Has anyone calculated the average Elo rating of a chess computer as a function of the number of half moves or plys ahead it can look. I realise that the Elo is also a function of the choice of move then taken which may differ from engine to engine.

  • This is likely (if not guaranteed) to be very different for each major chess engine. Oct 9, 2014 at 13:52
  • 1
    Yes I mention that in the question. I am really just looking for an average estimate.
    – Dom
    Oct 9, 2014 at 15:36

2 Answers 2


There is a paper, which examines this relationship for Houdini 1.5.


On page 77 you get the relevant table:

depth (ply): elo:

20    2894

19    2828

18    2761

17    2695

16    2629

15    2563


8     2099

7     2033

6     1966

This is an area that academic can write papers on it. The relationships is complicated and might not be quantified.

Essentially, it's a non-linear relationship where the improvement is most obvious in shallow depth. The benefit diminishes as the engine go deeper and deeper in the search.

Reference: https://www.chessprogramming.org/Depth

Look for the "Diminishing Returns" section and you'll know more.

  • Thanks for that reference. It provides some useful relative advantages between a n-ply and an n+1-ply engine. I was looking for an absolute Elo but I accept now that that may not be possible.
    – Dom
    Oct 10, 2014 at 14:26
  • 1
    Absolute Elo is not possible because it varies from one engine to another. There is simply no formula.
    – SmallChess
    Oct 10, 2014 at 14:52

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