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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 | : Urban Larsson |
| Publisher | : |
| Total Pages | : 490 |
| Release | : 2019 |
| Genre | : |
| ISBN | : 9781108641999 |
| 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 | : Gerolamo Cardano |
| Publisher | : Courier Dover Publications |
| Total Pages | : 64 |
| 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 | : Horace C. Levinson |
| Publisher | : Courier Corporation |
| Total Pages | : 388 |
| Release | : 2001-01-01 |
| Genre | : Mathematics |
| ISBN | : 9780486419978 |
In simple, non-technical language, this volume explores the fundamentals governing chance and applies them to sports, government, and business. Topics includenbsp;the theory of probability in relation to superstitions, betting odds, warfare,nbsp;social problems, stocks, and other areas. "Clear and lively ...nbsp;remarkably accurate." —Scientific Monthly.
| Author | : Manfred Eigen |
| Publisher | : Princeton University Press |
| Total Pages | : 372 |
| Release | : 1993-04-11 |
| Genre | : Law |
| ISBN | : 9780691025667 |
Using 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.
| Author | : |
| Publisher | : |
| Total Pages | : 400 |
| Release | : 1909 |
| Genre | : Chess |
| ISBN | : |
