Answers.Body: <p>Chess hasn't been solved and it won't be in the next decades (barring ridiculous computing advancement involving quantum computing or such drastic changes).</p>
  
  <p>You can calculate in your head for the first move: White has 20 options and black has 20 responses; we already have 400 possible positions. This number grows ridiculously fast, the number of possible positions for an 80 move game is unimaginably huge.</p>
  
  <p>Also, if chess were solved, chess tournaments and championships would basically be exercises in memorisation, rendering it pointless. (EDIT: this is rather overstated, see comments.)</p>
  
  <p>Currently, chess is solved for any position with seven pieces (including kings). The latest estimate I heard for 8-men tablebases was somewhere in the 2020s, and of course the time needed for an additional piece grows exponentially. I don't expect to see chess anywhere <em>near</em> solved in my lifetime (again, barring truly exceptional computing advancements).</p>
  
Answers.ContentLicense: CC BY-SA 3.0
Answers.CreationDate: 2016-01-23T23:49:27.533Z
Answers.Text: There are already 7-man tablebases.
Answers.UserDisplayName: Tony Ennis
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Answers.CreationDate: 2016-01-23T23:50:07.363Z
Answers.Text: Really? Where? Then I misremembered, please replace 6 with 7 and 7 with 8. @TonyEnnis
Answers.UserDisplayName: 11684
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Answers.CreationDate: 2016-01-24T00:28:38.223Z
Answers.Text: 6 is available online for free. 7 is for-purchase.  http://tb7.chessok.com/
Answers.UserDisplayName: Tony Ennis
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Answers.CreationDate: 2016-01-24T14:12:21.307Z
Answers.Text: Per ETD's comment, even if chess were solved, humans would *not* be able to memorize the solution. So the comment about "pointless" is incorrect.
Answers.UserDisplayName: Jeff Y
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Answers.CreationDate: 2016-01-28T18:48:24.440Z
Answers.Text: @JeffY Point taken, although solving chess would drastically change the nature of tournaments.
Answers.UserDisplayName: 11684
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Answers.CreationDate: 2016-01-29T11:54:48.563Z
Answers.Text: @11684 How so? Does having 7-piece tablebases drastically change the nature of endgame play in tournaments? I don't see it.
Answers.UserDisplayName: Jeff Y
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Answers.CreationDate: 2016-01-29T21:57:21.440Z
Answers.Text: @JeffY we would gain an enormous amount of information about the game, even without memorising concrete lines; some endgames which were always thought to be a draw turned out to be a win and vice versa, we learned from tablebases. What we could learn from a 32 piece tablebase would be far more significant. Opening theory would need to be drastically updated. Maybe there are some as of yet unknown subtleties. But of course all of this is just speculation until chess is fully solved.
Answers.UserDisplayName: 11684
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Answers.Text: @11684 All true. But how would that change *tournaments*? I can see that it might open a whole lot *more* opening lines (as non-losers), although I can't see having  to memorize any less to play them. And I can see that it would change postmortems of games certainly. But I just don't see human-vs-human games being affected in any significant way, just as human-vs-human 7-piece endgames are not affected by presence of 7-piece tablebases.
Answers.UserDisplayName: Jeff Y
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Answers.Text: I understand your points, you might well be right. I think it comes down to how good Grandmasters are at generalising the information gained from the Solution (and to what degree this information is generalisable). My remark about opening theory is rather inaccurate in combination with my remark about not memorising concrete lines - in case of opening theory memorisation is of course inevitable, but it wouldn't be more work than current day theory. @JeffY
Answers.UserDisplayName: 11684
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Answers.Text: @11684 I think John Nunn has tried to do this with endgames and tablebases. http://www.amazon.com/Nunns-Chess-Endings-John-Nunn/dp/1906454213 The reviews make is sound like the message is very hard to digest. But maybe you're right that Grandmasters will be able to glean something...
Answers.UserDisplayName: Jeff Y
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Answers.CreationDate: 2016-12-18T14:53:14.167Z
Answers.Text: @11684 I think you are underestimating how soon chess will be solved. "The time needed for an additional piece [may grow] exponentially" but so does the speed of our computers. http://chess.stackexchange.com/questions/16117/when-will-we-solve-chess
Answers.UserDisplayName: ma11hew28
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Answers.CreationDate: 2016-12-18T16:29:09.963Z
Answers.Text: @mattdipasquale Although it is true the speed of our computers has grown exponentially, the growth factor is only 2, whereas the factor of adding another piece is much larger.
Answers.UserDisplayName: 11684
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Answers.CreationDate: 2016-12-18T16:58:37.277Z
Answers.Text: The growth factor may be 2 now, but it's increasing exponentially according to [Ray Kurzweil's Law of Accelerating Returns](http://www.kurzweilai.net/the-law-of-accelerating-returns).
Answers.UserDisplayName: ma11hew28
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Answers.CreationDate: 2016-12-18T22:03:39.453Z
Answers.Text: I don't know about this law. I based my answer and comments on Moore's law, and besides that I'm expecting the increasing curve of processing speed to flatten because we have arrived at a point where CPUs are reaching hard limits like the maximum speed of an electrical signal traveling from RAM to the CPU. Without transforming the basic structure of CPUs, soon we'll be at maximum speed. @mattdipasquale
Answers.UserDisplayName: 11684
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Answers.UserDisplayName: 11684
Answers.Body: <p>Chess games may be finite but the number of possible games is beyond imagining.</p>
  
  <p>There is no known sequence of moves that guarantees either side a win or draw.</p>
  
