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Could Stockfish beat Magnus Carlsen if its moves were calculated with the UCI command "go depth 16"? If not, how can I find the depth "d" at which Stockfish's strength surpasses top GMs?

We assume Magnus has standard time controls, and Stockfish limited only by search depth.

I would love to see a graph of Stockfish ELO (against an opponent with standard time controls) vs search depth. Does anything similar exist?

Context: I'm analyzing GM games to see when humans make mistakes, like this. I want to set my search depth "d" so that when the engine and human moves disagree, I can be confident that the human has made a mistake.

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    Tough question. If you're using Stockfish (or better programs) with opening books and endgame tables, it's a fair bet that if the human and player disagree, the human has almost certainly erred. I would not know how to meaningfully limit the engine to a certain depth. I don't think it's a fixed thing - they will play deeper if they are not in a position of quiescence.
    – Tony Ennis
    Dec 17, 2014 at 3:25
  • This is a very tough question because nobody knows unless Carlsen himself sits and plays Stockfish for every depth.
    – ABCD
    Dec 17, 2014 at 5:07
  • Note that there're handful of graphs played between computers for various depth. It's easy to generate. But it's impossible to generate one for human GMs because there is no data.
    – ABCD
    Dec 17, 2014 at 5:09
  • Search depth is a fuzzy concept for modern engines. They usually go selectively much deeper. If you just cut off all the calculation after x ply, I'm not sure you'll even reach GM strength before depth 25+.
    – BlindKungFuMaster
    Dec 17, 2014 at 7:58
  • In case you do the Kaggle competition: If you want to analyse 50000 games to a depth that equates to something like 2900 Elo … you'll need a lot of cpu hours.
    – BlindKungFuMaster
    Dec 17, 2014 at 8:01

3 Answers 3

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There actually is an ambitiously worked out answer out there:

http://web.ist.utl.pt/diogo.ferreira/papers/ferreira13impact.pdf

On page 77 you get the relevant table:

depth: elo:

20    2894

19    2828

18    2761

17    2695

16    2629

15    2563

…

So my comment was slightly off, depth 20 is already very strong. Still the point remains, that it is hard to compare search depth between different engines, because it is never brute force and selectively they go much deeper than the given depth. (In the paper they used Houdini 1.5, maybe some engine expert can relate Houdini-search depth to Stockfish search depth.)

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    Note that the paper get the data by self-playing. This implies the resulting Elo might not be very representative.
    – ABCD
    Dec 17, 2014 at 10:00
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    I only skimmed the paper, but I think they anchor the Elo at depth 20 with some comparison to top level games and only get the depth-difference = winning percentage = elo-difference by self playing. So at least the depth 20 = 2894 Elo should be the most precise pair.
    – BlindKungFuMaster
    Dec 17, 2014 at 10:18
  • Ferreira tried to estimate Houdini's strength based on the degree to which its move suggestions lined up with Kramnik et al playing in the London Chess Classic 2011. The error margin for such an estimate must be huge.
    – A passerby
    Sep 29, 2015 at 11:34
  • Stockfish tends to report higher depths than Houdini or Komodo for the same time frame. Depth reporting is not standardized at all, and may mean very different things depending on the engine.
    – A passerby
    Sep 29, 2015 at 11:39
  • @BlindKungFuMaster Good point. It seems that since it's anchored at depth 20, the shallower the depth, the less precise. For example, depth 8 = 2099 Elo, depth 7 = 2033 Elo, depth 6 = 1966 Elo, and the Elo delta between levels is quite consistently 66 Elo. So extrapolating, depth 5 = 1900, depth 4 = 1834, depth 3 = 1768, depth 2 = 1702, and depth 1 = 1636. Which all seem rather high. Other users have run tests, and the Elo delta actually increases as the search depth decreases, which makes some intuitive sense.
    – Dalmazio
    Apr 22, 2017 at 8:38
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Deep Blue will have a higher rating as it was a supercomputer. Do note that all chess engines have a higher rating of 3000+, which no human has been able to achieve so far.

I give Deep Blue as an example because there is something called as adaptability. Adaptability is what chess programmers use to make a chess engine preform better. In 1996 when Garry Kasparov beat Deep Blue, IBM enhanced Deep Blue to hide the computer’s weaknesses that Kasparov unfolded during his play. They covered their actions up, strengthened Deep Blue, and then it went on to defeat Kasparov in th 1997 rematch.

Chess engines derive their strength based upon the play/ELo from the best players. If you are just seeing a higher number and make your decision, then that would not be the best way to judge. I would say that Magnus Carlsen’s best play will defeat Stockfish’s best play any day.

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Yes, Brainfish 221119 Depth 16 can beat Carlsen even if it only runs at 2000 Kn/s in the starting position. Brainfish 221119 depth 16 has an 2820 ELO rating.

This 2820 ELO Rating is Standard Rating, not Rapid or Blitz Rating.

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    Any reference for this?
    – roim
    Jan 28, 2021 at 23:18

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