An Information Theoretic Analysis of Decision in Computer Chess

TL;DR

This paper presents an information theoretic framework for decision-making in computer chess, mathematically justifying the fractional ply search algorithm and explaining its effectiveness in maximizing information gain.

Contribution

It provides a rigorous mathematical foundation for the fractional ply scheme, linking it to information theory and deriving key parameters from first principles.

Findings

The fractional ply search is justified by information theory.

The key parameter of the fractional ply scheme is derived from fundamental principles.

The algorithm effectively navigates along lines of maximum information gain.

Abstract

The basis of the method proposed in this article is the idea that information is one of the most important factors in strategic decisions, including decisions in computer chess and other strategy games. The model proposed in this article and the algorithm described are based on the idea of a information theoretic basis of decision in strategy games . The model generalizes and provides a mathematical justification for one of the most popular search algorithms used in leading computer chess programs, the fractional ply scheme. However, despite its success in leading computer chess applications, until now few has been published about this method. The article creates a fundamental basis for this method in the axioms of information theory, then derives the principles used in programming the search and describes mathematically the form of the coefficients. One of the most important parameters of the fractional ply search is derived from fundamental principles. Until now this coefficient has been usually handcrafted or determined from intuitive elements or data mining. There is a deep, information theoretical justification for such a parameter. In one way the method proposed is a generalization of previous methods. More important, it shows why the fractional depth ply scheme is so powerful. It is because the algorithm navigates along the lines where the highest information gain is possible. A working and original implementation has been written and tested for this algorithm and is provided in the appendix. The article is essentially self-contained and gives proper background knowledge and references. The assumptions are intuitive and in the direction expected and described intuitively by great champions of chess.