A Generalized Framework for Analyzing Capturing Races in Go

Capturing races or semeai are an important element of Go strategy and tactics. We extend previous work on semeai [1] by introducing a more general framework for analyzing semeai, based on the new concepts of conditional combinatorial games and liberty count games. We show how this framework encompasses earlier concepts such as plain liberty regions and plain eye regions. Furthermore, we discuss how to use upper and lower bounds on such games in a semeai solver. 1 Capturing Races in Go Figure 1: Two simple semeai A semeai in the game of Go can be defined informally as “a race to capture between two adjacent groups that cannot both live”. Figure 1 shows two simple cases. In earlier work [1, 2], we gave more formal definitions of semeai, and described nine different classes of semeai. Semeai of classes 0, 1 and 2 can be detected and evaluated statically, without search. The other classes cover semeai that can be resolved by search, potential semeai, and unclear situations which might end up as a race to capture. This paper contains the following contributions: 1. Section 2 develops a general framework for analyzing semeai in terms of conditional combinatorial games and liberty count games. This framework provides a new basis for the previous model introduced in [1] that used eye and liberty regions. 2. Section 3 extends the semeai analysis framework for cases where an exact game may be difficult to compute, but an easier to obtain upper or lower bound can lead to a resolution of the semeai problem. We only seek to determine the win/loss/seki outcome of a semeai. We do not consider other issues here, such as maximizing the score, computing the combinatorial game value, or determining whether winning a semeai is beneficial at all [1]. In the remainder of this paper we will use the following terms that were defined in [1]: Essential and nonessential block, outside liberty, plain outside liberty, shared liberty, eye, plain eye, nakade, class semeai. 2 Conditional Combinatorial Games Conditional combinatorial games (ccg) are an abstraction of play in a local region that is part of a semeai. In some states nonlocal information is required to determine whether a move is possible. For example, the last liberty in an eye can be taken only as the last overall liberty of a block surrounding the eye. 2.1 Conditional Combinatorial Games and their Context A conditional combinatorial game (ccg) is defined recursively just like a combinatorial game in terms of sets of