Is there a historic example of a chess game that has, to date, resisted all computerized attempts to find a better sequence of moves? In other words, a "perfect" game?
CLARIFICATION
I should have made it clearer that I'm not looking for a perfect (without the quotes) game. That probably will never exist.
But is there a game that no computer has ever been able to improve as of this date?
In my opinion, it's almost impossible to say that a game is perfect if you include the opening. If you take the first few moves as a given (for example 1. e4 e5), then it is possible to say that a series of moves is perfect.
One example of a so-called perfect game is the Immortal Draw. Carl Hamppe and Philipp Meitner played to a draw in 1872, and in the next century, no improvements have been found for the game. It has stood up to all sorts of computer analysis and GM analysis.
Obviously the argument can be made that there is a "flaw" in the first 3 moves - maybe 1. e4 is not best, or 3. Na4 was an error, but if we ignore those 3 moves, every move starting with move 4 has held up as arguably the best move. For instance, 7. Qe1 is often given as an option for white, but black can once again sac his queen for a perpetual check.
While there are certainly other lines that draw, the game line is the most beautiful IMHO.
[FEN ""]
[Event "Vienna 1872"]
[White "Carl Hamppe"]
[Black "Philipp Meitner"]
[Site "Vienna"]
[Result "1/2-1/2"]
[PlyCount "36"]
1. e4 e5 2. Nc3 Bc5 3. Na4 Bxf2+ 4. Kxf2 Qh4+ 5. Ke3 Qf4+ 6. Kd3 d5 7. Kc3 (7.
Qe1 Nf6 8. g3 Qg4 9. Bh3 dxe4+ 10. Kc3 Nd5+ 11. Kb3 Nc6 $1 12. Bxg4 Na5+ $11)
7... Qxe4 8. Kb3 Na6 9. a3 Qxa4+ 10. Kxa4 Nc5+ 11. Kb4 a5+ 12. Kxc5 Ne7 13.
Bb5+ Kd8 14. Bc6 (14. Nf3 $4 b6#) 14... b6+ 15. Kb5 Nxc6 16. Kxc6 (16. Ka4 Nd4
17. Qf1 Bd7+ 18. Qb5 Bxb5#) 16... Bb7+ 17. Kb5 (17. Kxb7 Kd7 18. Qg4+ Kd6 19.
Qe6+ fxe6 20. Nf3 Rhb8#) 17... Ba6+ 18. Kc6 Bb7+ 1/2-1/2
To know that a game is "perfect", you have to solve the entire chess game space.
What you're really asking is whether grandmasters have played a game where a computer would have played the same moves (for both sides)? Assumptions about computer and the analysis time for the computer need to be made. I think it's possible to find such a game, but as you let the computer think longer and longer the number of results will dwindle to 0. If you limit it to only one side, you might find more games.
IF we assume that chess is a theoretical draw, then any move that doesn't lose is "perfect" in the theoretical sense.
I think there have been many perfect games. Take game 2 of Anand-Carlsen:
[FEN ""]
[Event "Anand-Carlsen World Championship"]
[Site "Chennai IND"]
[Date "2013.11.10"]
[EventDate "2013.11.07"]
[Round "2"]
[Result "1/2-1/2"]
[White "Viswanathan Anand"]
[Black "Magnus Carlsen"]
[ECO "B18"]
[WhiteElo "2775"]
[BlackElo "2870"]
[PlyCount "50"]
1.e4 c6 2.d4 d5 3.Nc3 dxe4 4.Nxe4 Bf5 5.Ng3 Bg6 6.h4 h6 7.Nf3
e6 8.Ne5 Bh7 9.Bd3 Bxd3 10.Qxd3 Nd7 11.f4 Bb4+ 12.c3 Be7
13.Bd2 Ngf6 14.O-O-O O-O 15.Ne4 Nxe4 16.Qxe4 Nxe5 17.fxe5 Qd5
18.Qxd5 cxd5 19.h5 b5 20.Rh3 a5 21.Rf1 Rac8 22.Rg3 Kh7 23.Rgf3
Kg8 24.Rg3 Kh7 25.Rgf3 Kg8 1/2-1/2
I cannot believe that either player had a lost position at any moment, so no mistakes were made in the theoretical sense, so that was a perfect game.
It's similar to playing a drawn tablebase endgame position against an engine that uses the tablebase. It's usually incredibly easy to draw, because the engine doesn't care about making life hard for you. E.g., in a drawn R + pawn v R position, it will often just give away the pawn. That's not worse than other drawing moves, according to the tablebase. It's flawless chess.
