Mathematical Go: Revisited

TL;DR

This paper critiques the mathematical foundations of the book Mathematical Go, proposing that Fraser Stewart's scoring play game theory provides a more accurate framework for analyzing Go's mathematical structure.

Contribution

It introduces a new theoretical approach based on scoring play games, challenging previous definitions and demonstrating its applicability to Go.

Findings

Stewart's scoring play theory better models Go's structure

Previous theories are based on incorrect definitions

Mathematical properties of Go are unique among scoring games

Abstract

In this paper we will look at the book Mathematical Go by Elwyn Berlekamp and David Wolfe \cite{MG}, and argue that the definitions and theories that they use are not the correct ones. We will argue that the new theory of scoring play games as developed by Fraser Stewart \cite{FS, FSP} is the proper way to analyse the game because it gives us the actual mathematical foundation for developing further theories for Go. We will also show that the reason the methods in the book Mathematical Go appear to work is coincidentally because the game Go has some very nice properties and show that these theories would not work for other scoring play games.