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Answers.UserDisplayName: Tony Ennis
Answers.Body: <p>In 1949 information scientist Shannon produced an estimate that it would take 10^90 years to solve chess with 1 MHz computer. Computer power and storage technology has improved considerably since then (aka Moore's law), where computer power and storage capacity doubles every year. That taken into account, it would take approximately 300 years to come up with a computer, that would be 10^90 times more powerful than Shannon's 1 MHz machine. There are no forseeable restraints in computer development. For example Intel's 4004 was made with 10 micrometer photolithography technology whereas current i9s are made with 14 nm technology. When the cores are becoming both more powerful and smaller, it is easy to stuff more cores in a same physical size than the previous years half as powerful ancestors. In photolithography we have just entered ultraviolet wavelength category of below 10 nm, but there exists wavelenghts such as gamma rays, whose wavelength is 1 picometer (that is 10.000 more smaller). A hydrogen atom is 0,1 nm in size, but i.e. quarks are about 200 times smaller than 1 picometer (that is 0.43 x 10^−15 mm, <a href="https://www.theguardian.com/science/life-and-physics/2016/apr/07/how-big-is-a-quark" rel="noreferrer">https://www.theguardian.com/science/life-and-physics/2016/apr/07/how-big-is-a-quark</a>)</p>
  
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Answers.UserDisplayName: Markku Litola
Answers.Body: <p>Here's an answer I originally wrote at <a href="https://cstheory.stackexchange.com/questions/6563/what-is-the-computational-complexity-of-solving-chess/38102#38102">https://cstheory.stackexchange.com/questions/6563/what-is-the-computational-complexity-of-solving-chess/38102#38102</a>.</p>
  
  <p>A perfect chess player will always force a win when they can force a win and force a draw when they can force a draw. Of course, at any point if they can force a win, they can also force a draw. Also when ever one player can't force a win, the other player can force a draw. Chess without the 50 move rule or 3 fold repetition rule might not be as hard to solve as you think. It can be shown that adding in the 3 fold repetition rule makes no difference to whether a player can force a win or a draw. The number of possible ways a game can go after n moves keeps growing exponentially with n. The number of states that can occur after n moves on the other hand doesn't keep on growing exponentially because it can't exceed the total number of possible states that can occur in a legal game. According to <a href="https://en.wikipedia.org/wiki/Game_complexity" rel="nofollow noreferrer">https://en.wikipedia.org/wiki/Game_complexity</a>, there are about 10^47 states that can occur in a legal game of chess.</p>
  
  <p>Chess can be solved as follows: take a set of states that we can prove contains all states that can occur in a legal game of chess without the 3-fold repetition rule or 50 move rule. Two different states could have the same arrangement of chess pieces and differ by whose turn it is, whether you have the right to capture by en passant, and whether a given king or rook has the right to ever castle again. Next, take all states where the minimum number of moves white can force a win in is 1 which must occur on white's turn. Next take all states where the minimum number of moves white can force a win in is 2, which means it's black's turn and no matter which move they can make, white can force a win in 1 move. Next take all states where the minimum number of moves white can force a win in is 3, which means white has a move that will give them a forced win in 2 moves but can't force a win in 1 move. Next take all states where the minimum number of moves white can force a win in is 4, which means it's black's turn and no matter which move they make, white can force a win in 3 moves but white can't currently force a win in 2 moves. Once we get to a number such that there are no states where the minimum number of moves white can force a win in is that number, we've already found all the states that white can force a win in. We can find all states that black can force a win in in a similar way. All the remaining states are ones where both players can force a draw.</p>
  
  <p>Since there are about 10^47 states that can occur in a legal game of chess, it would take more than our lifetime to use brute force to build a computer that will play chess perfectly no matter how it's opponent plays. I believe it hasn't been proven that there's no much shorter algorithm that can tell you how to play perfectly no matter how your opponent plays. For instance maybe only a small fraction of states that can occur in a legal game can occur in a game where you play the way that algorithm tells you to play so that algorithm works even though it only tells you how to play perfectly in all states that can occur when you have always followed that algorithm since the beginning of the game but not in all states that can occur in a legal game. Maybe in addition to that, that algorithm is a complex algorithm that for each state that can occur in a game where you have always followed it, takes way fewer steps to compute an optimal move than the number of states that can occur in a game where you have always followed it. According to <a href="http://onlinelibrary.wiley.com/doi/10.1002/sres.2171/abstract" rel="nofollow noreferrer">http://onlinelibrary.wiley.com/doi/10.1002/sres.2171/abstract</a>, the evolutionary learning laboratories are planning to solve complex problems. Maybe some day, they'll figure out a complex strategy for playing chess perfectly. Maybe even if an algorithm that's very short and takes very few steps to compute an optimal move in any state that can occur in a game where you have always followed that algorithm doesn't exist, that still doesn't stop a human from being able to learn how to play chess perfectly. Maybe a human could continuously figure things out and retain what they figured out figure more things out from what they previously figured out and retain them by some complex method, be able to figure out from the pieces of information they previously figured out how to play perfectly with a 90 minute base time and 30 second increments in any state that can occur in a game where they play the way they play after learning way fewer bits of information than the number of states that can occur in a game where they play the way they do which they can learn in their life time especially if the technology to live 6000 years gets invented.</p>
  
  <p>It's probably even simpler for a player to have a strategy that ensures that if their opponent plays perfectly, they will also play perfectly. I suspect both players have a forced draw from the beginning of the game. It's probably simpler to have a strategy that forces a draw than a strategy that guarantees that if your opponent gives you a forced win, you will not lose it. A strategy that forces a draw is also a strategy that ensures that if your opponent plays perfectly, you will play perfectly. If they play perfectly, they will not give you a forced win in the first place so you will not lose a forced win after they give you one.</p>
  
