Quantifying the Degradation of Human Decision-Making Under Time Pressure Through the Self-Information of Chess

Though it is well established that time pressure has detrimental effects on human cognition, its relative effects across different levels of competency remain largely unquantified. To address this gap, we extend Claude Shannon's work in information theory to the game of chess. To quantify the quality of human decision-making in a chess game, we calculate the probability of all legal moves in a given position from engine evaluations using a softmax function. Then, we sum the Shannon information of each played move in a single game to obtain the game's total surprisal. By applying this framework to a large dataset of $22,500$ chess games from the lichess.org Open Database, our results show that time pressure does not affect individuals of different skill levels uniformly. Highly skilled players effectively utilize additional time to improve decision quality, decreasing surprisal, whereas less skilled players exhibit poor baseline decision quality, high surprisal, which does not improve with additional time. These findings highlight the importance of distinguishing between skill-based and time-based limiting factors in any cognitive performance-based context, such as timed test-taking.