Games of No Chance
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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, 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 a...
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, 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 new 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.
Table of contents:
Part I. All Games Bright and Beutiful: 1. The angel problem John H. Conway; 2. Scenic trail ascending from sea-level Nim to Alpine chess Avierzi Fraenkel; 3. What is a game? Richard K. Guy; 4. Impartial games Richard K. Guy; 5. Championship-level play of dots-and-boxes Julian West; 6. Championship-level play of domineering Julian West; 7. The gamesman's toolkit David Wolfe; Part II. Strides on Classical Ground: 8. Solving Nine-Men Morris Ralph Gasser and Tinsley; 9. Human perfection at checkers? Jonathan Schaeffer and Robert Lake; 10. On numbers and endgames: combinatorial game theory in chess endgames Noam D. Elkies; 11. Multilinear algebra and chess endgames Lewis Stiller; 12. Using similar positions to search game trees Yasuhito Kawano; 13. Where is the 'Thousand-Dollar Ko'? Elwyn Berklekamp and Yonghoan Kim; 14. Eyespace values in Go, Landman; 15. Loopy games and Go David Moews; 16. Experiments in computer Go endgames Martin Muller and Ralph Gasser; Part III. Taming the Menagerie: 17. Sowing games Jeff Erickson; 18. New toads and frogs results Jeff Erickson; 19. A graphical, X-based front-end for domineering Dan Garcia; 20. Infinitesimals and coin-sliding David Moews; 21. Geography played on products of directed cycles Richard J. Nowakowski and David G. Poole; 22. Pentominoes: a first player win Hilarie K. Orman; 23. New values for top entails West; 24. Take-away games Michael Zieve; Part IV. New Theoretical Vistas: 25. The economist's view of combinatorial games Elwyn Berklekamp; 26. Games with infinitely many moves and slightly imperfect information (extended abstract) David Blackwell; 27. The reduced canonical form of a game, Calistrate; 28. Error-correcting codes derived from combinatorial games Avierzi Fraenkel; 29. Tutoring strategies in game-tree search (extended abstract) Hiroyuki Iida, Yoshiyuki Kotani and Jos W. H. M. Uiterwijk; 30. About David Richman James G. Propp; 31. Richman games Andrew J. Lazarus, Daniel E. Loeb, James G. Propp and Daniel Ullman; 32. Stable winning coalitions Daniel E. Loeb; Part V. Coda: Unsolved Problems in Combinatorial Games Richard K. Guy; 33. Combinatorial games: selected bibliography with a succint gourmet introduction Avierzi Fraenkel.
This book deals with combinatorial games, that is, games not involving chance or hidden information. The first part of the book will be accessible to anyone, regardless of background. For those who want to delve more deeply, the book also contains combinatorial studies of chess and Go, plus reports on computer advances and new theoretical approaches.
A fascinating look at the mathematics behind games such as checkers, chess, Go, Nim, and Nine-Men Morris.
Table of contents:
Part I. All Games Bright and Beutiful: 1. The angel problem John H. Conway; 2. Scenic trail ascending from sea-level Nim to Alpine chess Avierzi Fraenkel; 3. What is a game? Richard K. Guy; 4. Impartial games Richard K. Guy; 5. Championship-level play of dots-and-boxes Julian West; 6. Championship-level play of domineering Julian West; 7. The gamesman's toolkit David Wolfe; Part II. Strides on Classical Ground: 8. Solving Nine-Men Morris Ralph Gasser and Tinsley; 9. Human perfection at checkers? Jonathan Schaeffer and Robert Lake; 10. On numbers and endgames: combinatorial game theory in chess endgames Noam D. Elkies; 11. Multilinear algebra and chess endgames Lewis Stiller; 12. Using similar positions to search game trees Yasuhito Kawano; 13. Where is the 'Thousand-Dollar Ko'? Elwyn Berklekamp and Yonghoan Kim; 14. Eyespace values in Go, Landman; 15. Loopy games and Go David Moews; 16. Experiments in computer Go endgames Martin Muller and Ralph Gasser; Part III. Taming the Menagerie: 17. Sowing games Jeff Erickson; 18. New toads and frogs results Jeff Erickson; 19. A graphical, X-based front-end for domineering Dan Garcia; 20. Infinitesimals and coin-sliding David Moews; 21. Geography played on products of directed cycles Richard J. Nowakowski and David G. Poole; 22. Pentominoes: a first player win Hilarie K. Orman; 23. New values for top entails West; 24. Take-away games Michael Zieve; Part IV. New Theoretical Vistas: 25. The economist's view of combinatorial games Elwyn Berklekamp; 26. Games with infinitely many moves and slightly imperfect information (extended abstract) David Blackwell; 27. The reduced canonical form of a game, Calistrate; 28. Error-correcting codes derived from combinatorial games Avierzi Fraenkel; 29. Tutoring strategies in game-tree search (extended abstract) Hiroyuki Iida, Yoshiyuki Kotani and Jos W. H. M. Uiterwijk; 30. About David Richman James G. Propp; 31. Richman games Andrew J. Lazarus, Daniel E. Loeb, James G. Propp and Daniel Ullman; 32. Stable winning coalitions Daniel E. Loeb; Part V. Coda: Unsolved Problems in Combinatorial Games Richard K. Guy; 33. Combinatorial games: selected bibliography with a succint gourmet introduction Avierzi Fraenkel.
This book deals with combinatorial games, that is, games not involving chance or hidden information. The first part of the book will be accessible to anyone, regardless of background. For those who want to delve more deeply, the book also contains combinatorial studies of chess and Go, plus reports on computer advances and new theoretical approaches.
A fascinating look at the mathematics behind games such as checkers, chess, Go, Nim, and Nine-Men Morris.