  <p>Update:</p>
  
  <p>According to <a href="https://www.youtube.com/watch?v=mOqmLYlFdBo" rel="nofollow noreferrer">https://www.youtube.com/watch?v=mOqmLYlFdBo</a>, AlphaZero is a neural network that plays chess better than any other chess program including Stockfish. After it was created, it gained that ability in only a few hours. I don't know exactly how it works but I believe it does something like simulate natural selection on chess strategies. Suppose you have some beings playing rated chess tournaments with a 90 minute base time and 30 second increments except that there is no 3-fold repetition rule or 50 rule and there is no resigning and each game counts as a draw if nobody checkmates after 4,000 moves. Furthermore, suppose they have no interaction with one another except for the tournaments where they are randomly paired with somebody of a very similar rating and their probability of cloning themselves in a lab is tiny t approximately 1 in a billion each time they play a game and varies linearly with their rating after the game and that there are a billion individuals and each time one is created, a randomly picked one disappears. You may be thinking natural selection cannot select for a new trait if there isn't an advantageous pathway towards it. I'm not sure that's the case. Some individuals might have genome that gives a small chance of undergoing a partially ordered major rearrangement when it produces its clone. Then very rarely and occasionally, the rearrangement will improve the chess playing strategy. Then the descendants of the single mutant clone will multiply into very large numbers. Then that will select for the tendency to rarely and occasionally mutate in a random way. Then that can lead to evolution of creatures that are really good at trying different ways of thinking until they come up with a solution.</p>
  
Answers.ContentLicense: CC BY-SA 3.0
Answers.CreationDate: 2017-11-30T17:21:49.657Z
Answers.Text: The link to your answer on computer-science-SE is helpful. However, I am not sure it was worth copy-pasting its whole text.
Answers.UserDisplayName: Evargalo
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Answers.Text: Dead link to the original answer? Also, I don’t think it’s true that “at any point if they can force a win, they can also force a draw”.
Answers.UserDisplayName: Ry-
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2021-09-12T17:23:56.193Z
Answers.Text: As Ry mentioned, we can easily imagine scenarios where if forcing a win you cannot force a draw. Easiest way is to imagine a mate in 1 or loose situation. Unless we of course count the "hey, I have mate like this, would you like to draw?" situation (and the other player would obviously answer yes).
Answers.UserDisplayName: zozo
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Answers.CreationDate: 2017-04-30T22:46:04.720Z
Answers.LastActivityDate: 2020-06-13T03:25:11.827Z
Answers.LastEditDate: 2020-06-13T03:25:11.827Z
Answers.UserDisplayName: Timothy
Answers.Body: <p>Another point is that the chess game is finite but only with the 75 move rule (the game is drawn if there are no captures or pawn moves for 75 moves). Before, this the rule with draw by consecutive threefold repetition of the position, the so-called 'German Rule', allowed an infinite number of games <a href="http://homepages-fb.thm.de/boergens/english/stamps/briefmarke059engl.htm" rel="nofollow noreferrer">as shown by Max Euwe</a>.</p>
  
Answers.ContentLicense: CC BY-SA 3.0
Answers.CreationDate: 2017-01-17T10:32:10.873Z
Answers.Text: With the rule of three times the same position the game would be obviously finite. Just think that there is a finite number of possible positions and that every position can be repeated at most twice.
  
  The linked article shows that game can be infinite under the "German rule", which asks for the same sequence to be played from same position three times *consecutively*
Answers.UserDisplayName: sharcashmo
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Answers.CreationDate: 2017-01-17T11:46:54.310Z
Answers.Text: Thanks, i messed up with my explanation, it's three times the same sequence of moves :).
Answers.UserDisplayName: Sylvain Julmy
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Answers.CreationDate: 2016-05-20T10:57:40.630Z
Answers.LastActivityDate: 2018-09-27T15:11:08.333Z
Answers.LastEditDate: 2018-09-27T15:11:08.333Z
Answers.UserDisplayName: Sylvain Julmy
Answers.Body: <p>We know that an optimal strategy exists since when in a game there are a finite amount of players and a finite amount of strategies for each player, one can show that a Nash equilibra exists (so you are playing your optimal response to the other player's optimal response and viceversa).</p>
  
  <p>The thing is that even if we know that such strategy exists, we don't know exactly which strategy is it because of computational limitations.</p>
  
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Answers.CreationDate: 2016-05-18T17:48:48.037Z
Answers.LastActivityDate: 2016-05-18T17:48:48.037Z
Answers.UserDisplayName: user10321
Answers.Body: <p>no</p>
  
  <p>we cannot say who should win or if it should be a draw</p>
  
  <p>there are way too many move combinations to even try to compute the answer with current technology by trying all possible moves and seeing the results</p>
  
  <p>then we would have to prune backwards to see what the answer would be and if it were unique</p>
  
  <p>and if we could the game would not be fun any longer </p>
  
Answers.ContentLicense: CC BY-SA 3.0
Answers.CreationDate: 2016-11-27T22:39:52.230Z
Answers.Text: "if we could the game would not be fun any longer" --> People still play connect-4 and some other solved games.
Answers.UserDisplayName: Franck Dernoncourt
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Answers.CreationDate: 2016-02-06T04:14:24.440Z
Answers.LastActivityDate: 2016-02-06T04:14:24.440Z
Answers.UserDisplayName: joe sixpak
Answers.Body: <p>At the beginning of the 20th century, the belief that chess would be solved soon (called "the draw death of chess") was popular. The world champion J.-R. Capablanca tended to believe so. The games of the match Capablanca-Alekhine (almost all in the Queen's Gambit Declined) also confirmed this belief. See, for example: <a href="https://en.wikipedia.org/wiki/Capablanca_chess" rel="nofollow">https://en.wikipedia.org/wiki/Capablanca_chess</a> .</p>
  
  <p>The revolution of modern openings (King's Indian etc), then the revolution of artificial intelligence provided intuitive proofs that solving chess is not so simple. Indeed, today grandmaster games are often analyzed using a program and this reveals lines that the players (even the best ones) oversaw during the game.</p>
  
