# 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:** 2
**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:** [February 15, 2005, 3:09am UTC](https://boards.straightdope.com/t/more-chess-moves-than-atoms-in-universe/290029/21 "2005-02-15T03:09:31Z")
Oh, I can reconstruct how the game started; that’s easy! Now, how it looked after the first move is a bit less trivial… And pawns can indeed promote to queens, **Meeko** , but I’m not sure I see the relevance to that… Incidentally, they can also promote to rooks, bishops, or knights, if the promoting player so desires, but this essentially never happens outside of chess puzzles. They cannot, however, promote to kings, remain as pawns after reaching the 8th rank, promote to nonstandard chess pieces, or promote to a piece of a different color (this last one also has shown up in a puzzle or two, and in fact it was such a puzzle that inspired the change in rules to disallow it). Also, you’ve all missed one other condition for a draw in chess, which is in fact the most common: If both players agree that a game is a draw, it’s a draw. ---
**Author:** ![by-tor](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/by-tor/32/266_2.png) [@by-tor](https://boards.straightdope.com/u/by-tor)\ **Post date:** [February 15, 2005, 3:28am UTC](https://boards.straightdope.com/t/more-chess-moves-than-atoms-in-universe/290029/22 "2005-02-15T03:28:34Z")
Is this the visible universe they are talking about? Or are they talking about the whole universe, most of which we can’t see, let alone know how much matter is in it? ---
**Author:** ![borschevsky](https://avatars.discourse-cdn.com/v4/letter/b/97f17d/32.png) [@borschevsky](https://boards.straightdope.com/u/borschevsky)\ **Post date:** [February 15, 2005, 3:38am UTC](https://boards.straightdope.com/t/more-chess-moves-than-atoms-in-universe/290029/23 "2005-02-15T03:38:46Z")
> [@Meeko](#): > > 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. Yes, those puzzles are called _proof games_. I know of one computer program for solving such problems: [Natch](http://natch.free.fr/Natch.html). ---
**Author:** ![zoid](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/zoid/32/336_2.png) [@zoid](https://boards.straightdope.com/u/zoid)\ **Post date:** [February 15, 2005, 3:47am UTC](https://boards.straightdope.com/t/more-chess-moves-than-atoms-in-universe/290029/24 "2005-02-15T03:47:36Z")
I can’t believe no one has posted this yet: [Great short story by Isaac Asimov](http://www.research.ibm.com/deepblue/learn/html/e.8.2.html) ---
**Author:** ![shijinn](https://avatars.discourse-cdn.com/v4/letter/s/cc9497/32.png) [@shijinn](https://boards.straightdope.com/u/shijinn)\ **Post date:** [February 15, 2005, 4:54am UTC](https://boards.straightdope.com/t/more-chess-moves-than-atoms-in-universe/290029/25 "2005-02-15T04:54:16Z")
click [here](http://home.earthlink.net/~mrob/pub/math/numbers-12.html) if you like numbers. > [@](#): > > … > 5.23198…×10[sup]49[/sup] > This is an upper bound on the number of possible chess positions, by my reckoning. It allows between 2 and 32 pieces in play, with no more than 16 of one color, including exactly one king of each color, and up to 8 pawns of each color (any of which might have been promoted to another piece). It is higher than Shannon’s estimate because it allows pawn promotion. > The number of possible chess _game_s is much higher. See also 4.63×10[sup]170[/sup]. > … > 1×10[sup]110 [/sup] > An estimate of the number of subatomic particles that it would take to fill all the space in the universe. See also 2.835×10[sup]183[/sup]. (From Straight Dope) > … > 4.63×10[sup]170[/sup] > This is (approximately) the number of possible positions in Go, played on a 19×19 board, as given by M. Beeler in HAKMEM item 96. See also 1.15x10[sup]42[/sup]. > … > [sub]10[/sub]10[sup]50[/sup] > An estimate of the number of possible chess games, given by G. H. Hardy (“Ramanujan: Twelve Lectures on Subjects Suggested by His Life and Work”, 1999). See also 1.15x10[sup]42[/sup]. > … these numbers close enough? ---
