Answers.Body: <p>No, it would not be possible for such a database to exist. Calculating it would require an infeasibly large computer and the calculation would take so long that your computer wouldn't exist for long enough to complete the task.</p>
  
  <p>Claude Shannon estimated that there are around <a href="https://en.wikipedia.org/wiki/Shannon_number" rel="noreferrer">10<sup>43</sup> possible positions</a> in chess and your database would need to store the outcome of all of these (this would be, essentially, a 32-man <a href="https://en.wikipedia.org/wiki/Endgame_tablebase" rel="noreferrer">tablebase</a>). However, it is estimated that the <a href="http://education.jlab.org/qa/mathatom_05.html" rel="noreferrer">Earth contains only about 10<sup>50</sup> atoms</a> so, even if you could build a memory cell out of just 10,000,000 atoms, you would still need a computer the size of the Earth just to store all the positions.</p>
  
  <p>But such a huge computer brings big problems. The earth's diameter is about 12,800 kilometres and light takes about 43ms to cross that distance.  That means that, if a clock cycle lasts longer than 43ms, then not only do you have horrible <a href="https://en.wikipedia.org/wiki/Clock_skew" rel="noreferrer">clock skew</a> but different parts of your computer aren't even on the same clock cycle. Avoiding this limits your clock speed to about 23.5Hz (not GHz or MHz; just Hz).  Even if you could completely evaluate a position in a single clock cycle, that means your computer would take about 4.3x10<sup>41</sup> seconds to complete its task. That's about 1.4x10<sup>34</sup> years. That's 14 million billion billion billion years.</p>
  
  <p>Astrophysicists believe that the universe will look <a href="https://en.wikipedia.org/wiki/Future_of_an_expanding_universe" rel="noreferrer">radically different</a> in 1.4x10<sup>34</sup> years than it does now. By then, stars will have long ago ceased to exist and even elements that are in no meaningful sense radioactive will have undergone large amounts of radioactive decay. Even the protons that form atomic nuclei will have undergone significant radioactive decay.  So your earth-sized computer simply won't exist any more.</p>
  
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Answers.Text: I'm thinking some of this reasoning is a bit flawed; you don't need to access the *entire* storage at the same time just to evaluate a position. You could partition it based on, say, king position and number of pieces. But it's still obviously nowhere near feasible.
Answers.UserDisplayName: D M
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Answers.UserDisplayName: David Richerby
Answers.Body: <p>I think Daniel's answer is excellent (+1) but want to add a few thoughts anyway.</p>
  
  <p>Would a 32-piece tablebase really replace chess engines?
  The answer is definitely no!</p>
  
  <p>To play good chess, more information is needed than whether a move is winning, drawing or losing. Of course such a database would be unbeatable, but it would hardly beat anybody either. </p>
  
  <p>To play chess strongly it is not enough to chose a non-losing move at every turn. Of the many drawing moves in each position, there are only a few that put real pressure on the opponent. </p>
  
  <p>Existing chess engines are made significantly stronger by accessing tablebases. But as the databases grow, the access time would become a prohibiting factor long before using every atom in the universe for memory ;-).</p>
  
  <p>So I think your conclusion is just wrong:
  Such a database would never lose and hardly ever win. It wouldn't tell us anything about openings except that almost all of them are draws.
  We could probably devise new algorithms to mine this database and come up with interesting conclusions about all kinds of positions, but I think this wouldn't change the world of chess in any significant way.</p>
  
