This book, defined, if not created, the field of mathematical game theory when it was introduced 25 years ago. In it Conway (mathematics, Princeton U.) explores the strengths of various positions in several games and arrives at a new class of numbers, called surreal numbers, which include both real numbers and ordinal numbers; these surreal numbers are applied in the author's mathematical analysis of game strategies. This new edition has been supplemented with new developments in game theory and a concentration on the additive theory of partizan games. Annotation c. Book News, Inc., Portland, OR (booknews.com)