Assessing the Difficulty of Chess Tactical Problems

Abstract—We investigate experts ’ ability to assess the difficulty of a mental task for a human. The final aim is to find formalized measures of difficulty that could be used in automated assessment of the difficulty of a task. In experiments with tactical chess problems, the experts ’ estimations of difficulty are compared to the statistic-based difficulty ratings on the Chess Tempo website. In an eye tracking experiment, the subjects ’ solutions to chess problems and the moves that they considered are analyzed. Performance data (time and accuracy) are used as indicators of subjectively perceived difficulty. We also aim to identify the attributes of tactical positions that affect the difficulty of the problem. Understanding the connection between players’ estimation of difficulty and the properties of the search trees of variations considered is essential, but not sufficient, for modeling the difficulty of tactical problems. Our findings include that (a) assessing difficulty is also very difficult for human experts, and (b) algorithms designed to estimate difficulty should interpret the complexity of a game tree in the light of knowledge-based patterns that human players are able to detect in a chess problem