Winning ways for your mathematical plays. Vol. 1. (Q2703803)

The first edition of \textit{Winning Ways} appeared in two volumes in 1982 (see Zbl 0485.00025). At the time, it provided an innovative general theory of winning and losing positions in a variety of games. After twenty years, the area of combinatorial games has become firmly established and engages the attention of researchers in several areas. This book is the second edition of the first half, \textit{Spade Work}, of the old Volume 1. Very little has been changed; 161 mistakes have been corrected; additions have been made to the chapter appendices and references have been updated. NEWLINENEWLINENEWLINEThe games discussed generally involve two players, no chance elements, complete information and no ties. Typical is Hackenbush, a vehicle for introducing the evaluation of positions as a kind of Dedekind cut between the available moves of the opponents; these values can have the structure of a number system that contains infinitely large and small elements, generalizing both the Dedekind reals and the ordinals. The game of Nim, representative of impartial games in which both players have the same options at any time, are analyzed to determine winning strategies by the Sprague-Grundy theory. There is a detailed study of a variety of specific examples.