5

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.

  • 1
    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 '14 at 3:25
  • This is a very tough question because nobody knows unless Carlsen himself sits and plays Stockfish for every depth. – SmallChess Dec 17 '14 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. – SmallChess Dec 17 '14 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 '14 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 '14 at 8:01
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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.)

  • 1
    Note that the paper get the data by self-playing. This implies the resulting Elo might not be very representative. – SmallChess Dec 17 '14 at 10:00
  • 2
    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 '14 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 '15 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 '15 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 '17 at 8:38
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Deep blue will have a higher rating as it was a Super Computer . ok please note that all Chess Engines have a higher rating of 3000 + which no Human has been able to achieve till date . Why I gave the example of Deep Blue ....Please understand it deeper . There is something called as Adaptability which the Chess programmers do to make the Chess Engine better . In 1996 when Kasparov beat Deep Blue then IBM enhanced Deep blue to cover up the Weaknesses which Garry unfolded during his play . They covered it up and strengthen it and then it was made to defeat Kasparov back again in 1997 . 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 challenge "The Best play from Carlsen will defeat the best Play of Stockfish any day ".

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