**Author:** ![Saltire](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/saltire/32/553_2.png) [@Saltire](https://boards.straightdope.com/u/Saltire)\ **Post date:** [February 15, 2005, 5:13am UTC](https://boards.straightdope.com/t/more-chess-moves-than-atoms-in-universe/290029/26 "2005-02-15T05:13:49Z")
> [@zoid](#): > > I can’t believe no one has posted this yet: > > [Great short story by Isaac Asimov](http://www.research.ibm.com/deepblue/learn/html/e.8.2.html) Definitely a great story. Definitely a short story (only 180 words). But not an Asimov story. It was written by Arthur C. Clarke. It was published in Asimov’s magazine. ---
**Author:** ![zoid](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/zoid/32/336_2.png) [@zoid](https://boards.straightdope.com/u/zoid)\ **Post date:** [February 15, 2005, 5:35am UTC](https://boards.straightdope.com/t/more-chess-moves-than-atoms-in-universe/290029/27 "2005-02-15T05:35:09Z")
> [@Saltire](#): > > Definitely a great story. Definitely a short story (only 180 words). But not an Asimov story. It was written by Arthur C. Clarke. It was published in Asimov’s magazine. I apologize for any misinformation, it was unintentional. I stand corrected. It IS a great read though 😉 ---
**Author:** ![RayMan](https://avatars.discourse-cdn.com/v4/letter/r/e495f1/32.png) [@RayMan](https://boards.straightdope.com/u/RayMan)\ **Post date:** [February 15, 2005, 5:38am UTC](https://boards.straightdope.com/t/more-chess-moves-than-atoms-in-universe/290029/28 "2005-02-15T05:38:05Z")
> [@emarkp](#): > > 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. According to USCF rules, either player may claim draw after 50 move _pairs_ have been completed, without a piece being captured or a pawn having moved. King versus king, knight, and bishop is a textbook won position for the side with the minor pieces–this checkmate can be obtained in less than 50 moves, provided the player knows how to do so. I admit, it is very difficult. This assumes, of course, that there are no other pieces on the board, or some other contrived position where one side may force stalemate or capture one of the minor pieces (if the bishop or knight is captured, the position is a textbook draw). Chess puzzlers are such an inventive group, that I felt I had to qualify my post with that last sentence, lest I invite a nitpick! ---
**Author:** ![glee](https://avatars.discourse-cdn.com/v4/letter/g/b5a626/32.png) [@glee](https://boards.straightdope.com/u/glee)\ **Post date:** [February 15, 2005, 10:24am UTC](https://boards.straightdope.com/t/more-chess-moves-than-atoms-in-universe/290029/29 "2005-02-15T10:24:02Z")
> [@MotherBrain](#): > > Is it true that there are more possible chess moves than atoms in the universe? Fox + James (‘The Complete Chess Addict’) estimate the number of possible different 40 move games as 25 \* 10^115.# They also say the number of estimated electrons in the Universe is 10 ^ 79. ---
**Author:** ![glee](https://avatars.discourse-cdn.com/v4/letter/g/b5a626/32.png) [@glee](https://boards.straightdope.com/u/glee)\ **Post date:** [February 15, 2005, 10:25am UTC](https://boards.straightdope.com/t/more-chess-moves-than-atoms-in-universe/290029/30 "2005-02-15T10:25:39Z")
> [@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? I posted in another thread that a chess game must end by checkmate, stalemate, 3 time repetition or the 50 move rule. Fox + James say the longest possible game is 5,949 moves. ---
**Author:** ![glee](https://avatars.discourse-cdn.com/v4/letter/g/b5a626/32.png) [@glee](https://boards.straightdope.com/u/glee)\ **Post date:** [February 15, 2005, 10:28am UTC](https://boards.straightdope.com/t/more-chess-moves-than-atoms-in-universe/290029/31 "2005-02-15T10:28:15Z")
> [@Exapno Mapcase](#): > > IIRC, after 30 moves this is an automatic stalemate. 50 moves, provided neither payer has moved a pawn or made a capture. The World Chess Federation (FIDE) did allow 100 moves in certain positions, after it was shown one side could win by force, but olny taking longer than 50 moves (to move a pawn or make a capture). ---