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Answers.Text: You have misunderstood what the database would contain. Each possible move would be marked as either "If I play this, my opponent can force a win whatever I do next", "If I play this, I can force a win whatever my opponent does next" or "draw". So you wouldn't be playing "non-losing moves at every turn": you'd be playing forced wins at every turn, as long as such a move existed.
Answers.UserDisplayName: David Richerby
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Answers.Text: Well, actually I understood exactly what the database would contain … The point I was trying to make is that in high level chess games "There Are No Forced Wins!" in more than 90% of the positions. And you need way more information than "this move draws and this move loses", to actually get to a winning position against a decent player.
Answers.UserDisplayName: BlindKungFuMaster
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Answers.Text: To give an example: In the starting position, in all likelihood, the only information in the database would be "All moves draw.". So you would be completely on your own. And if you are completely on your own, how do you get a winning position against a strong player? The answer is: You don't. Your position will get worse and worse up to the point were you follow the one and only drawing line.
Answers.UserDisplayName: BlindKungFuMaster
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Answers.Text: The point is that the current position usually isn't "you win". For example it is very likely that there is no forced win in the starting position.
Answers.UserDisplayName: BlindKungFuMaster
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Answers.UserDisplayName: BlindKungFuMaster
Answers.Body: <p>I think someday chess will be solved.  Why?  Because, well, not that long ago, playing chess against a computer was weird and unthinkable! How could you train a computer to play chess?  Well, they did it! (In addition, the idea of a computer was strange...)
  My point is, it might seem weird because we've never seen of or heard of it.  Its not something we can easily imagine.  But technology is expanding at an exponential rate.  I wouldn't be surprised if in the near future (10+ years) that it is solved, in one form or another.</p>
  
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Answers.Text: The obstacle to solving chess is the literally astronomical amount of data you'd need to sort through. Shannon estimated that there are [roughly 10^43 positions](https://en.wikipedia.org/wiki/Shannon_number) in chess and you'd need to store the outcome for every one of those. To put this into perspective, the earth contains [about 10^50 atoms](http://education.jlab.org/qa/mathatom_05.html) so, even if you could build a memory cell from 10,000,000 atoms, you'd still need to convert the whole earth into a memory bank just to store the result!
Answers.UserDisplayName: David Richerby
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Answers.Text: @DavidRicherby Let's say chess is a draw with best play. Then for every white move, there is an adequate response for black. To the next white move, black also has an adequate response, and so on. It is conceivable that building such a "draw tree" requires a lot less than 10^43 positions.
Answers.UserDisplayName: Dag Oskar Madsen
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Answers.Text: @DagOskarMadsen Yes, it's possible that actually storing the tree would require much less memory (though still an astronomical amount). However, the current technique for *building* such trees is to do retrograde analysis from all ending positions, which does require building the complete database of what to do in every position, as at least an intermediate stage.
Answers.UserDisplayName: David Richerby
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Answers.CreationDate: 2024-07-27T22:36:55.917Z
Answers.Text: It's been 10 years.
Answers.UserDisplayName: farooq
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Answers.CreationDate: 2014-12-13T18:28:41.237Z
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Answers.UserDisplayName: Ryan Orr
Answers.Body: <p>Back in college in the early 1980s, I read in a game playing text that if a computer could plan, evaluate and execute a move, any single move, from the start of the game to all possible conclusions every 1/3 of a nanosecond, that is approximately 3 <em>billion</em> moves/second, to do this for every conceivable outcome would take 10 to the 120th centuries to complete.  And who has that long to wait?</p>
  
  <p>Another staggering statistic?  You've obvious heard of a googol?  Not THE Google, but the number?  It is 10 to the 100th power.  A 10 followed by 100 zeros.  Now imagine the googolplex.  That's 10 to the googol'th power.</p>
  
  <p>I've read that there isn't enough of <em>anything</em> in the known universe, not even atoms, to require using the googleplex.  In fact, even the googol is too big to describe anything.  You should check out some of the astonishing trivia about these numbers.</p>
  
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Answers.UserDisplayName: Jon
Answers.Body: <p>If you use "pruning" you can delete the bad options (the ones that will lead you to a loss for sure) and keep on looping while pruning. This way you might have enough memory to store the "good" options.</p>
  
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Answers.UserDisplayName: ElieH
Answers.Body: <p>Although it might not be possible to realise chess in a database in this universe, the abstract structure of the game can be said to exist as a finite mathematical object. One can reason about it and conclude that it has a definite result, although we might not know what that is. And then if you view it as a matrix you can ask questions like what is the maximum eigenvalue of chess approximately. Indeed Plato thought that numbers have real existence, so I guess he would say that the chess game exists in the same sublime and unhelpful way.</p>
  
  <p>But more practically, I could imagine an advanced quantum computer might genuinely be able to represent this, and indeed solve chess. The jury is still out as to the capabilities of this technology, but in principle I can’t see that it’s impossible</p>
  
