An Application of Mathematical Game Theory to Go Endgames: some Width-Two-Entrance Rooms With and Without Kos

The author is part of a research group under the supervision of Professor Berlekamp. The group is studying the late-stage endgame of Go and has extended the theory of quasi-loopy games using the concept of a ko-master. This paper discusses some width-two-entrance rooms with and without kos that have arisen in this study. 1. Easy Examples without Kos Figure 1.1 shows a simple width-two-entrance 5-room position. Though it is easily analyzed by mathematicians, it is difficult even for strong Go players to determine the best move. Black’s two options from Figure 1.1 are shown in Figures 1.2 and 1.3, and White’s two options are shown in Figures 1.4 and 1.5.