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I've found "average centipawn loss" calculated for some recent World Championship games, for example Magnus Carlsen vs Ian Nepomniachtchi, 2021 World Chess Championship.

Is there some "acl" calculation for other World Champions throughout chess history?

Who was the best ever "computer", the ultimate question...

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  • Is the ACL calculation provided by the Lichess server-side analysis sufficient? Commented Aug 25, 2022 at 15:11
  • Answer is going to depend on the exact version of the engine of your choice, and the chosen hardware. Commented Aug 26, 2022 at 20:59

2 Answers 2

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Magnus Carlsen's moves are the ones most likely to match a computer's.

In some ways this isn't surprising. After all, chess playing strength has increased over time; Carlsen can learn from Kasparov, Fischer, Capablanca et al, but not vice versa.

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  • 4
    and Carlsen can also learn from the 3000+ strength engines themselves. Commented Aug 25, 2022 at 18:04
  • 3
    The big surprise with that measurement is how good Kramnik was. The top 4 is the consensus best 3 ever, plus Kramnik at 2nd! Commented Aug 25, 2022 at 22:58
  • The wikipedia links to a great research article from Jean-Marc Alliot: fivethirtyeight.com/features/….
    – Danijel
    Commented Aug 26, 2022 at 8:06
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I did some comparison, but this is old. See ThinkerJudge in my github repository.

There are scripts there that you can use to create new analysis with latest stockfish.

Features

A. Average error in centipawn (low is better) per game
B. Overall average error in centipawn (low is better)
C. Move Number with 50 to 100 cp error from a playable position (-50/50) cp, (high or None is better)
D. Move Number with 101 to 300 cp error from a playable position (-50/50) cp, (high or None is better)
E. Move Number with 301 to 500 cp error from a playable position (-50/50) cp, (high or None is better)

enter image description here

I ran the calsen/nepomniachtchi match with stockfish 15. See plot below.

Do not interpret this plot as comparing player's error from different years. But you can compare players from same year. For example carlsen 2021 vs nepomniachtchi 2021, or Fischer 1972 vs Spassky 1972 and others.

enter image description here

Feature C table.

C. Move Number with 50 to 100 cp error from a playable position (-50/50) cp, (high or None is better)
+-----------+------------------+-----------+------------------------+
|   GameNum | Nepomniachtchi   | Carlsen   |   Nepomniachtchi_score |
+===========+==================+===========+========================+
|         1 | None             | 27        |                    0.5 |
+-----------+------------------+-----------+------------------------+
|         2 | None             | 17        |                    0.5 |
+-----------+------------------+-----------+------------------------+
|         3 | None             | None      |                    0.5 |
+-----------+------------------+-----------+------------------------+
|         4 | None             | 18        |                    0.5 |
+-----------+------------------+-----------+------------------------+
|         5 | None             | None      |                    0.5 |
+-----------+------------------+-----------+------------------------+
|         6 | 52               | None      |                    0   |
+-----------+------------------+-----------+------------------------+
|         7 | None             | None      |                    0.5 |
+-----------+------------------+-----------+------------------------+
|         8 | None             | None      |                    0   |
+-----------+------------------+-----------+------------------------+
|         9 | None             | None      |                    0   |
+-----------+------------------+-----------+------------------------+
|        10 | None             | None      |                    0.5 |
+-----------+------------------+-----------+------------------------+
|        11 | None             | None      |                    0   |
+-----------+------------------+-----------+------------------------+

ThinkerJudge's feature C tells us which player commits mistake first, how much error from a playable position and what move number. From the table above in game 1, Carlsen commit mistake first at move number 27. This error is in the range 50 to 100 CP, from a playable position +/- 50 CP. If it is None that means the player had not made a mistake in the range 50 to 100 CP from a playable position +/- 50 CP.

That table C is based from Stockfish 15 analysis at 5 sec per position on 4 threads using i7-2600K 3.4 Ghz 4-core processor.

Looking at the game analysis, the computer suggestion and evaluation is this.

27. Re3 { -0.24/27 } ( 27. Re3 { -0.24/27 } ) 27... Kf8 { -0.25/26 } ( 27... g6 { 0.26/30 } )

The actual move is Kf8 with an evaluation of -0.25 pawn unit. Score is from side to move point of view or (SPOV), meaning after Kf8 black is slightly inferior. The computer suggested g6 with a positive score favoring black.

Error = 0.26 - (-0.25) or 0.51 pawn unit or 51 CP (centipawn) unit.

That result is within the condition specified in Table C feature.

C. Move Number with 50 to 100 cp error from a playable position (-50/50) cp

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