  <p>This being said, an "absolute computational power" can indeed solve chess in the sense of the theory of computation.</p>
  
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Answers.CreationDate: 2016-05-19T12:42:19.490Z
Answers.LastActivityDate: 2016-05-19T12:42:19.490Z
Answers.UserDisplayName: Alexandre Aksenov
Answers.Body: <p>The human mind is much more complex than a tic-tac-toe game. So, you can find a good strategy for play such game.</p>
  
  <p>Chess is quite diferent. Chess is a heuristic game.</p>
  
  <p>you can not put a soldier in charge above a general. The mind of a general is much more complex than a soldier mind, in military terms. It is only a analogy.</p>
  
  <p>Complexity, that is what matters.</p>
  
  <p>You need to be more complex than chess. It is impossible, but you must try, you need to try. You can achieve it in several levels. Many factors are involved. Efforts are important, but many of us make great efforts with poor results. But there are people who made little efforts and achieve excellent results.</p>
  
  <p>Nature is unfair.</p>
  
  <p>But if you learn chess at age of five your chances will be better than if you learn the game at age of ten.</p>
  
  <p>Of course, if you used to stay lots of hours in front of TV when you was a child you wasted your intelligence.</p>
  
  <p>Last, but not least, sorry about my english.</p>
  
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Answers.CreationDate: 2016-01-28T22:46:33.973Z
Answers.LastActivityDate: 2016-01-28T22:46:33.973Z
Answers.UserDisplayName: Fred
Answers.Body: <p>2000-3000 elos more to go until perfect play, so the current
  top engines could at least double their strength.
  Chess is actually closer to its infancy than to its later stages.
  For example, current top engines would guess only one out of 5 
  best opening moves.
  Still a long way to go.</p>
  
Answers.ContentLicense: CC BY-SA 3.0
Answers.CreationDate: 2017-12-01T09:56:28.110Z
Answers.Text: How do you get to that number?
Answers.UserDisplayName: Annatar
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Answers.CreationDate: 2017-12-02T07:50:11.607Z
Answers.Text: Different tests have been conducted and reported on Talkchess forum, the most advanced chess forum on the Internet, but my observations also point in that direction. Also, by comparing the engine evaluations 20 years ago, now, and what could still be improved in that area.
Answers.UserDisplayName: Lyudmil Tsvetkov
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Answers.CreationDate: 2017-12-01T07:15:20.553Z
Answers.LastActivityDate: 2017-12-01T07:15:20.553Z
Answers.UserDisplayName: Lyudmil Tsvetkov
Answers.Body: <p>Because of the observation you make, that the tree of possible game paths for chess is finite, chess is indeed solv<strong>able</strong> in exactly the same sense that tic-tac-toe is. So optimal strategies for chess do exist; however, no one has any idea what they are. Whereas tic-tac-toe is solved thanks to a quite small space of possible games, chess is nowhere near solved because its space of possible games far outstrips what could be dealt with by current computing technology.</p>
  <p>As noted in another answer, endgame tablebases exhibit optimal play for all positions with limited numbers of pieces. So in those settings, we have solutions that are as explicit and concrete as are those for tic-tac-toe. But it's important to note that while one can easily teach/remember the optimal strategy for tic-tac-toe and swiftly become a perfect unassisted tic-tac-toe player, the amount of information behind, say, the <a href="https://web.archive.org/web/20220518132941/https://chessok.com/?page_id=27966" rel="noreferrer">7-piece Lomonosov tablebases</a>, is 140 terabytes. There is no concise description of optimal 7-man strategy that one could learn/remember and then play perfectly without assistance.</p>
  
