The dots-and-boxes game: sophisticated child’s play

Elwyn R. Berlekamp1568811292, 9781568811291

Many of us remember playing the game Dots-and-Boxes as children. It is a familiar paper-and-pencil game for two players who start from a square or rectangular array of dots and take turns in joining two horizontally or vertically adjacent dots. If a player completes the fourth side of a square (box), he initials that box and must then draw another line. When all the boxes have been completed, the game ends and whoever has initialed more boxes is declared the winner. Dots-and-Boxes is, like other good games, remarkable in that it can be played on several different levels of sophistication. This deceptively simple game, however, is more than just child’s play. Dots-and-Boxes strategy serves as an introduction to mathematical game theory, a subject that has earned the prominent mathematician John Nash a Nobel Prize in Economics. This book is an essential guide to the game of Dots-and-Boxes and its mathematical underpinnings. Chapters on strategy are interspersed with 100 sample problems and their strategic solutions. The book will appeal to a diverse range of readers, from casual players seeking to improve their play to mathematicians interested in the more sophisticated strategy techniques.