Table Of ContentDistinguished Dissertations
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Extensional Constructs in Intensional Type Theory
Martin Hofmann
Theorem Proving with the Real Numbers
John Harrison
Hardware Evolution: Automatic Design ofE lectronic Circuits in Reconfigurable
Hardware by Artificial Evolution
Adrian Thompson
Games and Full Abstraction for a Functional Metalanguage with Recursive Types
Guy McCusker
Ian Frank
Search and Planning
Under Incomplete
Information
AS tudy Using Bridge Card Play
, Springer
Ian Frank, BSc, MSc, PhD
Electrotechnical Laboratory, 1-1-4 Umezono, Tsukuba-shi, Ibaraki-ken,
Japan 305
Series Editor
C.J. van Rijsbergen
British Library Cataloguing in Publication Data
Frank, Ian
Search and planning under incomplete information: a study
using bridge card play. -(Distinguished dissertations)
I.Game theory 2.Contract bridge -Mathematics
I.Title
S19.3
Library of Congress Cataloging-in-Publication Data
Frank, Ian, 1967-
Search and planning under incomplete information: a study using
bridge card play 1 Ian Frank.
p. cm. --(CPHC/BCS distinguished dissertations)
(Distinguished dissertations)
Includes bibliographical references (p. ) and index.
ISBN-13: 978-1-4471-1596-0 e-ISBN-13: 978-1-4471-1594-6
DOl: 10.1007/978-1-4471-1594-6
1. Contract bridge--Data processing. 2. FINESSE (computer file)
3. Artificial intelligence--Computer programs. I. Title.
II. Series. III. Series: Distinguished dissertations (Springer-Verlag)
GVI282.7.D38F73 1998
79S.41'S'028S--dc2198-6797
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© Springer-Verlag London Limited 1998
Softcover reprint of the hardcover 18t edition 1998
The use of registered names, trademarks etc. in this publication does not imply, even in the absence of a
specific statement, that such names are exempt from the relevant laws and regulations and therefore free
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The publisher makes no representation, express or implied, with regard to the accuracy of the information
contained in this book and cannot accept any legal responsibility or liability for any errors or omissions
that may be made.
Typesetting: Camera ready by author
34/3830-543210 Printed on acid-free paper
Preface
This book updates the thesis I produced for my PhD at the Department of
Artificial Intelligence of the University of Edinburgh, correcting errors, and
improving some of the formatting and readability. Since the original work
was completed (early 1996), research has progressed. Most notably, the public
profile of AI and game-playing has reached new heights with the feats of the
chess computer DEEPER BLUE (which surely uses AI, no matter what IBM
would have us believe). Although less heralded, the ability of computers to
play Bridge (the main example domain in this book) has also increased.
In July of 1997 a world championship for computer Bridge programs was
hosted by the American Contract Bridge League in Albuquerque, New Mex
ico. This contest was won by a program called Bridge Baron, produced by
Great Game Products. Bridge Baron incorporates knowledge-based planning
techniques developed by Stephen Smith and Dana Nau [1, 2].
Progress has also been made on the contrasting, more brute-force, approach
of sampling the possible card distributions. In particular, Matt Ginsberg has
developed a fast double-dummy solver based on partition search [3]. Ginsberg's
program fared poorly in the 1997 Bridge championships, but Ginsberg himself
reports very promising results [4] on a hard set of complete Bridge deals taken
from the Bridge tutoring program Bridge Master.
At the same time, the FINESSE system described in this book has also im
proved. The prm algorithm presented in Chapter 7 has been found to perform
very well both on Bridge problems and on random game trees [5]. In fact, the
most recent version of FINESSE uses an iterated version of the prm algorithm to
completely solve the 650 single-suit problems from the Encyclopedia of Bridge.
This updated version of FINESSE consistently finds optimal strategies for the
maximum possible number of tricks (against best defence), and also reveals
new errors in the Encyclopedia's solutions. Thus, it can be said to perform at
and above expert level for this task. Further, it seems that the principles 'of
the prm framework can be used in both knowledge-based and brute-force ar
chitectures to improve accuracy. Investigating whether such enhancements can
produce the ultimate goal of consistent expert-level play on full Bridge deals is
now an important topic for ongoing research.
v
Credits
Grateful acknowledgement is made to the following for permission to reproduce
material used in creating figures in this book. Every reasonable effort has been
made to contact the copyright holders of the material used here. Omissions
brought to our attention will be corrected in future editions.
Figure 2.2, D. Khemani, 'Planning with thematic actions', in Proceedings
of the Second International Conference on AI Planning Systems (A IPS-
94), page 292, Menlo Park, CA, 1994. AAAI Press. Reproduced with
the permission of the American Association for Artificial Intelligence.
Figure 2.4, S.J.J. Smith and D.S. Nau, 'Strategic planning for imper
fect information games', in Games: Planning and Learnin9, Papers from
the 1993 Fall Symposium, page 90, AAAI Press, 1993. Reprinted with
permission of the author.
Figure 2.5, J. Schaeffer, P. Lu, D. Szafron, and R. Lake, 'A re-examination
of brute-force search', in Games: Planning and Learning, Papers from
the 1993 Fall Symposium, page 54, AAAI Press, 1993. Reprinted with
permission of the author.