Answers.ContentLicense: CC BY-SA 3.0
Answers.CreationDate: 2016-01-24T04:51:09.733Z
Answers.Text: It may help to mention that there is a lack of consensus as to whether the initial position is a forced win for white, a draw, or even (by some bizarrely complex zugzwang) a forced win for black.  This means that we don't even know whether playing the optimal strategy can guarantee a draw.
Answers.UserDisplayName: Kevin
Answers.ContentLicense: CC BY-SA 3.0
Answers.CreationDate: 2016-01-24T14:18:13.383Z
Answers.Text: There is no "lack of consensus". Overwhelming consensus is "draw": https://en.wikipedia.org/wiki/First-move_advantage_in_chess.
Answers.UserDisplayName: Jeff Y
Answers.ContentLicense: CC BY-SA 3.0
Answers.CreationDate: 2016-01-24T17:05:21.747Z
Answers.Text: @JeffY Maybe there is some sense of consensus, but we can't know until we have 32-men tablebases.
Answers.UserDisplayName: 11684
Answers.ContentLicense: CC BY-SA 3.0
Answers.CreationDate: 2016-01-24T18:05:43.520Z
Answers.Text: No, **overwhelming** consensus, based on results and analysis, human and machine.
Answers.UserDisplayName: Jeff Y
Answers.ContentLicense: CC BY-SA 3.0
Answers.CreationDate: 2016-01-24T18:29:22.363Z
Answers.Text: @JeffY, I think that instead of the distracting phrase about "lack of consensus," Kevin really meant to just focus on there being a "lack of proof." I think we all agree that, no matter any overwhelming consensus of opinion that exists (and I agree with you that most tend to believe the game is a theoretical draw), and no matter any empirical evidence from the many games played by humans and/or engines (both of which play sub-optimally), none of it rules out with certainty any of the theoretical possibilities for chess (win for white/draw/win for black).  .....
Answers.UserDisplayName: ETD
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Answers.CreationDate: 2016-01-24T18:32:04.867Z
Answers.Text: In short, I think JeffY is absolutely right that there is a sizable consensus of *belief* that chess is a theoretical draw, and that's perfectly consistent with the accurate point from Kevin and 11684 that we still don't *know* whether chess is a theoretical draw or not. I think you all probably see eye-to-eye more than the comments above suggest at first glance.
Answers.UserDisplayName: ETD
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Answers.CreationDate: 2016-01-27T08:55:50.580Z
Answers.Text: I'm just wondering, what is the maximum possible number of chess moves, What is the maximum number of different chess games?
Answers.UserDisplayName: Tobi Alafin
Answers.ContentLicense: CC BY-SA 3.0
Answers.CreationDate: 2016-12-03T08:14:54.807Z
Answers.Text: Is there an approximate number. Can't we use combinatorics to determine a nice upper limit?
Answers.UserDisplayName: Tobi Alafin
Answers.ContentLicense: CC BY-SA 3.0
Answers.CreationDate: 2017-05-08T19:43:24.790Z
Answers.Text: You did not prove that a human can't learn how to play Chess perfectly in tournaments unassisted in their life time, and you certainly didn't prove that Chess requires as much time to solve as the number of legal games that can occur with the 50 move rule. My answer doesn't claim to know things that haven't been proven.
Answers.UserDisplayName: Timothy
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Answers.CreationDate: 2017-05-08T20:11:40.623Z
Answers.Text: @Timothy, I agree that I didn't prove those things; but I also didn't intend to make such claims in the first place. Where I wrote, for instance, "There is no concise description of optimal 7-man strategy that one could learn," I didn't intend to claim that it's a *theoretically impossibility* for such a concise description to exist; rather, I meant no more and no less than that, at present, the most compact presentation available of 7-man strategy is the 140 terabytes of tablebases. (cont.)
Answers.UserDisplayName: ETD
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Answers.CreationDate: 2017-05-08T20:13:11.700Z
Answers.Text: ... So that if one were naively hoping to memorize 7-man strategy as straightforwardly as one can memorize tic-tac-toe strategy, one simply cannot do so with the 7-man solutions that we have at hand. That is the extent of my claim, and any stronger claim is not intended. I hope that clarifies.
Answers.UserDisplayName: ETD
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Answers.CreationDate: 2017-05-08T20:28:04.677Z
Answers.Text: I was trying to write my comment as feedback for future Stack Exchange answers and not as absolutely insisting on future answers being a certain way.
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Answers.Text: @TobiAlafin: The number of different chess games is unknown because the number of available moves from each position in the tree of moves has not be cataloged.
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Body: <p>Chess is a zero-sum game of limited decisions. The number of possible moves at any given point, and the number of possible states of the board, are all finite.</p>
  
  <p>Tic-Tac-Toe, is one of the easiest examples of a solved game. I can't remember how many years it's been since I last lost a Tic-Tac-Toe match. Does any such "optimal strategy" exist for chess?</p>
  
  <p>Is there any strategy that will guarantee the player would grasp victory or, at worst, a draw?</p>
  
  <p>If there is, please shed some light on it.</p>
  
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2020-06-13T12:19:50.467Z
Comments.Text: Please note that, if such a strategy was known, chess would be a very uninteresting game. The fact taht this site exists is probably good evidence that chess isn't solved.
Comments.UserDisplayName: David
Tags: <strategy><theory><solving>
Title: Is chess a solved game?
ThreadText: # Is chess a solved game?
  
  (Asked by: username_0 on 2016-01-23)
  
  Chess is a zero-sum game of limited decisions. The number of possible moves at any given point, and the number of possible states of the board, are all finite.
  
  Tic-Tac-Toe, is one of the easiest examples of a solved game. I can't remember how many years it's been since I last lost a Tic-Tac-Toe match. Does any such "optimal strategy" exist for chess?
  
  Is there any strategy that will guarantee the player would grasp victory or, at worst, a draw?
  
  If there is, please shed some light on it.
  
  **Tags:** strategy, theory, solving
  
  > **Comments:**
  > **username_1**: Please note that, if such a strategy was known, chess would be a very uninteresting game. The fact taht this site exists is probably good evidence that chess isn't solved.  
  
  ---
  
  ## 11 answers
  
  ### Answer by username_20 on 2016-01-24. Score: 40 | Accepted answer
  
  Because of the observation you make, that the tree of possible game paths for chess is finite, chess is indeed solv**able** in exactly the same sense that tic-tac-toe is. So optimal strategies for chess do exist; however, no one has any idea what they are. Whereas tic-tac-toe is solved thanks to a quite small space of possible games, chess is nowhere near solved because its space of possible games far outstrips what could be dealt with by current computing technology.
  
  As noted in another answer, endgame tablebases exhibit optimal play for all positions with limited numbers of pieces. So in those settings, we have solutions that are as explicit and concrete as are those for tic-tac-toe. But it's important to note that while one can easily teach/remember the optimal strategy for tic-tac-toe and swiftly become a perfect unassisted tic-tac-toe player, the amount of information behind, say, the [7-piece Lomonosov tablebases](https://web.archive.org/web/20220518132941/https://chessok.com/?page_id=27966), is 140 terabytes. There is no concise description of optimal 7-man strategy that one could learn/remember and then play perfectly without assistance.
  
