Luck, Logic and White Lies: The Mathematics of Games
The book is divided into three parts, roughly corresponding to the topics indicated in the title of the book. Games of chance are investigated in the first part. The influence of randomness is typical for roulette and various dice and card games. In the middle part, the second type of game is analyzed (combinatorial games, e.g., chess and go). The book ends up with strategic games. Rock-paper-scissors is the most simple and well-known game considered in this part. The author reviews mathematical methods that have been developed for different types of games according to their character. For games of chance, an important mathematical tool is provided by probability theory, which can help to answer questions such as the probability for a particular player to win as well as more complicated questions. Combinatorial games are investigated by means of combinatorial game theory. Due to a large number of combinations involved, it is necessary to look for algorithms and computational procedures in order to solve specific problems. Mathematical game theory is applied to the analysis of strategic games. Many other examples of more or less known games are used to explain the mathematical methods considered (e.g., backgammon, Monopoly, blackjack, nim, domino, memory, mastermind, poker, checkers, Hex, Le Her, baccarat, nine men's morris, go-moku). The book is well-written and can be recommended to all readers with an interest in game theory. Although a lot of mathematics is used in the text, it doesn't require a deep mathematical background. There are many references (mostly in German) helping to find more detailed information about considered topics.