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Answers.LastEditDate: 2020-03-30T09:33:24.920Z
Answers.UserDisplayName: Laska
Answers.Body: <p>I believe your question essentially boils down to the topic of whether it is possible to completely "solve" chess.  Wikipedia has an <a href="http://en.wikipedia.org/wiki/Solving_chess">excellent article</a> on the topic which should give you a good overview.</p>
  
  <p>To summarise, the number of possible game variations in chess is estimated to be 10^120.  This is a staggeringly huge number, for comparison, consider that the number of atoms in the observable universe is <a href="https://en.wikipedia.org/wiki/Observable_universe">estimated to be around 10^80</a>.  In other words, if you were using the entire observable universe as your hard drive, you'd still need to store 10^40 combinations of chess games on <em>each atom</em>, in order to simply store it all.  Needless to say, this is so far beyond our current and forseeable technologies that most people consider it to be completely impossible.</p>
  
  <p>Chess endgames are considerably less complex, and we've got to a point where it's possible to calculate all possible combinations for <a href="http://en.wikipedia.org/wiki/Endgame_tablebase">five-piece and six-piece endgames</a>.  These are typically huge undertakings done by reasearchers with access to supercomputers, and the resulting endgame databases are huge (on the order of hundreds of terabytes).  Each time a new piece is added, the size and complexity of the calculations goes up exponentially, which means that in the forseeable future, we can expect these results to expand by only a few pieces.</p>
  
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Answers.Text: +1 but your analysis is wrong. To store a tablebase, you only need to store each position, not each possible game. Shannon estimates that there are about [10^43 positions](https://en.wikipedia.org/wiki/Shannon_number), which compares to [about 10^50 atoms in the earth](http://education.jlab.org/qa/mathatom_05.html). So you might solve chess by [turning the whole earth into a computer](https://en.wikipedia.org/wiki/Places_in_The_Hitchhiker%27s_Guide_to_the_Galaxy#Earth).
Answers.UserDisplayName: David Richerby
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Answers.Text: Actually there are 7-man tablebases now, but it required a supercomputer to calculate (over the course of several months) and the storage is ridiculously huge. Regarding storage space; 5-man is about 7.5Gb for Nalimov tables and about 1Gb for Syzygy, while 6-man is around 1.15Tb for Nalimov and 150Gb for Syzygy.
Answers.UserDisplayName: Ben
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Answers.LastEditDate: 2013-06-05T08:10:24.707Z
Answers.UserDisplayName: Daniel B
Body: <p>Imagine that there is a chess database of every possible move and position. This database contains all possible moves from opening to end game.</p>
  
  <p>If I played using my intuition against a chess engine, it can predict which move will make me lose and win.</p>
  
  <p>So this means there is no need for a "chess engine" because all of the possible moves are already recorded.</p>
  
  <p>If such a database exists it would have the following advantages:</p>
  
  <ul>
  <li>In fast blitz games, chess engine will definitely lose against chess possibility move database.</li>
  <li>We can exactly know which opening will have more opportunity to win against the others.</li>
  </ul>
  
  <p>Or if such a database didn't already exist we could have a mathematical calculation of all possible moves from opening till end game.</p>
  
