1. Introduction

In the two-player strategy game of Go, it can happen that an endgame position splits up into several non-interacting subpositions. Since each player must then move in just one of the subpositions on his turn, the whole position will then be the so-called disjunctive compound, or sum, of the subpositions. As it turns out, we can then apply to these Go endgames the theory of partizan combinatorial games with finite play under disjunctive composition, as found in Winning Ways [Berlekamp et al. 1982], Chapters 1-8, or On Numbers and Games [Conway 1976].

This paper assumes that the reader is already somewhat familiar with Go and with the application of this theory to Go, as given in [Wolfe 1991; Berlekamp and Wolfe 1994]. In Chapter 11 of Winning Ways there is a theory of partizan combinatorial games with possibly infinite play under disjunctive composition. These games are there called loopy, since what was a game tree in the finite play case is now a game graph, perhaps with cycles. We review this theory of loopy games and show how it can be applied to Go, which also has cycles.