Abstract. Applications of combinatorial game theory to Go have, so far, been focused on endgames and eyespace values, but CGT can be applied to any situation that involves counting. In this paper, we will show how CGT can be used to count liberties in Go semeai (capturing races).

Our method of analyzing capturing races applies when there are either no shared liberties or only simple shared liberties. It uses combinatorial game values of external liberties to give an evaluation formula for the outcome of the capturing races.

Introduction

Combinatorial game theory (CGT) has been applied to many kinds of existing games and has produced a lot of excellent results. In the case of Go, applications have focused on endgames and eyespace values so far, but CGT can be applied to any situation that involves counting. In this paper, we will show another application of CGT to Go, that is, to count liberties in capturing races. A capturing race, or semeai, is a particular kind of life and death problem in which two adjacent opposing groups fight to capture each other's group. In addition to the skills involved in openings and endgames, skills in winning capturing races are an important factor in a player's strength at Go. In order to win a complicated capturing race, various techniques, such as counting liberties, taking away the opponent's liberties and extending selfliberties, are required in addition to wide and deep reading.