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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?

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I don't see a real answer to this question. Is a game imperfect already when the chosen opening system provides worse winning chances than a different system? What about move order issues to avoid certain systems? How will you measure a move (or a game full of moves) as being perfect when the resulting positions are not fully analyzed but measured by imperfect evaluation methods only? Is an evaluation difference of 0.02 points an indication of imperfection? –  Ray May 10 '12 at 20:42
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How do you know the computer's choice of moves is actually an "improvement?" –  BlueRaja - Danny Pflughoeft May 11 '12 at 4:13
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6 Answers

up vote 15 down vote accepted

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
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Very interesting game, and opening... –  Wes Freeman May 15 '12 at 3:26
    
Not sure about 8...Na6. Think I'll start a question about it. –  Wes Freeman May 15 '12 at 3:42
    
+1 this is one of my favorite games of all time. –  BlueRaja - Danny Pflughoeft May 15 '12 at 18:06
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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.

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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.

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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.

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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.

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Once the game is solved, there will be :·) –  Nikana Reklawyks Nov 20 '12 at 3:33
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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.

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