Chess variation entropy and engine relevance for humans

TL;DR

This paper introduces a method to quantify the complexity of chess move sequences using entropy, revealing that most humans struggle with high-entropy variations, especially when engine evaluations are modest, highlighting limitations in current AI evaluations for practical human use.

Contribution

The study applies entropy to measure move sequence complexity in chess, demonstrating its relevance for understanding human-AI interaction and decision-making difficulty.

Findings

Most human players struggle with high-entropy variations.

Engine evaluations often mask move complexity, especially when |E|<100 centipawns.

High-entropy variations are common and challenging for non-expert players.

Abstract

Modern chess engines significantly outperform human players and are essential for evaluating positions and move quality. These engines assign a numerical evaluation $E$ to positions, indicating an advantage for either white or black, but similar evaluations can mask varying levels of move complexity. While some move sequences are straightforward, others demand near-perfect play, limiting the practical value of these evaluations for most players. To quantify this problem, we use entropy to measure the complexity of the principal variation (the sequence of best moves). Variations with forced moves have low entropy, while those with multiple viable alternatives have high entropy. Our results show that, except for experts, most human players struggle with high-entropy variations, especially when $|E|<100$ centipawns, which accounts for about $2/3$ of positions. This underscores the need for AI-generated evaluations to convey the complexity of underlying move sequences, as they often exceed typical human cognitive capabilities, reducing their practical utility.