  <p>Would it be possible for such a database to exist?</p>
  
Comments.ContentLicense: CC BY-SA 3.0
Comments.CreationDate: 2014-12-04T12:25:19.890Z
Comments.Text: No, it is not possible with any imaginable technology.
Comments.UserDisplayName: Tony Ennis
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2019-08-19T09:35:35.373Z
Comments.Text: Yes, I think it would be possible. But only if the database was more like a neural network, taking moves that caused it to lose and deleting them. That calculation is based on exponentiating(bear with me) all possible actions in a chess game at move one, to move 100 or something. Meanwhile if we got rid of repeats, ((Ke3 Ke4 Ke3 Ke4) looping) 10^120 could probably become something like 10^70. That is still ridiculously huge but if we somehow were able to encode it onto a 4D plane (Which I believe is possible) it would be child’s play.
Comments.UserDisplayName: user19889
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2020-03-31T05:17:37.093Z
Comments.Text: Hey, I am new in this community and I'm from MathStack. Just to share that there are fewer atoms in the Universe than the number of Chess Games possible in a chess match. Try Shannon Number (https://www.youtube.com/watch?v=Km024eldY1A).
Comments.UserDisplayName: Sujit Bhattacharyya
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2021-05-31T06:55:25.617Z
Comments.Text: This is intended to be a comment an all comment on this subject.
  All are making assumptions without proof. Shannon's number is garbage. The possible number of unique positions at a certain ply depth is quite a bit smaller than some power of the branching factor.
Comments.UserDisplayName: Mario
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2021-08-02T18:22:37.177Z
Comments.Text: Couldn't you crack this problem with a sufficiently powerful quantum computer?
Comments.UserDisplayName: HyperNym
Tags: <opening><theory><endgame><middlegame><database>
Title: Database of every possible move in chess
ThreadText: # Database of every possible move in chess
  
  (Asked by: username_0 on 2013-06-05)
  
  Imagine that there is a chess database of every possible move and position. This database contains all possible moves from opening to end game.
  
  If I played using my intuition against a chess engine, it can predict which move will make me lose and win.
  
  So this means there is no need for a "chess engine" because all of the possible moves are already recorded.
  
  If such a database exists it would have the following advantages:
  
  * In fast blitz games, chess engine will definitely lose against chess possibility move database.
  * We can exactly know which opening will have more opportunity to win against the others.
  
  Or if such a database didn't already exist we could have a mathematical calculation of all possible moves from opening till end game.
  
  Would it be possible for such a database to exist?
  
  **Tags:** opening, theory, endgame, middlegame, database
  
  > **Comments:**
  > **username_1**: No, it is not possible with any imaginable technology.  
  > **username_2**: Yes, I think it would be possible. But only if the database was more like a neural network, taking moves that caused it to lose and deleting them. That calculation is based on exponentiating(bear with me) all possible actions in a chess game at move one, to move 100 or something. Meanwhile if we got rid of repeats, ((Ke3 Ke4 Ke3 Ke4) looping) 10^120 could probably become something like 10^70. That is still ridiculously huge but if we somehow were able to encode it onto a 4D plane (Which I believe is possible) it would be child’s play.  
  > **username_3**: Hey, I am new in this community and I'm from MathStack. Just to share that there are fewer atoms in the Universe than the number of Chess Games possible in a chess match. Try Shannon Number (https://www.youtube.com/watch?v=Km024eldY1A).  
  > **username_4**: This is intended to be a comment an all comment on this subject. All are making assumptions without proof. Shannon's number is garbage. The possible number of unique positions at a certain ply depth is quite a bit smaller than some power of the branching factor.  
  > **username_5**: Couldn't you crack this problem with a sufficiently powerful quantum computer?  
  
  ---
  
  ## 7 answers
  
  ### Answer by username_15 on 2013-06-05. Score: 36 | Accepted answer
  
  I believe your question essentially boils down to the topic of whether it is possible to completely "solve" chess. Wikipedia has an [excellent article](http://en.wikipedia.org/wiki/Solving_chess) on the topic which should give you a good overview.
  
  To summarise, the number of possible game variations in chess is estimated to be 10^120. This is a staggeringly huge number, for comparison, consider that the number of atoms in the observable universe is [estimated to be around 10^80](https://en.wikipedia.org/wiki/Observable_universe). In other words, if you were using the entire observable universe as your hard drive, you'd still need to store 10^40 combinations of chess games on *each atom*, in order to simply store it all. Needless to say, this is so far beyond our current and forseeable technologies that most people consider it to be completely impossible.
  
  Chess endgames are considerably less complex, and we've got to a point where it's possible to calculate all possible combinations for [five-piece and six-piece endgames](http://en.wikipedia.org/wiki/Endgame_tablebase). These are typically huge undertakings done by reasearchers with access to supercomputers, and the resulting endgame databases are huge (on the order of hundreds of terabytes). Each time a new piece is added, the size and complexity of the calculations goes up exponentially, which means that in the forseeable future, we can expect these results to expand by only a few pieces.
  
