The Impact of the Search Depth on Chess Playing Strength

Abstract

How deep does a chess Grandmaster think? This question has been asked many times, and yet there is hardly a definite answer. Raw depth and pure calculation are certainly not the only factors in the thinking process of a chess player, but it would be interesting to know more about the relationship between search depth and playing strength, so that the strength of a given player (which is usually expressed in terms of an Elo rating) can be said to correspond to a certain equivalent depth (of some given engine). Since the thinking depth of a human player is difficult to determine, we carry out an experiment with a chess engine running at different search depths in order to obtain an average score that can be translated into a rating difference in the Elo scale. However, knowing the rating difference is not sufficient; we need have at least one value of engine depth for which the corresponding Elo rating has been estimated, so that the Elo ratings for other values of search depth can also be determined. In order to obtain the Elo rating that corresponds to HOUDINI 1.5a 64-bit running at a fixed iteration depth of 20 plies, we carry out an analysis of the quality of play at the Candidates Tournament 2013. From these results, we show how the search depth of that particular engine correlates with the Elo ratings of human players. The paper also discusses related work on self-play experiments and the effect of diminishing returns, which becomes apparent in our experiment.