Innovation and Nested Preferential Growth in Chess Playing Behavior

TL;DR

This paper analyzes how innovation and preferential growth mechanisms shape decision-making in chess, revealing power-law exploration decay, vocabulary-like growth, and a nested Yule-Simon model that explains these phenomena.

Contribution

It introduces a novel nested Yule-Simon model to explain innovation and preferential growth in chess move sequences, extending understanding of complex decision-making.

Findings

Exploration probability decreases as a power law with move frequency.

Chess move sequences follow Heaps' law, similar to vocabulary growth.

A nested Yule-Simon process reproduces empirical observations.

Abstract

Complexity develops via the incorporation of innovative properties. Chess is one of the most complex strategy games, where expert contenders exercise decision making by imitating old games or introducing innovations. In this work, we study innovation in chess by analyzing how different move sequences are played at the population level. It is found that the probability of exploring a new or innovative move decreases as a power law with the frequency of the preceding move sequence. Chess players also exploit already known move sequences according to their frequencies, following a preferential growth mechanism. Furthermore, innovation in chess exhibits Heaps' law suggesting similarities with the process of vocabulary growth. We propose a robust generative mechanism based on nested Yule-Simon preferential growth processes that reproduces the empirical observations. These results, supporting the self-similar nature of innovations in chess are important in the context of decision making in a competitive scenario, and extend the scope of relevant findings recently discovered regarding the emergence of Zipf's law in chess.