  > **Comments:**
  > **username_6**: +1 but your analysis is wrong. To store a tablebase, you only need to store each position, not each possible game. Shannon estimates that there are about [10^43 positions](https://en.wikipedia.org/wiki/Shannon_number), which compares to [about 10^50 atoms in the earth](http://education.jlab.org/qa/mathatom_05.html). So you might solve chess by [turning the whole earth into a computer](https://en.wikipedia.org/wiki/Places_in_The_Hitchhiker%27s_Guide_to_the_Galaxy#Earth).  
  > **username_16**: Actually there are 7-man tablebases now, but it required a supercomputer to calculate (over the course of several months) and the storage is ridiculously huge. Regarding storage space; 5-man is about 7.5Gb for Nalimov tables and about 1Gb for Syzygy, while 6-man is around 1.15Tb for Nalimov and 150Gb for Syzygy.  
  
  ---
  
  ### Answer by username_6 on 2014-12-15. Score: 13
  
  No, it would not be possible for such a database to exist. Calculating it would require an infeasibly large computer and the calculation would take so long that your computer wouldn't exist for long enough to complete the task.
  
  Claude Shannon estimated that there are around [1043 possible positions](https://en.wikipedia.org/wiki/Shannon_number) in chess and your database would need to store the outcome of all of these (this would be, essentially, a 32-man [tablebase](https://en.wikipedia.org/wiki/Endgame_tablebase)). However, it is estimated that the [Earth contains only about 1050 atoms](http://education.jlab.org/qa/mathatom_05.html) so, even if you could build a memory cell out of just 10,000,000 atoms, you would still need a computer the size of the Earth just to store all the positions.
  
  But such a huge computer brings big problems. The earth's diameter is about 12,800 kilometres and light takes about 43ms to cross that distance. That means that, if a clock cycle lasts longer than 43ms, then not only do you have horrible [clock skew](https://en.wikipedia.org/wiki/Clock_skew) but different parts of your computer aren't even on the same clock cycle. Avoiding this limits your clock speed to about 23.5Hz (not GHz or MHz; just Hz). Even if you could completely evaluate a position in a single clock cycle, that means your computer would take about 4.3x1041 seconds to complete its task. That's about 1.4x1034 years. That's 14 million billion billion billion years.
  
  Astrophysicists believe that the universe will look [radically different](https://en.wikipedia.org/wiki/Future_of_an_expanding_universe) in 1.4x1034 years than it does now. By then, stars will have long ago ceased to exist and even elements that are in no meaningful sense radioactive will have undergone large amounts of radioactive decay. Even the protons that form atomic nuclei will have undergone significant radioactive decay. So your earth-sized computer simply won't exist any more.
  
  > **Comments:**
  > **username_7**: I'm thinking some of this reasoning is a bit flawed; you don't need to access the *entire* storage at the same time just to evaluate a position. You could partition it based on, say, king position and number of pieces. But it's still obviously nowhere near feasible.  
  
  ---
  
  ### Answer by username_8 on 2014-12-04. Score: 6
  
  I think username_15's answer is excellent (+1) but want to add a few thoughts anyway.
  
  Would a 32-piece tablebase really replace chess engines?
  The answer is definitely no!
  
  To play good chess, more information is needed than whether a move is winning, drawing or losing. Of course such a database would be unbeatable, but it would hardly beat anybody either.
  
  To play chess strongly it is not enough to chose a non-losing move at every turn. Of the many drawing moves in each position, there are only a few that put real pressure on the opponent.
  
  Existing chess engines are made significantly stronger by accessing tablebases. But as the databases grow, the access time would become a prohibiting factor long before using every atom in the universe for memory ;-).
  
  So I think your conclusion is just wrong:
  Such a database would never lose and hardly ever win. It wouldn't tell us anything about openings except that almost all of them are draws.
  We could probably devise new algorithms to mine this database and come up with interesting conclusions about all kinds of positions, but I think this wouldn't change the world of chess in any significant way.
  
