Answers.Body: <p>The moment we knew that a variation would be winning for either White or Black, the other side would never go for that variation. E.g. after 1. g4 e5, White will never play 2. f3 because we know that variation is winning for Black.</p>
  
  <p>But there are some openings which have been analyzed to a draw by repetition of moves, even before the computer era, e.g. the Greco variation of the main line (Giuoco Piano) of the Italian game:</p>
  
  <pre><code>[FEN ""]
  1. e4 e5 2. Nf3 Nc6 3. Bc4 Bc5 4. c3 Nf6 5. d4 exd4 6. cxd4 Bb4+ 7. Nc3 Nxe4 8. O-O Bxc3 9. d5 Bf6 10. Re1 Ne7 11. Rxe4 d6 12. Bg5 Bxg5 13. Nxg5 O-O 14. Nxh7 Kxh7 15. Qh5+ Kg8 16. Rh4 f5 17. Qh7+ Kf7 18. Rh6 Rg8 19. Re1 Qf8 20. Bb5 Rh8 21. Qxh8 gxh6 22. Qh7+ Kf6 23. Rxe7 Qxe7 24. Qxh6+ Kf7 25. Qh7+
  </code></pre>
  
  <p>Almost all deviations after move 8 or so have been proven either to draw as well, or to lead to a worse position.</p>
  
Answers.ContentLicense: CC BY-SA 3.0
Answers.CreationDate: 2016-07-16T17:11:35.777Z
Answers.Text: That's remarkable ! Are you saying that G4 e5 f3 has been solved as winning for black ? In other words there's a special case of chess solved with just three moves ?
Answers.UserDisplayName: Saikat
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Answers.CreationDate: 2016-07-16T17:14:46.690Z
Answers.Text: I see what you mean now. Black wins by check mating Qh4.
Answers.UserDisplayName: Saikat
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Answers.CreationDate: 2016-07-16T07:24:05.107Z
Answers.LastActivityDate: 2016-07-16T07:40:07.277Z
Answers.LastEditDate: 2016-07-16T07:40:07.277Z
Answers.UserDisplayName: Glorfindel
Answers.Body: <p>There are algorithms/chess engines that can heuristically evaluate a position and provide a score which can be proxied for who is winning.</p>
  
  <p>Completely analyzing an opening would require an engine to follow all paths or at least all reasonable paths (heuristically determined). This is computationally very time-intensive and we are very far from compute power that can do that for us. </p>
  
Answers.ContentLicense: CC BY-SA 3.0
Answers.CreationDate: 2016-07-16T15:43:34.810Z
Answers.Text: Would you say quantum computing could solve chess ?
Answers.UserDisplayName: Saikat
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Answers.CreationDate: 2016-07-17T01:23:15.963Z
Answers.Text: @user230452 it cannot.
Answers.UserDisplayName: Jimmy360
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Answers.Text: @Jimmy360 Why not ?
Answers.UserDisplayName: Saikat
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Answers.CreationDate: 2016-07-17T04:33:57.393Z
Answers.Text: @user230452 quantum computer uses quits instead of bits. Even so, calculation show that qc's cannot solve chess.
Answers.UserDisplayName: Jimmy360
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Answers.CreationDate: 2016-07-17T05:09:18.320Z
Answers.Text: @Jimmy360 Can you present the calculation ?
Answers.UserDisplayName: Saikat
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Answers.Text: @user230452 "NP is the class of problems solved in exponential time and checked in polynomial time. Quantum computing merges P and NP, ie, NP problems can be solved in polynomial time on a quantum computer but does not change much in the classes upper than that. So, no. The game of chess is still hard for a quantum computer."- Quora. Therefore, it has to do with the famous equation N = NP.
Answers.UserDisplayName: Jimmy360
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Answers.Text: @Jimmy360 I always thought chess was NP-complete. Is it in a class above NP ?
Answers.UserDisplayName: Saikat
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Answers.CreationDate: 2016-07-17T15:32:38.310Z
Answers.Text: @user230452 it is NP but likely not N
Answers.UserDisplayName: Jimmy360
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Answers.CreationDate: 2017-07-24T10:32:22.117Z
Answers.Text: @Jimmy360 chess, being a finite game, is trivially solved in O(1) time and space. If you want to talk about N = NP, pick something that doesn't have a fixed size...
Answers.UserDisplayName: RemcoGerlich
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Answers.Text: It's funny to see discussions about "N = NP". Do you even know what these stand for? And do you have any *credible* sources for quantum computers being able to efficiently solve all problems in NP? Sounds like pure bs to me.
Answers.UserDisplayName: TMM
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Answers.Text: @TMM that's certainly not what I said
Answers.UserDisplayName: Jimmy360
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Answers.Text: You said (quoted) that quantum computers "merge P and NP" and that they can solve NP problems in polynomial time, which is utter nonsense. And like I said, I'd like to see more credible sources that quantum computers cannot solve chess, other than "they use qubits" or "calculations show this". (And I am not aware of any hardness results about chess in general - as far as I know, it may be solvable some day by a classical computer as well.)
Answers.UserDisplayName: TMM
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Answers.UserDisplayName: Jubin Chheda
Answers.Body: <p>I must say at a high level for example in the Grünfeld Indian there is a lot to be memorized, and possible to be memorized. People have considerable trouble against a stable player like MVL employing it. A lot of lines are forced and have an outcome.</p>
  <p>Still, it will probably take some time before all life is out of the opening. Yet, the main lines have dried out as interesting terrain.</p>
  
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Answers.UserDisplayName: David Miedema
Body: <p>While, I'm fully aware that the number of chess moves exceeds the number of atoms in the universe greatly, and so solving it is a problem that falls in NP, I was wondering if certain variations of it can be solved.</p>
  
  <p>I know that chess itself can't be solved.* But, is it possible to solve at least a few openings ? What I mean is, is it possible for computers to definitely say "For this variation of the Sicilian Defense, White is winning." or "For this variation of the Queen's Gambit, Black is winning." Are there special cases where it is possible to say exactly which side is winning after 7-8 moves?
  (* - Strictly speaking, it has not been proven that chess cannot be solved. It cannot be solved by a brute force search of the game-tree, because such a graph is too large. But not all algorithms have been excluded in their ability to solve chess).</p>
  
Tags: <game-complexity>
Title: Is it possible to fully analyse, at least some openings of chess?
ThreadText: # Is it possible to fully analyse, at least some openings of chess?
  
