"Winning Ways" is a two-volume book
about mathematical game
s. All of the games discussed in the book have perfect information
(i.e. nothing is concealed from any of the player
s at any time) and no chance
moves. Most of them also satisfy other criteria, for example that there are only two players (called Left and Right) who move alternate
ly, that the game cannot go on forever, and that the first player to have no legal move
Volume 1, "Games in General", discusses the theory of games and introduces formal ways of describing a position in a game and assigning a value to it. It begins with a game called Blue-Red Hackenbush, in which the value of every position can be represented as a number, which roughly means that this game is equivalent to giving Left that number of free moves. (The number can be negative, meaning Right has free moves, or non-integral. Zero is the value of any game in which the first player loses.) Games with a numerical value are "cold" - you'd prefer to miss moves if you could - but many games are "hot", and the theory of assigning a "temperature" to games is discussed in detail. There is also a lot of discussion of "impartial" games (games where in any position, both players have the same legal moves) - these all have the same value as some position in the game of Nim.
Volume 2, "Games in Particular", discusses strategies for playing some specific mathematical games. The game of Fox and Geese is analysed and assigned a value, and the game of Sylver Coinage which has the interesting property that it can go on for any finite number of moves but will definitely terminate is also analysed. The last few chapters deal with games for one or zero players: topological puzzles, peg solitaire, and the Game of Life.