Connection Games: Variations on a Theme

Connection games constitute certain kinds of board game that share a common feature: the main goal is to develop or complete a connection of some sort before the other players do. The games have plenty of applications in many areas, in particular in economy. The classic connection game is called Hex, invented in the 40’s by Danish mathematician Piet Hein and reinvented shortly afterwards by the famous John Nash. The subject of connection games had been studied with growing interest through the second half of the twentieth century and has seen a real boom since 2000. By the outbreak of 21st century, connection games had finally earned certain recognition as a distinct genre of board game. Connection games can be described mathematically but they can also be enjoyed by players with no mathematical education whatsoever. The introduction of connection games to the public was established through Martin Gardner's Scientific American article ‘Concerning the Game of Hex, which May be Played on the Tiles of the Bathroom Floor’, which was published in 1957.
It seems that time has come for a comprehensive book dedicated purely to connection games to appear. And here it is! This book by C. Browne is a true masterpiece in an area in which such a thing was desperately needed and there is no doubt that it will become a classic. Moreover, it is likely to attract many people not only to connection games or strategy games, but, in general, to mathematics. What a blessing! The book is a skilful blend of history, graph theory, psychology, philosophy, strategy and tactics, and, most of all, it is an encyclopedia of games, plenty of which haven't been published before. The book is unbearably entertaining and dangerous too; one should certainly not open it unless one has a free two hours or so.
First of all, the book describes a precise definition of what is exactly meant by a connection game. Examples illustrate why for example Go or Tic Tac Toe are not connection games. The notions of adjacency, connection, pattern, duality, switching games, graphs, edges, vertices, deadlocks and more are explained thoroughly, correctly and completely, and yet the expository is carefully kept light enough in order not to scare away math-phobic readers. The main part of the text is devoted to a detailed description of the games (Part II). Each game has its own section in which the rules, strategy and tactics, history and variants are described together with interesting notes. Although the games are examined in detail, the emphasis is on exploring their philosophy, fundamental nature and what distinguishes them from other games.
Many games are published here for the first time. Most of them have been invented since 2000, many by the author of the book (such as the intriguing three-dimensional game Druid). One of the things I like most about this book is that it concentrates solely on board games. Computer games are excluded unless they have a reasonable board version. OK. Enough! Don't read this review. Read the book. It is simply a great one.

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