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Games of No Chance 5

Urban Larsson, editor
Cambridge University Press
Publication Date: 
Number of Pages: 
Mathematical Sciences Research Institute Publications (Book 70)
[Reviewed by
Tricia Muldoon Brown
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As you would expect, Games of No Chance 5 is the fifth book in a Mathematical Sciences Research Institute series that reports on some activities and questions posed at the Combinatorial Game Theory Workshop held at Banff International Research Station in 2011.  The first volume of the series was published in 1994 after the initial Combinatorial Games Workshop with subsequent volumes appearing since.  (See for example the reviews of Games of No Chance 3, More Games of No Chance, and Games of No Chance.)
This series focuses on combinatorial games in which randomness does not play a part, that is, games that do not involve things like dice or hidden cards.  The advantage to studying these games of no chance is that players (and researchers) have complete information about the possible set of moves on each turn with no dependence on chance.  This does not, however, imply that games of no chance are easily understood; for example, consider the complexity of game of no chance like chess. Featured in this volume are well-known games and their variations such as Nim or Go, but also lesser known games like Phutball and Officers.  The editor has separated the volume in two sections which are composed of seven survey articles and 16 research articles.
The survey papers are a good place to turn to get an overview of the state of the field or to consider new developments for several types of games such as scoring games, misère, and partisan misère games.  Some surveys are separated into various sections with different authors writing different parts.  Within each section or chapter open problems or extensions are almost always provided.  I especially looked forward to Nowakowski's “Unsolved problems in combinatorial games,” a staple of the Games of No Chance series, and it did not disappoint.  This list was begun in 1991 and each iteration has been updated with new problems and advances or solutions to previous problems.  In this volume 68 problems are discussed.
Also in the first part of the book, you can find Singmaster's survey, “A historical tour of binary and tours,” which is quite interesting for those interested in the history of mathematics as well as the theory of games.  Some nice depictions of primary source material from Arabic, Chinese, Egyptian, European, Japanese and North American mathematicians are provided.  This chapter first discusses the development and use of binary in codes and games such as Chinese Rings.  In the second part of the chapter Hamilton circuits are provided under the auspice of knight's tours and the Icosian game.  Finally, specific games are discussed namely a detailed look is taken at the Tower of Hanoi puzzle.
The second section of the book contains research papers consisting of results either presented or discusses at the BIRS workshop.  These are further divided into categories.  Four articles discuss placement games and simplicial complexes, three articles address games and number theory, four are on subjects considered classic games of no chance, three more are “conceptualizers,” and two look at computational aspects.  These chapters are all stand-alone research articles with less introductory details as compared to the survey papers.  More subject specific prior knowledge is required from the readers in this section.
Overall this volume has several strengths.  There is an excellent “About this book” section introducing each article, providing minimal background, some results, and giving motivation for reading the paper.  Often previous work in the area is also cited here giving the reader and opportunity to review references before they begin.  The figures and notation are nicely done and easy to read.  All chapters include an abstract and list of references.  In a collection like this, I find this presentation preferable to a massive bibliography at the end of the entire text.  Finally, while the papers themselves are good, the myriad source material accompanying the topics is extremely helpful in directing the reader to background and further study topics.
Despite a temptation to classify recreational mathematics as easy or a gateway into more complex math, this volume of research into combinatorial games is not for a novice.  In different parts of the book you will need a strong foundation in mathematical notation and discrete structures. Further, while the survey papers are well-written and include the necessary definitions and introductions to the games studied, they quickly move into the serious mathematics involved in analyzing these games.  The volume is appropriate for researchers and students who have had a combinatorics or advanced discrete structures course in computer science with some comfort level of functions, matrices, graphs, trees, and other combinatorial structures.


Tricia Muldoon Brown ( is an Associate Professor of Mathematics at Georgia Southern University with interests in combinatorics, recreational mathematics, and sports.

See the publisher's web page.