  > **Comments:**
  > **username_6**: You have misunderstood what the database would contain. Each possible move would be marked as either "If I play this, my opponent can force a win whatever I do next", "If I play this, I can force a win whatever my opponent does next" or "draw". So you wouldn't be playing "non-losing moves at every turn": you'd be playing forced wins at every turn, as long as such a move existed.  
  > **username_8**: Well, actually I understood exactly what the database would contain … The point I was trying to make is that in high level chess games "There Are No Forced Wins!" in more than 90% of the positions. And you need way more information than "this move draws and this move loses", to actually get to a winning position against a decent player.  
  > **username_8**: To give an example: In the starting position, in all likelihood, the only information in the database would be "All moves draw.". So you would be completely on your own. And if you are completely on your own, how do you get a winning position against a strong player? The answer is: You don't. Your position will get worse and worse up to the point were you follow the one and only drawing line.  
  > **username_8**: The point is that the current position usually isn't "you win". For example it is very likely that there is no forced win in the starting position.  
  
  ---
  
  ### Answer by username_9 on 2014-12-13. Score: 3
  
  I think someday chess will be solved. Why? Because, well, not that long ago, playing chess against a computer was weird and unthinkable! How could you train a computer to play chess? Well, they did it! (In addition, the idea of a computer was strange...)
  My point is, it might seem weird because we've never seen of or heard of it. Its not something we can easily imagine. But technology is expanding at an exponential rate. I wouldn't be surprised if in the near future (10+ years) that it is solved, in one form or another.
  
  > **Comments:**
  > **username_6**: The obstacle to solving chess is the literally astronomical amount of data you'd need to sort through. Shannon estimated that there are [roughly 10^43 positions](https://en.wikipedia.org/wiki/Shannon_number) in chess and you'd need to store the outcome for every one of those. To put this into perspective, the earth contains [about 10^50 atoms](http://education.jlab.org/qa/mathatom_05.html) so, even if you could build a memory cell from 10,000,000 atoms, you'd still need to convert the whole earth into a memory bank just to store the result!  
  > **username_10**: @username_6 Let's say chess is a draw with best play. Then for every white move, there is an adequate response for black. To the next white move, black also has an adequate response, and so on. It is conceivable that building such a "draw tree" requires a lot less than 10^43 positions.  
  > **username_6**: @username_10 Yes, it's possible that actually storing the tree would require much less memory (though still an astronomical amount). However, the current technique for *building* such trees is to do retrograde analysis from all ending positions, which does require building the complete database of what to do in every position, as at least an intermediate stage.  
  > **username_11**: It's been 10 years.  
  
  ---
  
  ### Answer by username_12 on 2019-08-28. Score: 2
  
  Back in college in the early 1980s, I read in a game playing text that if a computer could plan, evaluate and execute a move, any single move, from the start of the game to all possible conclusions every 1/3 of a nanosecond, that is approximately 3 *billion* moves/second, to do this for every conceivable outcome would take 10 to the 120th centuries to complete. And who has that long to wait?
  
  Another staggering statistic? You've obvious heard of a googol? Not THE Google, but the number? It is 10 to the 100th power. A 10 followed by 100 zeros. Now imagine the googolplex. That's 10 to the googol'th power.
  
  I've read that there isn't enough of *anything* in the known universe, not even atoms, to require using the googleplex. In fact, even the googol is too big to describe anything. You should check out some of the astonishing trivia about these numbers.
  
  
  ---
  
  ### Answer by username_13 on 2020-04-11. Score: 1
  
  If you use "pruning" you can delete the bad options (the ones that will lead you to a loss for sure) and keep on looping while pruning. This way you might have enough memory to store the "good" options.
  
  
  ---
  
  ### Answer by username_14 on 2020-03-30. Score: 0
  
  Although it might not be possible to realise chess in a database in this universe, the abstract structure of the game can be said to exist as a finite mathematical object. One can reason about it and conclude that it has a definite result, although we might not know what that is. And then if you view it as a matrix you can ask questions like what is the maximum eigenvalue of chess approximately. Indeed Plato thought that numbers have real existence, so I guess he would say that the chess game exists in the same sublime and unhelpful way.
  
  But more practically, I could imagine an advanced quantum computer might genuinely be able to represent this, and indeed solve chess. The jury is still out as to the capabilities of this technology, but in principle I can’t see that it’s impossible
  
  
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