Eur. Phys. J. B 80, 555–563 (2011)
DOI: 10.1140/epjb/e2011-10905-8
Regular Article
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The aggregate complexity of decisions in the game of Go
M.S. Harr´e
1,a
, T. Bossomaier
2
, A. Gillett
1
, and A. Snyder
1
1
The Centre for the Mind, The University of Sydney, 2006 Sydney, Australia
2
Centre for Research in Complex Systems, Charles Sturt University, Australia
Received 21 November 2010 / Received in final form 2 March 2011
Published online 24 March 2011 –
c
EDP Sciences, Societ`a Italiana di Fisica, Springer-Verlag 2011
Abstract. Artificial intelligence (AI) research is fast approaching, or perhaps has already reached, a bottle-
neck whereby further advancement towards practical human-like reasoning in complex tasks needs further
quantified input from large studies of human decision-making. Previous studies in psychology, for example,
often rely on relatively small cohorts and very specific tasks. These studies have strongly influenced some of
the core notions in AI research such as the reinforcement learning and the exploration versus exploitation
paradigms. With the goal of contributing to this direction in AI developments we present our findings on
the evolution towards world-class decision-making across large cohorts of subjects in the formidable game
of Go. Some of these findings directly support previous work on how experts develop their skills but we also
report on several previously unknown aspects of the development of expertise that suggests new avenues
for AI research to explore. In particular, at the level of play that has so far eluded current AI systems for
Go, we are able to quantify the lack of ‘predictability’ of experts and how this changes with their level of
skill.
1 Introduction
This work uses very large databases of professional and
amateur players of the game of Go in order to understand
the properties of the choices made by populations of play-
ers of a known rank. We take a large and tactically well
studied area of the Go board and empirically derive a com-
pletegametreeofeverychoice made by players according
to their rank. Sorting our results according to this rank,
from lowest to highest amateurs and then lowest to high-
est professionals, provides a very fine grained data-set of
changes in behavioural patterns across large populations
as they acquire exceptionally high levels of skill in one of
the most formidable popular games played today.
The underlying principle of this work is to move the
analysis of complex decision tasks away from the detailed
local analysis of strongly interacting elements and further
towards the domain of weakly interacting contextual ele-
ments of a situation. Previous work on Go has successfully
shown the utility of seeing the board in terms of the indi-
vidual pieces (called stones) that have strong local inter-
actions [1]. This technique was used to estimate territory
and as a possible foundation on which a decision model
could be based. A similar approach views the Go board
as a ‘conditional random field’ [1,2], a technique that is
able to relax the strong independence assumptions of hid-
den markov models and stochastic grammars [3]. Other
directions have considered local patterns of stones for de-
a
e-mail: mike@centreforthemind.com
cision making [4,5], the representation of the board as a
graph [6] and the formal analysis of endgame positions in
terms of independent subgames [7]. This work is intended
to inform the next generation of AI systems in regard to
the complexity of decisions within the context of learn-
ing better play through an understanding of the changing
contextual dependency of decisions. This perspective im-
plies that whilst we study populations of players and their
choices what we have in mind is a single AI that is able to
make choices that are consistent with players of a certain
skill.
The paper is laid out in the following manner. We first
introduce the game of Go along with its basic principles
and how we constructed the game trees of decisions from
databases. Then the necessary tools of information theory
are introduced and described. The game trees are then
analysed in terms of information theory and our principal
findings are presented. Finally we discuss the consequences
of these findings in the context of other research.
2 The game of Go
The game of Go is more than 2 000 years old and still
holds a significant cultural place in many asian countries.
Despite a vast array of information and analysis that is
available to players on almost every aspect of Go strategy,
possibly even surpassing that of Chess, the rules of the
game are deceptively simple. There are two players each
of which plays with either black or white stones on a board