**Author:** ![glee](https://avatars.discourse-cdn.com/v4/letter/g/b5a626/32.png) [@glee](https://boards.straightdope.com/u/glee)\ **Post date:** [February 15, 2005, 10:33am UTC](https://boards.straightdope.com/t/more-chess-moves-than-atoms-in-universe/290029/32 "2005-02-15T10:33:27Z")
> [@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. As borschevsky said, Natch is a computer program to solve proof chess games (where a particular position can only be reached after the stated number of moves in one way.) > [@chrisk](#): > > 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. I think this is composed by Dunsany. > [@chrisk](#): > > 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. You can also agree a draw and claim a 3-time repetition. The 50 move rule (not 30) is called the ‘50 move rule’! ---
**Author:** ![glee](https://avatars.discourse-cdn.com/v4/letter/g/b5a626/32.png) [@glee](https://boards.straightdope.com/u/glee)\ **Post date:** [February 15, 2005, 10:34am UTC](https://boards.straightdope.com/t/more-chess-moves-than-atoms-in-universe/290029/33 "2005-02-15T10:34:54Z")
> [@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. 50 moves (but the position must be exactly the same). It isn’t an automatic draw - the player to move can claim, but doesn’t have to. ---
**Author:** ![glee](https://avatars.discourse-cdn.com/v4/letter/g/b5a626/32.png) [@glee](https://boards.straightdope.com/u/glee)\ **Post date:** [February 15, 2005, 10:39am UTC](https://boards.straightdope.com/t/more-chess-moves-than-atoms-in-universe/290029/34 "2005-02-15T10:39:07Z")
> [@emarkp](#): > > Also note that USCF rules might be different on that point (but probably aren’t). Federations have limited jurisdiction on what they can change (time limits are one example). > [@emarkp](#): > > 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. K vs. K+N+B is mate in 33 moves maximum (and usually shorter). I think the game that caused FIDE (World Chess Federation) to apply 100 moves was by Grandmaster Timman. It was K, R + pa2 v K, black-squared bishop and pa3. ---
**Author:** ![glee](https://avatars.discourse-cdn.com/v4/letter/g/b5a626/32.png) [@glee](https://boards.straightdope.com/u/glee)\ **Post date:** [February 15, 2005, 10:40am UTC](https://boards.straightdope.com/t/more-chess-moves-than-atoms-in-universe/290029/35 "2005-02-15T10:40:49Z")
> [@Meeko](#): > > No no, You can promote Pawns to Queens right? > Maybe we mean “fairy chess pieces” :eek: Squirels, KnightRiders, Windmills, Jokers, Wafils, Edgehogs… You can promote to rook, bishop or knight as well. It’s spelled Nightrider! ---
**Author:** ![glee](https://avatars.discourse-cdn.com/v4/letter/g/b5a626/32.png) [@glee](https://boards.straightdope.com/u/glee)\ **Post date:** [February 15, 2005, 10:44am UTC](https://boards.straightdope.com/t/more-chess-moves-than-atoms-in-universe/290029/36 "2005-02-15T10:44:34Z")
> [@RayMan](#): > > King versus king, knight, and bishop is a textbook won position for the side with the minor pieces–this checkmate can be obtained in less than 50 moves, provided the player knows how to do so. I admit, it is very difficult. It’s not as difficult as people think. I teach it to pupils at my School! Nopw if you want difficult, try K+2B v K+N, or even K+R+B v K+2N. Worst case = mate in 223 moves (Nunn ’ Secrets of Pawnless Endings’). ---
**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, 12:24pm UTC](https://boards.straightdope.com/t/more-chess-moves-than-atoms-in-universe/290029/37 "2005-02-15T12:24:24Z")
[QUOTE=Chronos] They cannot, however, promote to kings, remain as pawns after reaching the 8th rank, promote to nonstandard chess pieces, or promote to a piece of a different color (this last one also has shown up in a puzzle or two, and in fact it was such a puzzle that inspired the change in rules to disallow it). [QUOTE] What about a Knight? You mean you can’t play chess with a Horse of a different color? 😃 Also, chaning Colors of a pawn? I assume (Hopefully) you mean black to white or vice-versa. If Not, Chess is becomming way to much like Magic The Gathering. * * * Pawn 1 Creature-Chess Piece At the end of your upkeep choose any one color. Pawn becomes that color until your next upkeep. If this is done put a time counter on Pawn. At any time there are 8 or more time counters on pawn, it looses all abilities and becomes a copy of any other chess piece besides Pawn. ## If a creature could deal damage to Pawn, but does not, you may tap this card to remove that creature from the game. 1/1 ---
