Winning Ways for Your Mathematical Plays

This book was originally published in 2 volumes in 1982. A second edition was released in 4 volumes starting in 2001.

These four volumes (Spades, Hearts, Clubs and Diamonds) explore the foundations and current research in the field of combinatorial games (i.e. games for 2 players with alternating turns, no hidden information, and no chance). It is the definitive work about such games.

In Volume 1, the authors do the spadework, presenting theories and techniques to "dissect" games of varied structures and formats in order to develop winning strategies. Their focus is on "adding games," including Nim, Hackenbush, and Kayles. The inclusion of many examples helps the reader to put the mathematical analysis to immediate use.

In Volume 2, the authors have a Change of Heart and bend the rules of Volume 1 to apply them to games that may continue indefinitely or in which "winning" is not necessarily making the last move, such as Cut-cake and Loopy Hackenbush.

In Volume 3, the authors examine Games played in Clubs, giving case studies for coin and paper-and-pencil games, such as Dots and Boxes and Nimstring.

In Volume 4, the authors present a Diamond of a find, covering one-player games such as Solitaire and ponder subjects and questions such as, Purging Pegs Properly, Pursuing Puzzles Purposefully, and What is Life?