What is the Elo rating of a chess computer that can only look 1, 2, 3, ... moves ahead 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 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://chessprogramming.wikispaces.com/Depth

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