalemate is lifted. In other words, if A wants to play on, he may immediately make any other legal move that he can, without a response from B other than the verbal response ‘stalemate’. > - if A’s move keeps B under stalemate, he can continue to move or change his mind and accept the draw. If it lifts the stalemate and allows B one or more legal moves, B must now make one of them. > - in the case of a double stalemate… (A has no further legal moves himself, which is possible although I cannot remember an example,) then the draw is final with no exceptions. I thought there was a whole series of Chess problems where the entire concept of the puzzle was to your self reconstruct how the game started. [Next page](https://boards.straightdope.com/t/more-chess-moves-than-atoms-in-universe/290029.md?page=2)