**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:** [February 15, 2005, 9:34pm UTC](https://boards.straightdope.com/t/more-chess-moves-than-atoms-in-universe/290029/38 "2005-02-15T21:34:10Z")
I did actually see a chess puzzle once where white was to move, and could (if it were allowed, as it used to be) checkmate by promoting a pawn to a black bishop (this worked by trapping the black king, since you can’t capture your own piece). In fact, the puzzle was set up in such a way that if White made any other move (including promoting to a white piece), Black had mate in two. You also can’t promote a pawn to a green piece, or a blue piece, or an ultraviolet piece, but that’s hardly interesting (though I appreciate the M:tG analogy :)). **glee** , are you sure about your two examples? I’m not convinced that K+2B can beat K+N (it seems like the opponent could force a trade of knight for bishop), and K+R+B vs. K+2N looks like an easy win for K+R+B (he should be able to force a trade of the bishop for one knight, and then either capture the other knight or keep it at a distance using the rook, leaving the textbook K+R vs. K). ---
**Author:** ![chrisk](https://avatars.discourse-cdn.com/v4/letter/c/6de8d8/32.png) [@chrisk](https://boards.straightdope.com/u/chrisk)\ **Post date:** [February 15, 2005, 9:49pm UTC](https://boards.straightdope.com/t/more-chess-moves-than-atoms-in-universe/290029/39 "2005-02-15T21:49:23Z")
> [@Chronos](#): > > You also can’t promote a pawn to a green piece, or a blue piece, or an ultraviolet piece, but that’s hardly interesting (though I appreciate the M:tG analogy :)). That reminds me, if I can hop games for a minute, to a bridge joke I heard about a man playing bridge in hell, with the devil as one of his opponents. Guy picks up a perfect lay-down hand… ace-king-queen in all four suits, plus a stray jack. Depending on which version of the joke, he is sometimes wary enough to ask the devil about certain possible variants of bridge in hell that might defeat this hand… if there are other cards that rank above ace, maybe. But he doesn’t find the trick in any event, and bids seven no trumps, which the devil doubles and he, nervously, redoubles. The devil leads out the ace of a strange green suit. “Having no hippogriffs?” The poor guy admits that he has none of these hippogriffs, and thirteen of them are led out against him, sinking him for a horrible loss. 😉 (what else do you expect??) ---
**Author:** ![glee](https://avatars.discourse-cdn.com/v4/letter/g/b5a626/32.png) [@glee](https://boards.straightdope.com/u/glee)\ **Post date:** [February 15, 2005, 11:15pm UTC](https://boards.straightdope.com/t/more-chess-moves-than-atoms-in-universe/290029/40 "2005-02-15T23:15:27Z")
> [@Chronos](#): > > **glee** , are you sure about your two examples? I’m not convinced that K+2B can beat K+N (it seems like the opponent could force a trade of knight for bishop), and K+R+B vs. K+2N looks like an easy win for K+R+B (he should be able to force a trade of the bishop for one knight, and then either capture the other knight or keep it at a distance using the rook, leaving the textbook K+R vs. K). I’m certain - it’s all information from computer databases. Basically the program generates all legal positions of the pieces required, then sorts them into order of mate, 1 move away from mate etc. So if you have a forced win in a position, the computer can keep giving you the correct move to play. Similarly it can give drawing lines. In K+2B v K+N, the N **can’t** exchange itself for a bishop. In K+R+B vs. K+2N, there’s usually no point in exchanging B for N, since **most positions with K+R v K+N are drawn**. [Previous page](https://boards.straightdope.com/t/more-chess-moves-than-atoms-in-universe/290029.md?page=1) [Next page](https://boards.straightdope.com/t/more-chess-moves-than-atoms-in-universe/290029.md?page=3)