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Author: Urban Larsson
Publisher: Cambridge University Press
Published: 2019-05-09
Total Pages: 499
ISBN-13: 1108485804
DOWNLOAD EBOOKSurveys the state-of-the-art in combinatorial game theory, that is games not involving chance or hidden information.
Author: Richard J. Nowakowski
Publisher: Cambridge University Press
Published: 1998-11-13
Total Pages: 556
ISBN-13: 9780521646529
DOWNLOAD EBOOKIs Nine-Men Morris, in the hands of perfect players, a win for white or for black - or a draw? Can king, rook, and knight always defeat king and two knights in chess? What can Go players learn from economists? What are nimbers, tinies, switches and minies? This book deals with combinatorial games, that is, games not involving chance or hidden information. Their study is at once old and young: though some games, such as chess, have been analyzed for centuries, the first full analysis of a nontrivial combinatorial game (Nim) only appeared in 1902. The first part of this book will be accessible to anyone, regardless of background: it contains introductory expositions, reports of unusual tournaments, and a fascinating article by John H. Conway on the possibly everlasting contest between an angel and a devil. For those who want to delve more deeply, the book also contains combinatorial studies of chess and Go; reports on computer advances such as the solution of Nine-Men Morris and Pentominoes; and theoretical approaches to such problems as games with many players. If you have read and enjoyed Martin Gardner, or if you like to learn and analyze new games, this book is for you.
Author: Michael H. Albert
Publisher: Cambridge University Press
Published: 2009-05-29
Total Pages: 577
ISBN-13: 0521861349
DOWNLOAD EBOOKThis fascinating look at combinatorial games, that is, games not involving chance or hidden information, offers updates on standard games such as Go and Hex, on impartial games such as Chomp and Wythoff's Nim, and on aspects of games with infinitesimal values, plus analyses of the complexity of some games and puzzles and surveys on algorithmic game theory, on playing to lose, and on coping with cycles. The volume is rounded out with an up-to-date bibliography by Fraenkel and, for readers eager to get their hands dirty, a list of unsolved problems by Guy and Nowakowski. Highlights include some of Siegel's groundbreaking work on loopy games, the unveiling by Friedman and Landsberg of the use of renormalization to give very intriguing results about Chomp, and Nakamura's "Counting Liberties in Capturing Races of Go." Like its predecessors, this book should be on the shelf of all serious games enthusiasts.
Author: Richard Nowakowski
Publisher: Cambridge University Press
Published: 2002-11-25
Total Pages: 552
ISBN-13: 9780521808323
DOWNLOAD EBOOKThis 2003 book provides an analysis of combinatorial games - games not involving chance or hidden information. It contains a fascinating collection of articles by some well-known names in the field, such as Elwyn Berlekamp and John Conway, plus other researchers in mathematics and computer science, together with some top game players. The articles run the gamut from theoretical approaches (infinite games, generalizations of game values, 2-player cellular automata, Alpha-Beta pruning under partial orders) to other games (Amazons, Chomp, Dot-and-Boxes, Go, Chess, Hex). Many of these advances reflect the interplay of the computer science and the mathematics. The book ends with a bibliography by A. Fraenkel and a list of combinatorial game theory problems by R. K. Guy. Like its predecessor, Games of No Chance, this should be on the shelf of all serious combinatorial games enthusiasts.
Author: Richard J. Nowakowski
Publisher: Cambridge University Press
Published: 2015-04-16
Total Pages: 351
ISBN-13: 1107011035
DOWNLOAD EBOOKCombinatorial games are the strategy games that people like to play, for example chess, Hex, and Go. They differ from economic games in that there are two players who play alternately with no hidden cards and no dice. These games have a mathematical structure that allows players to analyse them in the abstract. Games of No Chance 4 contains the first comprehensive explorations of misère (last player to move loses) games, extends the theory for some classes of normal-play (last player to move wins) games and extends the analysis for some specific games. It includes a tutorial for the very successful approach to analysing misère impartial games and the first attempt at using it for misère partisan games. Hex and Go are featured, as well as new games: Toppling Dominoes and Maze. Updated versions of Unsolved Problems in Combinatorial Game Theory and the Combinatorial Games Bibliography complete the volume.
