user3999: 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.

user825: 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.

user4362: There is a paper, which examines this relationship for Houdini 1.5.
http://web.ist.utl.pt/diogo.ferreira/papers/ferreira13impact.pdf
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


3999: <p>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.</p>
 825: <p>This is an area that academic can write papers on it. The relationships is complicated and might not be quantified.</p>
<p>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.</p>
<p>Reference: <a href="https://www.chessprogramming.org/Depth" rel="nofollow noreferrer">https://www.chessprogramming.org/Depth</a></p>
<p>Look for the &quot;Diminishing Returns&quot; section and you'll know more.</p>
 4362: <p>There is a paper, which examines this relationship for Houdini 1.5.</p>
<p><a href="http://web.ist.utl.pt/diogo.ferreira/papers/ferreira13impact.pdf" rel="nofollow noreferrer">http://web.ist.utl.pt/diogo.ferreira/papers/ferreira13impact.pdf</a></p>
<p>On page 77 you get the relevant table:</p>
<pre><code>depth (ply): elo:

20    2894

19    2828

18    2761

17    2695

16    2629

15    2563

…

8     2099

7     2033

6     1966
</code></pre>