Figure 3.1, Reprinted from Artificial Intelligence, Vol 76, S. Kambham
pati, C. Knoblock, and Q. Yang, 'Planning as refinement search: A uni
fied framework for evaluating design tradeoffs in partial order planning',
page 172, July 1995, with kind permission of Elsevier Science - NL, Sara
Burgerharstraat 25, 1055 KV Amsterdam, The Netherlands.
Figure 3.2, Reprinted from Artificial Intelligence, Vol 76, S. Kambham
pati, C. Knoblock, and Q. Yang, 'Planning as refinement search: A uni
fied framework for evaluating design tradeoffs in partial order planning',
pages 177 - 178, July 1995, with kind permission of Elsevier Science -
NL, Sara Burgerharstraat 25, 1055 KV Amsterdam, The Netherlands.
Figure 3.4, Reprinted from Artificial Intelligence, Vol 76, S. Kambham
pati, C. Knoblock, and Q. Yang, 'Planning as refinement search: A uni
fied framework for evaluating design tradeoffs in partial order planning',
vii
viii Credits
pages 177 - 178, July 1995, with kind permission of Elsevier Science -
NL, Sara Burgerharstraat 25, 1055 KV Amsterdam, The Netherlands.
Figure 3.5 and Figure 8.11, Reprinted from Artificial Intelligence, Vol
76, S. Kambhampati, C. Knoblock, and Q. Yang, 'Planning as refine
ment search: A unified framework for evaluating design tradeoffs in par
tial order planning', page 188, July 1995, with kind permission of Else
vier Science - NL, Sara Burgerharstraat 25, 1055 KV Amsterdam, The
Netherlands.
Chapter 11 and Appendix C, Bridge card combinations and suggested
lines of play taken from the The Official Encyclopedia of Bridge, Amer
ican Contract Bridge League, Inc., 2990 Airways Boulevard, Memphis,
Tennessee 38116-3875, fifth edition, 1994. Reproduced with kind permis
sion of the American Contract Bridge League, Inc.
Foreword
In this book, we investigate problem-solving in domains featuring incomplete
information and multiple agents with opposing goals. In particular, we describe
FINESSE - a system that forms plans for the problem of declarer play in the
game of Bridge.
We begin by examining the problem of search. We formalise a best defence
model of incomplete information games in which equilibrium point strategies
can be identified, and identify two specific problems that can affect algorithms
in such domains. In Bridge, we show that the best defence model corresponds
to the typical model analysed in expert texts, and examine search algorithms
which overcome the problems we have identified.
Next, we look at how planning algorithms can be made to cope with the
difficulties of such domains. This calls for the development of new techniques
for representing uncertainty and actions with disjunctive effects, for coping
with an opposition, and for reasoning about compound actions. We tackle
these problems with an architecture that identifies and resolves conflicts on the
basis of probabilistic reasoning about resources. The prime contribution of this
architecture is that it can construct plans which succeed under a large number
of possible world states without having to consider each world state separately.
By casting our algorithm within the classical plan-space planning paradigm we
show how our techniques differ from, yet may be incorporated into, existing
planning architectures.
The original motivation for this work came from the field of mathematical
reasoning. In Edinburgh, a technique known as proof-planning has been de
veloped to control the search for the proofs of mathematical theorems. The
defining feature of this paradigm is that it restricts the available options at any
stage of planning to a pre-determined set of possibilities. By applying proof
planning techniques to the domain of Bridge (although currently only in the
sub-problem of play without a trump suit), FINESSE becomes capable of con
structing plans that look ahead right to the end of the tree of possible actions.
Against human players it is therefore less prone to the short-sightedness that
afflicts the traditional look-ahead approach. This allows it to solve problems
that are beyond the range of previous systems.
ix
x Foreword
We also describe two useful side-effects of formalising the way in which Bridge
can be played. Firstly, the high-level nature of the objects in FINESSE'S plans,
combined with the utilisation of a qualitative uncertainty representation lan
guage, gives the system the ability to produce meaningful textual explanations
for its actions. Secondly, by distilling the large diversity of card-play exam
ples found in the Bridge literature into a manageable number of concrete and
distinct manreuvres we arrive at a deeper understanding of the game itself.
Acknowledgements
Doing a PhD was hard! No, really, really hard! I couldn't possibly have got
through without help from countless people. I'd like to thank them all in a
great big list, but that would take too long. Here's a little list instead. Thanks
to:
• The Three Wise Men - Alan Bundy, David Basin, and Brian Drabble
- who were my supervisors for this research. For the ideas, the support,
the encouragement, the brainstorming sessions, for telling me when I was
too incoherent, and for finally getting me to submit. Thank you. Thank
you. Thank you.
• My friends. For just telling me I was too incoherent.
• My family. Of course. A special mention to My Dad, though, who
(voluntarily) saved my thesis from the fate of never being read by anyone
except academics.
This research was supported by an SERCjEPSRC Advanced Studentship to
the author, award number 92314771. It was also made possible by the rolling
funding BCjDAAD ARC grant (Project number 438) of the Mathematical
Reasoning Group at Edinburgh University.
Xl
