Evaluating territories of Go positions with capturing races

Summary

In analysing capturing races, or semeais, we have been focusing on the method to find which player wins the race so far, because whether to win or to lose the capturing race largely affects the territory score and it somtimes can decide the outcome of the game. But in order to evaluate the state of the game properly, we usually have to count the territory score precisely regardless of which player wins the race. Sometimes the loser of a capturing race has good moves although the moves don’t affect the status of winning or losing the race. In this paper, we propose a method for evaluating territory score in each decomposed subgame of a capturing race considering the status of the winner of the race.

Combinatorial game theory has been applied to many kinds of existing games and has produced many excellent results. In the case of the game of Go, applications of CGT have been focused on endgames [Berlekamp and Wolfe1994; Berlekamp 1996; Müller et al. 1996; Nakamura and Berlekamp 2003; Spight 2003] and eyespace values [Landman 1996] so far. But it can be applied to any situations that involve counting. Recently, we developed a new genre of application of CGT to Go, that is, to count liberties in capturing races [Nakamura 2003; Nakamura 2009; Nakamura 2006].

Capturing races, or semeai is a particular kind of life and death problem in which two adjacent opposing groups are each fighting to capture the opponent’s group. A player’s strength in Go depends on their skills in winning capturing races as well as opening and endgame skills. In order to win a complicated capturing race, various techniques in counting liberties, taking away the opponent’s liberties, and extending self-liberties, are required in addition to broad and deep reading. Human expert players usually count liberties for each part of the blocks involved in semeai, sum them, and decide the outcome. A position of capturing races can also be decomposed into independent subpositions, as in the cases of endgames and eyespaces, and we can apply CGT to analyse the capturing races. We propose a method of analysing capturing races that have no shared liberty or have only simple shared liberties, and then, using combinatorial game values of external liberties, give an evaluation formula to find the outcome of the capturing races.