  (Asked by: username_0 on 2016-07-16)
  
  While, I'm fully aware that the number of chess moves exceeds the number of atoms in the universe greatly, and so solving it is a problem that falls in NP, I was wondering if certain variations of it can be solved.
  
  I know that chess itself can't be solved.\* But, is it possible to solve at least a few openings ? What I mean is, is it possible for computers to definitely say "For this variation of the Sicilian Defense, White is winning." or "For this variation of the Queen's Gambit, Black is winning." Are there special cases where it is possible to say exactly which side is winning after 7-8 moves?
  (\* - Strictly speaking, it has not been proven that chess cannot be solved. It cannot be solved by a brute force search of the game-tree, because such a graph is too large. But not all algorithms have been excluded in their ability to solve chess).
  
  **Tags:** game-complexity
  
  
  ---
  
  ## 3 answers
  
  ### Answer by username_1 on 2016-07-16. Score: 7
  
  The moment we knew that a variation would be winning for either White or Black, the other side would never go for that variation. E.g. after 1. g4 e5, White will never play 2. f3 because we know that variation is winning for Black.
  But there are some openings which have been analyzed to a draw by repetition of moves, even before the computer era, e.g. the Greco variation of the main line (Giuoco Piano) of the Italian game:
  [FEN ""]
  1. e4 e5 2. Nf3 Nc6 3. Bc4 Bc5 4. c3 Nf6 5. d4 exd4 6. cxd4 Bb4+ 7. Nc3 Nxe4 8. O-O Bxc3 9. d5 Bf6 10. Re1 Ne7 11. Rxe4 d6 12. Bg5 Bxg5 13. Nxg5 O-O 14. Nxh7 Kxh7 15. Qh5+ Kg8 16. Rh4 f5 17. Qh7+ Kf7 18. Rh6 Rg8 19. Re1 Qf8 20. Bb5 Rh8 21. Qxh8 gxh6 22. Qh7+ Kf6 23. Rxe7 Qxe7 24. Qxh6+ Kf7 25. Qh7+
  
  Almost all deviations after move 8 or so have been proven either to draw as well, or to lead to a worse position.
  
  > **Comments:**
  > **username_0**: That's remarkable ! Are you saying that G4 e5 f3 has been solved as winning for black ? In other words there's a special case of chess solved with just three moves ?  
  > **username_0**: I see what you mean now. Black wins by check mating Qh4.  
  
  ---
  
  ### Answer by username_2 on 2016-07-16. Score: 3
  
  There are algorithms/chess engines that can heuristically evaluate a position and provide a score which can be proxied for who is winning.
  
  Completely analyzing an opening would require an engine to follow all paths or at least all reasonable paths (heuristically determined). This is computationally very time-intensive and we are very far from compute power that can do that for us.
  
  > **Comments:**
  > **username_0**: Would you say quantum computing could solve chess ?  
  > **username_3**: @user230452 it cannot.  
  > **username_0**: @username_3 Why not ?  
  > **username_3**: @user230452 quantum computer uses quits instead of bits. Even so, calculation show that qc's cannot solve chess.  
  > **username_0**: @username_3 Can you present the calculation ?  
  > **username_3**: @user230452 "NP is the class of problems solved in exponential time and checked in polynomial time. Quantum computing merges P and NP, ie, NP problems can be solved in polynomial time on a quantum computer but does not change much in the classes upper than that. So, no. The game of chess is still hard for a quantum computer."- Quora. Therefore, it has to do with the famous equation N = NP.  
  > **username_0**: @username_3 I always thought chess was NP-complete. Is it in a class above NP ?  
  > **username_3**: @user230452 it is NP but likely not N  
  > **username_4**: @username_3 chess, being a finite game, is trivially solved in O(1) time and space. If you want to talk about N = NP, pick something that doesn't have a fixed size...  
  > **username_5**: It's funny to see discussions about "N = NP". Do you even know what these stand for? And do you have any *credible* sources for quantum computers being able to efficiently solve all problems in NP? Sounds like pure bs to me.  
  > **username_3**: @username_5 that's certainly not what I said  
  > **username_5**: You said (quoted) that quantum computers "merge P and NP" and that they can solve NP problems in polynomial time, which is utter nonsense. And like I said, I'd like to see more credible sources that quantum computers cannot solve chess, other than "they use qubits" or "calculations show this". (And I am not aware of any hardness results about chess in general - as far as I know, it may be solvable some day by a classical computer as well.)  
  
  ---
  
  ### Answer by username_6 on 2020-08-04. Score: 0
  
  I must say at a high level for example in the Grünfeld Indian there is a lot to be memorized, and possible to be memorized. People have considerable trouble against a stable player like MVL employing it. A lot of lines are forced and have an outcome.
  
  Still, it will probably take some time before all life is out of the opening. Yet, the main lines have dried out as interesting terrain.
  
  
  ---
  
  