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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).

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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.

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    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 ? – Saikat Jul 16 '16 at 17:11
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    I see what you mean now. Black wins by check mating Qh4. – Saikat Jul 16 '16 at 17:14
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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.

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  • Would you say quantum computing could solve chess ? – Saikat Jul 16 '16 at 15:43
  • @user230452 it cannot. – Jimmy360 Jul 17 '16 at 1:23
  • @Jimmy360 Why not ? – Saikat Jul 17 '16 at 4:04
  • @user230452 quantum computer uses quits instead of bits. Even so, calculation show that qc's cannot solve chess. – Jimmy360 Jul 17 '16 at 4:33
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    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. – TMM Jul 26 '17 at 19:00
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It is impossible. There are over 9 million possible positions after the first 3 moves, let alone the whole game! If a computer was to analyse all the positions, then it would

  1. Crash

  2. Prove that Chess cannot be solved.

Even if we used a quantum computer, which calculates in increasing powers of 2, then we will still have a problem since the number of possible positions will be, I estimate 2^10^100.

So, we can't analyse openings in chess completely.

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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.

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