Combinatorial Analysis of Go Endgame Positions Public
McMillen, Jacob Aaron (2010)
Published
Abstract
Abstract
Combinatorial Analysis of Go Endgame Positions
By Jacob A. McMillen
Go is a two player skill game of Chinese origin. Although Go is
praised for having a simple
rule set, the game generates tremendous complexity. As such,
programmers have been
unable to design Go AI programs that exceed the level of
intermediate human players. By
using techniques of combinatorial theory, mathematicians have
recently developed methods
of determining optimal play on certain classes of Go positions. It
is our goal to present a
survey of these analytic methods. We will first provide an
introduction on the rules of Go
as well as relevant concepts of combinatorial game theory. We will
then proceed to solve
several categories of small Go positions and finally show how
to determine perfect play on
a full size Go endgame by way of partitioning into solvable
subgames.
Combinatorial Analysis of Go Endgame Positions
By
Jacob A. McMillen
B.S., SUNY Fredonia, 2005
Advisor: Ron Gould, Ph.D.
A thesis submitted to the Faculty of the
James T. Laney School of Graduate Studies of Emory University
in partial fulfillment of the requirements for the degree
of
Master of Science
in Mathematics
2010
Table of Contents
1 Overview: pg. 1
2 Combinatorial Games: pg. 3
3 Analyzing Go Positions: pg. 8
4 Current and Future Research: pg. 35
A Rules of Go: pg. 38
About this Master's Thesis
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