You could define a game as perfect when the engine evaluation of the position stays within some boundary (e.g. between +0.3 and -0.3) the entire game. It should be possible to find at least one game that satisfies this condition.
EDIT:
The question has been updated since last time: But is there a game that no computer has ever been able to improve as of this date? To answer this question, someone needs to automate the process of evaluating a game in this manner and then run this script on e.g. all GM games from some freely available database. I guess such games should be few in number and the shorter the game the higher the chance that it meets the requirement!
I honestly don't think you will ever find a "perfect" game just due to the fact that we are all human and we make mistakes. Bobby Fischer was once asked to name his best game and said it was his game with Donald Byrne, but it wasn't perfect.
Hungarian Writer Tibor Karolyi said that Anatoly Karpov came close to playing a mistake-free game at the 1974 chess Olympiad, but a tiny error deprived him from a "perfect" game.
But in the end, there is no perfect game and probably never will be.
I think there have probably been games that were perfect in that no one could substantively improve upon them. This will surely be less and less common as computers get stronger.
To me, it is still unclear what one would call perfect, but in terms of wins, Anderssen struck twice with the most unbelievable wins in the history of chess, which I'm going to paste here, the Immortal Game.
[FEN ""]
[Event "First International Tournament"]
[Site "London UK"]
[Date "1851.06.21"]
[Round "1"]
[Result "1-0"]
[White "Adolf Anderssen"]
[Black "Lionel Kieseritzky"]
[ECO "C33"]
[WhiteElo ""]
[BlackElo ""]
[PlyCount "50"]
1. e4 e5 2. f4 exf4 3. Bc4 Qh4 4. Kf1 b5 5. Bb5 Nf6 6. Nf3 Qh6 7. d3 Nh5 8. Nh4 Qg5 9. Nf5 c6 10. g4 Nf6 11. Rg1 cxb5 12. h4 Qg6 13. h5 Qg5 14. Qf3 Ng8 15. Bf4 Qf6 16. Nc3 Bc5 17. Nd5 Qb2 18. Bd6 Bg1 19. e5 Qa1 20. Ke2 Na6 21. Ng7 Kd8 22. Qf6 Nf6 23. Be7#
Here are the best moves according to Komodo 10:
[FEN ""]
1. d4 Nf6
2. c4 e6
3. Nf3 b6
4. g3 Ba6
5. Qa4 Bb7
6. Bg2 c5
7. O-O cxd4
8. Nxd4 Qc8
9. Bf4 Bxg2
10. Kxg2 Be7
11. Nc3 a6
12. f3 O-O
13. Rfd1 Qb7
14. Qb3 d6
15. Nc2 Qc7
16. Qa3 Rd8
17. Rac1 Nc6
18. Nb4 Ne5
19. Bxe5 dxe5
20. Rxd8+ Rxd8
21. Nxa6 Bxa3
22. Nxc7 Bxb2
23. Rd1 Rxd1
24. Nxd1 Ba3
25. Nf2 Nd7
26. Nd3 Bd6
27. Nb5 Be7
28. Nc3 Kf8
29. Kf2 f6
30. Ke3 Ke8
31. Na4 Kd8
32. Nc3 Kc7
33. Nb5+ Kc6
34. h3 Nc5
35. Nb4+ Kd7
36. Nd3 Nb7
37. Kd2 Kc6
38. g4 g6
39. Kc3 Na5
40. e4 g5
41. Nb4+ Kd7
42. Na6 Kc6
43. Nb8+ Kb7
44. Nd7 Nc6
45. Kb3 Nd4+
46. Nxd4 exd4
47. e5 fxe5
48. Nxe5 Kc7
49. Nd3 Kd7
50. Ne5+ Kd6
51. Nf7+ Kc5
52. Ne5 Bd6
53. Nd7+ Kc6
54. Nf6 Bf8
55. Ne4 h6
56. a4 Be7
57. Nf2 Bd8
58. Nd3 Bc7
59. Nb4+ Kc5
60. Na6+ Kd6
61. Kc2 e5
62. Nb4 Kc5
63. Kb3 Bd6
64. Nd5 Bf8
65. Nf6 Bg7
66. Nh5 Bf8
67. Ng3 Be7
68. Ne4+ Kc6
69. Kc2 Bc5
70. Kd3 Bb4