  > **Comments:**
  > **username_21**: It may help to mention that there is a lack of consensus as to whether the initial position is a forced win for white, a draw, or even (by some bizarrely complex zugzwang) a forced win for black.  This means that we don't even know whether playing the optimal strategy can guarantee a draw.  
  > **username_4**: There is no "lack of consensus". Overwhelming consensus is "draw": https://en.wikipedia.org/wiki/First-move_advantage_in_chess.  
  > **username_2**: @JeffY Maybe there is some sense of consensus, but we can't know until we have 32-men tablebases.  
  > **username_4**: No, **overwhelming** consensus, based on results and analysis, human and machine.  
  > **username_20**: @JeffY, I think that instead of the distracting phrase about "lack of consensus," username_21 really meant to just focus on there being a "lack of proof." I think we all agree that, no matter any overwhelming consensus of opinion that exists (and I agree with you that most tend to believe the game is a theoretical draw), and no matter any empirical evidence from the many games played by humans and/or engines (both of which play sub-optimally), none of it rules out with certainty any of the theoretical possibilities for chess (win for white/draw/win for black).  .....  
  > **username_20**: In short, I think JeffY is absolutely right that there is a sizable consensus of *belief* that chess is a theoretical draw, and that's perfectly consistent with the accurate point from username_21 and username_2 that we still don't *know* whether chess is a theoretical draw or not. I think you all probably see eye-to-eye more than the comments above suggest at first glance.  
  > **username_0**: I'm just wondering, what is the maximum possible number of chess moves, What is the maximum number of different chess games?  
  > **username_22**: @TobiAlafin: The number of different chess games is unknown because the number of available moves from each position in the tree of moves has not be cataloged.  
  > **username_0**: Is there an approximate number. Can't we use combinatorics to determine a nice upper limit?  
  > **username_7**: You did not prove that a human can't learn how to play Chess perfectly in tournaments unassisted in their life time, and you certainly didn't prove that Chess requires as much time to solve as the number of legal games that can occur with the 50 move rule. My answer doesn't claim to know things that haven't been proven.  
  > **username_20**: @username_7, I agree that I didn't prove those things; but I also didn't intend to make such claims in the first place. Where I wrote, for instance, "There is no concise description of optimal 7-man strategy that one could learn," I didn't intend to claim that it's a *theoretically impossibility* for such a concise description to exist; rather, I meant no more and no less than that, at present, the most compact presentation available of 7-man strategy is the 140 terabytes of tablebases. (cont.)  
  > **username_20**: ... So that if one were naively hoping to memorize 7-man strategy as straightforwardly as one can memorize tic-tac-toe strategy, one simply cannot do so with the 7-man solutions that we have at hand. That is the extent of my claim, and any stronger claim is not intended. I hope that clarifies.  
  > **username_7**: I was trying to write my comment as feedback for future Stack Exchange answers and not as absolutely insisting on future answers being a certain way.  
  
  ---
  
  ### Answer by username_2 on 2016-01-23. Score: 14
  
  Chess hasn't been solved and it won't be in the next decades (barring ridiculous computing advancement involving quantum computing or such drastic changes).
  
  You can calculate in your head for the first move: White has 20 options and black has 20 responses; we already have 400 possible positions. This number grows ridiculously fast, the number of possible positions for an 80 move game is unimaginably huge.
  
  Also, if chess were solved, chess tournaments and championships would basically be exercises in memorisation, rendering it pointless. (EDIT: this is rather overstated, see comments.)
  
  Currently, chess is solved for any position with seven pieces (including kings). The latest estimate I heard for 8-men tablebases was somewhere in the 2020s, and of course the time needed for an additional piece grows exponentially. I don't expect to see chess anywhere *near* solved in my lifetime (again, barring truly exceptional computing advancements).
  
  > **Comments:**
  > **username_3**: There are already 7-man tablebases.  
  > **username_2**: Really? Where? Then I misremembered, please replace 6 with 7 and 7 with 8. @TonyEnnis  
  > **username_3**: 6 is available online for free. 7 is for-purchase.  http://tb7.chessok.com/  
  > **username_4**: Per username_20's comment, even if chess were solved, humans would *not* be able to memorize the solution. So the comment about "pointless" is incorrect.  
  > **username_2**: @JeffY Point taken, although solving chess would drastically change the nature of tournaments.  
  > **username_4**: @username_2 How so? Does having 7-piece tablebases drastically change the nature of endgame play in tournaments? I don't see it.  
  > **username_2**: @JeffY we would gain an enormous amount of information about the game, even without memorising concrete lines; some endgames which were always thought to be a draw turned out to be a win and vice versa, we learned from tablebases. What we could learn from a 32 piece tablebase would be far more significant. Opening theory would need to be drastically updated. Maybe there are some as of yet unknown subtleties. But of course all of this is just speculation until chess is fully solved.  
  > **username_4**: @username_2 All true. But how would that change *tournaments*? I can see that it might open a whole lot *more* opening lines (as non-losers), although I can't see having  to memorize any less to play them. And I can see that it would change postmortems of games certainly. But I just don't see human-vs-human games being affected in any significant way, just as human-vs-human 7-piece endgames are not affected by presence of 7-piece tablebases.  
  > **username_2**: I understand your points, you might well be right. I think it comes down to how good Grandmasters are at generalising the information gained from the Solution (and to what degree this information is generalisable). My remark about opening theory is rather inaccurate in combination with my remark about not memorising concrete lines - in case of opening theory memorisation is of course inevitable, but it wouldn't be more work than current day theory. @JeffY  
  > **username_4**: @username_2 I think John Nunn has tried to do this with endgames and tablebases. http://www.amazon.com/Nunns-Chess-Endings-John-Nunn/dp/1906454213 The reviews make is sound like the message is very hard to digest. But maybe you're right that Grandmasters will be able to glean something...  
  > **username_5**: @username_2 I think you are underestimating how soon chess will be solved. "The time needed for an additional piece [may grow] exponentially" but so does the speed of our computers. http://chess.stackexchange.com/questions/16117/when-will-we-solve-chess  
  > **username_2**: @mattdipasquale Although it is true the speed of our computers has grown exponentially, the growth factor is only 2, whereas the factor of adding another piece is much larger.  
  > **username_5**: The growth factor may be 2 now, but it's increasing exponentially according to [Ray Kurzweil's Law of Accelerating Returns](http://www.kurzweilai.net/the-law-of-accelerating-returns).  
  > **username_2**: I don't know about this law. I based my answer and comments on Moore's law, and besides that I'm expecting the increasing curve of processing speed to flatten because we have arrived at a point where CPUs are reaching hard limits like the maximum speed of an electrical signal traveling from RAM to the CPU. Without transforming the basic structure of CPUs, soon we'll be at maximum speed. @mattdipasquale  
  
  ---
  
  ### Answer by username_3 on 2016-01-23. Score: 9
  
  Chess games may be finite but the number of possible games is beyond imagining.
  
