Games Of No Chance 5
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Author | : Urban Larsson |
Publisher | : Cambridge University Press |
Total Pages | : 499 |
Release | : 2019-05-09 |
Genre | : Computers |
ISBN | : 1108485804 |
Surveys 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 |
Total Pages | : 556 |
Release | : 1998-11-13 |
Genre | : Mathematics |
ISBN | : 9780521646529 |
Is 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 |
Total Pages | : 577 |
Release | : 2009-05-29 |
Genre | : Mathematics |
ISBN | : 0521861349 |
This 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 |
Total Pages | : 552 |
Release | : 2002-11-25 |
Genre | : Mathematics |
ISBN | : 9780521808323 |
This 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 |
Total Pages | : 351 |
Release | : 2015-04-16 |
Genre | : Mathematics |
ISBN | : 1107011035 |
Combinatorial 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 | : Samuel B. Smith |
Publisher | : Cambridge University Press |
Total Pages | : 393 |
Release | : 2015-06-29 |
Genre | : Business & Economics |
ISBN | : 1107084520 |
Games 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 | : Gerolamo Cardano |
Publisher | : Courier Dover Publications |
Total Pages | : 68 |
Release | : 2015-11-04 |
Genre | : Games & Activities |
ISBN | : 048680898X |
Mathematics 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 | : |
Publisher | : |
Total Pages | : 490 |
Release | : 2019 |
Genre | : Combinatorial group theory |
ISBN | : 9781108713658 |
Author | : Melvin Dresher |
Publisher | : Courier Corporation |
Total Pages | : 212 |
Release | : 2012-11-14 |
Genre | : Mathematics |
ISBN | : 0486150062 |
This text offers an exceptionally clear presentation of the mathematical theory of games of strategy and its applications to many fields including economics, military, business, and operations research.
Author | : James M. Van Verth |
Publisher | : CRC Press |
Total Pages | : 706 |
Release | : 2008-05-19 |
Genre | : Art |
ISBN | : 0123742978 |
Essential Mathematics for Games and Interactive Applications, 2nd edition presents the core mathematics necessary for sophisticated 3D graphics and interactive physical simulations. The book begins with linear algebra and matrix multiplication and expands on this foundation to cover such topics as color and lighting, interpolation, animation and basic game physics. Essential Mathematics focuses on the issues of 3D game development important to programmers and includes optimization guidance throughout. The new edition Windows code will now use Visual Studio.NET. There will also be DirectX support provided, along with OpenGL - due to its cross-platform nature. Programmers will find more concrete examples included in this edition, as well as additional information on tuning, optimization and robustness. The book has a companion CD-ROM with exercises and a test bank for the academic secondary market, and for main market: code examples built around a shared code base, including a math library covering all the topics presented in the book, a core vector/matrix math engine, and libraries to support basic 3D rendering and interaction.