Author:
Publisher:
Published: 2019
Total Pages: 490
ISBN-13: 9781108713658
DOWNLOAD EBOOKAuthor: Gerolamo Cardano
Publisher: Courier Dover Publications
Published: 2015-11-04
Total Pages: 68
ISBN-13: 048680898X
DOWNLOAD EBOOKMathematics was only one area of interest for Gerolamo Cardano ― the sixteenth-century astrologer, philosopher, and physician was also a prolific author and inveterate gambler. Gambling led Cardano to the study of probability, and he was the first writer to recognize that random events are governed by mathematical laws. Published posthumously in 1663, Cardano's Liber de ludo aleae (Book on Games of Chance) is often considered the major starting point of the study of mathematical probability. The Italian scholar formulated some of the field's basic ideas more than a century before the better-known correspondence of Pascal and Fermat. Although his book had no direct influence on other early thinkers about probability, it remains an important antecedent to later expressions of the science's tenets.
Author: David A. Blackwell
Publisher: Courier Corporation
Published: 2012-06-14
Total Pages: 388
ISBN-13: 0486150895
DOWNLOAD EBOOKEvaluating statistical procedures through decision and game theory, as first proposed by Neyman and Pearson and extended by Wald, is the goal of this problem-oriented text in mathematical statistics. First-year graduate students in statistics and other students with a background in statistical theory and advanced calculus will find a rigorous, thorough presentation of statistical decision theory treated as a special case of game theory. The work of Borel, von Neumann, and Morgenstern in game theory, of prime importance to decision theory, is covered in its relevant aspects: reduction of games to normal forms, the minimax theorem, and the utility theorem. With this introduction, Blackwell and Professor Girshick look at: Values and Optimal Strategies in Games; General Structure of Statistical Games; Utility and Principles of Choice; Classes of Optimal Strategies; Fixed Sample-Size Games with Finite Ω and with Finite A; Sufficient Statistics and the Invariance Principle; Sequential Games; Bayes and Minimax Sequential Procedures; Estimation; and Comparison of Experiments. A few topics not directly applicable to statistics, such as perfect information theory, are also discussed. Prerequisites for full understanding of the procedures in this book include knowledge of elementary analysis, and some familiarity with matrices, determinants, and linear dependence. For purposes of formal development, only discrete distributions are used, though continuous distributions are employed as illustrations. The number and variety of problems presented will be welcomed by all students, computer experts, and others using statistics and game theory. This comprehensive and sophisticated introduction remains one of the strongest and most useful approaches to a field which today touches areas as diverse as gambling and particle physics.
Author: Samuel B. Smith
Publisher: Cambridge University Press
Published: 2015-06-29
Total Pages: 393
ISBN-13: 1107084520
DOWNLOAD EBOOKGames and elections are fundamental activities in society with applications in economics, political science, and sociology. These topics offer familiar, current, and lively subjects for a course in mathematics. This classroom-tested textbook, primarily intended for a general education course in game theory at the freshman or sophomore level, provides an elementary treatment of games and elections. Starting with basics such as gambling, zero-sum and combinatorial games, Nash equilibria, social dilemmas, and fairness and impossibility theorems for elections, the text then goes further into the theory with accessible proofs of advanced topics such as the Sprague-Grundy theorem and Arrow's impossibility theorem. * Uses an integrative approach to probability, game, and social choice theory * Provides a gentle introduction to the logic of mathematical proof, thus equipping readers with the necessary tools for further mathematical studies * Contains numerous exercises and examples of varying levels of difficulty * Requires only a high school mathematical background.
Author: Manfred Eigen
Publisher: Princeton University Press
Published: 1993-04-11
Total Pages: 372
ISBN-13: 9780691025667
DOWNLOAD EBOOKUsing game theory and examples of actual games people play, Nobel laureate Manfred Eigen and Ruthild Winkler show how the elements of chance and rules underlie all that happens in the universe, from genetic behavior through economic growth to the composition of music. To illustrate their argument, the authors turn to classic games--backgammon, bridge, and chess--and relate them to physical, biological, and social applications of probability theory and number theory. Further, they have invented, and present here, more than a dozen playable games derived from scientific models for equilibrium, selection, growth, and even the composition of RNA.