  There is no known sequence of moves that guarantees either side a win or draw.
  
  
  ---
  
  ### Answer by username_6 on 2017-11-30. Score: 5
  
  In 1949 information scientist Shannon produced an estimate that it would take 10^90 years to solve chess with 1 MHz computer. Computer power and storage technology has improved considerably since then (aka Moore's law), where computer power and storage capacity doubles every year. That taken into account, it would take approximately 300 years to come up with a computer, that would be 10^90 times more powerful than Shannon's 1 MHz machine. There are no forseeable restraints in computer development. For example Intel's 4004 was made with 10 micrometer photolithography technology whereas current i9s are made with 14 nm technology. When the cores are becoming both more powerful and smaller, it is easy to stuff more cores in a same physical size than the previous years half as powerful ancestors. In photolithography we have just entered ultraviolet wavelength category of below 10 nm, but there exists wavelenghts such as gamma rays, whose wavelength is 1 picometer (that is 10.000 more smaller). A hydrogen atom is 0,1 nm in size, but i.e. quarks are about 200 times smaller than 1 picometer (that is 0.43 x 10^−15 mm, <https://www.theguardian.com/science/life-and-physics/2016/apr/07/how-big-is-a-quark>)
  
  
  ---
  
  ### Answer by username_11 on 2016-05-20. Score: 5
  
  Another point is that the chess game is finite but only with the 75 move rule (the game is drawn if there are no captures or pawn moves for 75 moves). Before, this the rule with draw by consecutive threefold repetition of the position, the so-called 'German Rule', allowed an infinite number of games [as shown by Max Euwe](http://homepages-fb.thm.de/boergens/english/stamps/briefmarke059engl.htm).
  
  > **Comments:**
  > **username_12**: With the rule of three times the same position the game would be obviously finite. Just think that there is a finite number of possible positions and that every position can be repeated at most twice.  The linked article shows that game can be infinite under the "German rule", which asks for the same sequence to be played from same position three times *consecutively*  
  > **username_11**: Thanks, i messed up with my explanation, it's three times the same sequence of moves :).  
  
  ---
  
  ### Answer by username_7 on 2017-04-30. Score: 4
  
  Here's an answer I originally wrote at <https://cstheory.stackexchange.com/questions/6563/what-is-the-computational-complexity-of-solving-chess/38102#38102>.
  
  A perfect chess player will always force a win when they can force a win and force a draw when they can force a draw. Of course, at any point if they can force a win, they can also force a draw. Also when ever one player can't force a win, the other player can force a draw. Chess without the 50 move rule or 3 fold repetition rule might not be as hard to solve as you think. It can be shown that adding in the 3 fold repetition rule makes no difference to whether a player can force a win or a draw. The number of possible ways a game can go after n moves keeps growing exponentially with n. The number of states that can occur after n moves on the other hand doesn't keep on growing exponentially because it can't exceed the total number of possible states that can occur in a legal game. According to <https://en.wikipedia.org/wiki/Game_complexity>, there are about 10^47 states that can occur in a legal game of chess.
  
  Chess can be solved as follows: take a set of states that we can prove contains all states that can occur in a legal game of chess without the 3-fold repetition rule or 50 move rule. Two different states could have the same arrangement of chess pieces and differ by whose turn it is, whether you have the right to capture by en passant, and whether a given king or rook has the right to ever castle again. Next, take all states where the minimum number of moves white can force a win in is 1 which must occur on white's turn. Next take all states where the minimum number of moves white can force a win in is 2, which means it's black's turn and no matter which move they can make, white can force a win in 1 move. Next take all states where the minimum number of moves white can force a win in is 3, which means white has a move that will give them a forced win in 2 moves but can't force a win in 1 move. Next take all states where the minimum number of moves white can force a win in is 4, which means it's black's turn and no matter which move they make, white can force a win in 3 moves but white can't currently force a win in 2 moves. Once we get to a number such that there are no states where the minimum number of moves white can force a win in is that number, we've already found all the states that white can force a win in. We can find all states that black can force a win in in a similar way. All the remaining states are ones where both players can force a draw.
  
  Since there are about 10^47 states that can occur in a legal game of chess, it would take more than our lifetime to use brute force to build a computer that will play chess perfectly no matter how it's opponent plays. I believe it hasn't been proven that there's no much shorter algorithm that can tell you how to play perfectly no matter how your opponent plays. For instance maybe only a small fraction of states that can occur in a legal game can occur in a game where you play the way that algorithm tells you to play so that algorithm works even though it only tells you how to play perfectly in all states that can occur when you have always followed that algorithm since the beginning of the game but not in all states that can occur in a legal game. Maybe in addition to that, that algorithm is a complex algorithm that for each state that can occur in a game where you have always followed it, takes way fewer steps to compute an optimal move than the number of states that can occur in a game where you have always followed it. According to <http://onlinelibrary.wiley.com/doi/10.1002/sres.2171/abstract>, the evolutionary learning laboratories are planning to solve complex problems. Maybe some day, they'll figure out a complex strategy for playing chess perfectly. Maybe even if an algorithm that's very short and takes very few steps to compute an optimal move in any state that can occur in a game where you have always followed that algorithm doesn't exist, that still doesn't stop a human from being able to learn how to play chess perfectly. Maybe a human could continuously figure things out and retain what they figured out figure more things out from what they previously figured out and retain them by some complex method, be able to figure out from the pieces of information they previously figured out how to play perfectly with a 90 minute base time and 30 second increments in any state that can occur in a game where they play the way they play after learning way fewer bits of information than the number of states that can occur in a game where they play the way they do which they can learn in their life time especially if the technology to live 6000 years gets invented.
  
  It's probably even simpler for a player to have a strategy that ensures that if their opponent plays perfectly, they will also play perfectly. I suspect both players have a forced draw from the beginning of the game. It's probably simpler to have a strategy that forces a draw than a strategy that guarantees that if your opponent gives you a forced win, you will not lose it. A strategy that forces a draw is also a strategy that ensures that if your opponent plays perfectly, you will play perfectly. If they play perfectly, they will not give you a forced win in the first place so you will not lose a forced win after they give you one.
  
  Update:
  
  According to <https://www.youtube.com/watch?v=mOqmLYlFdBo>, AlphaZero is a neural network that plays chess better than any other chess program including Stockfish. After it was created, it gained that ability in only a few hours. I don't know exactly how it works but I believe it does something like simulate natural selection on chess strategies. Suppose you have some beings playing rated chess tournaments with a 90 minute base time and 30 second increments except that there is no 3-fold repetition rule or 50 rule and there is no resigning and each game counts as a draw if nobody checkmates after 4,000 moves. Furthermore, suppose they have no interaction with one another except for the tournaments where they are randomly paired with somebody of a very similar rating and their probability of cloning themselves in a lab is tiny t approximately 1 in a billion each time they play a game and varies linearly with their rating after the game and that there are a billion individuals and each time one is created, a randomly picked one disappears. You may be thinking natural selection cannot select for a new trait if there isn't an advantageous pathway towards it. I'm not sure that's the case. Some individuals might have genome that gives a small chance of undergoing a partially ordered major rearrangement when it produces its clone. Then very rarely and occasionally, the rearrangement will improve the chess playing strategy. Then the descendants of the single mutant clone will multiply into very large numbers. Then that will select for the tendency to rarely and occasionally mutate in a random way. Then that can lead to evolution of creatures that are really good at trying different ways of thinking until they come up with a solution.
  
  > **Comments:**
  > **username_8**: The link to your answer on computer-science-SE is helpful. However, I am not sure it was worth copy-pasting its whole text.  
  > **username_9**: Dead link to the original answer? Also, I don’t think it’s true that “at any point if they can force a win, they can also force a draw”.  
  > **username_10**: As Ry mentioned, we can easily imagine scenarios where if forcing a win you cannot force a draw. Easiest way is to imagine a mate in 1 or loose situation. Unless we of course count the "hey, I have mate like this, would you like to draw?" situation (and the other player would obviously answer yes).  
  
  ---
  
  ### Answer by username_13 on 2016-05-18. Score: 3
  
  We know that an optimal strategy exists since when in a game there are a finite amount of players and a finite amount of strategies for each player, one can show that a Nash equilibra exists (so you are playing your optimal response to the other player's optimal response and viceversa).
  
  The thing is that even if we know that such strategy exists, we don't know exactly which strategy is it because of computational limitations.
  
  
  ---
  
  ### Answer by username_14 on 2016-02-06. Score: 2
  
  no
  
  we cannot say who should win or if it should be a draw
  
  there are way too many move combinations to even try to compute the answer with current technology by trying all possible moves and seeing the results
  
  then we would have to prune backwards to see what the answer would be and if it were unique
  
  and if we could the game would not be fun any longer
  
  > **Comments:**
  > **username_15**: "if we could the game would not be fun any longer" --> People still play connect-4 and some other solved games.  
  
  ---
  
  ### Answer by username_16 on 2016-05-19. Score: 2
  
  At the beginning of the 20th century, the belief that chess would be solved soon (called "the draw death of chess") was popular. The world champion J.-R. Capablanca tended to believe so. The games of the match Capablanca-Alekhine (almost all in the Queen's Gambit Declined) also confirmed this belief. See, for example: <https://en.wikipedia.org/wiki/Capablanca_chess> .
  
  The revolution of modern openings (King's Indian etc), then the revolution of artificial intelligence provided intuitive proofs that solving chess is not so simple. Indeed, today grandmaster games are often analyzed using a program and this reveals lines that the players (even the best ones) oversaw during the game.
  
  This being said, an "absolute computational power" can indeed solve chess in the sense of the theory of computation.
  
  
  ---
  
  ### Answer by username_17 on 2016-01-28. Score: 1
  
  The human mind is much more complex than a tic-tac-toe game. So, you can find a good strategy for play such game.
  
  Chess is quite diferent. Chess is a heuristic game.
  
  you can not put a soldier in charge above a general. The mind of a general is much more complex than a soldier mind, in military terms. It is only a analogy.
  
  Complexity, that is what matters.
  
  You need to be more complex than chess. It is impossible, but you must try, you need to try. You can achieve it in several levels. Many factors are involved. Efforts are important, but many of us make great efforts with poor results. But there are people who made little efforts and achieve excellent results.
  
  Nature is unfair.
  
  But if you learn chess at age of five your chances will be better than if you learn the game at age of ten.
  
  Of course, if you used to stay lots of hours in front of TV when you was a child you wasted your intelligence.
  
  Last, but not least, sorry about my english.
  
  
  ---
  
  ### Answer by username_18 on 2017-12-01. Score: -1
  
  2000-3000 elos more to go until perfect play, so the current
  top engines could at least double their strength.
  Chess is actually closer to its infancy than to its later stages.
  For example, current top engines would guess only one out of 5
  best opening moves.
  Still a long way to go.
  
  > **Comments:**
  > **username_19**: How do you get to that number?  
  > **username_18**: Different tests have been conducted and reported on Talkchess forum, the most advanced chess forum on the Internet, but my observations also point in that direction. Also, by comparing the engine evaluations 20 years ago, now, and what could still be improved in that area.  
  
  ---
  
  