More Games of No Chance

This 2003 book documents mathematical and computational advances in Amazons, Chomp, Dot-and-Boxes, Go, Chess, Hex, and more.

Richard Nowakowski (Edited by)

9780521155632, Cambridge University Press

Paperback, published 17 February 2011

548 pages
23.4 x 15.6 x 2.8 cm, 0.76 kg

"Combinatorial games provide the teacher with a creative means to allow students to explore mathematical ideas and develop problem-solving skills. While the rules are simple, there are rich mathematical theories underlying these games. Students are puzzled at first, and seem to make random moves. By encouraging them to start with simple games with a small number of pieces and then gradually increase the complexity, students are able to formulate and test their own theories for strategic solutions."
S. Wali Abdi, School Science and Mathematics

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.

Part I. The Big Picture: 1. Idempotents among partisan games Elwyn Berlekamp
2. On the lattice Structure of finite games Dan Calistrate, Marc Paulhus and David Wolfe
3. More infinite games John H. Conway
4. Alpha-Beta pruning under partial orders Matthew L. Ginsberg
5. The abstract structure of the group of games David Moews
Part II. The Old Classics: 6. Higher numbers in pawn endgames on large chessboards Noam D. Elkies
7. Restoring fairness to Dukego Greg Martin
8. Go thermography: the 4/21/98 Jiang-Rui endgame Bill Spight
9. An application of mathematical game theory to go endgames: some width-two-entrance rooms with and without Kos Takenobu Takizawa
10. Go endgames are PSPACE-hard David Wolfe
11. Global threats in combinatorial games: a computation model with applications to chess endgames Fabian Mäser
12. The games of hex: the hierarchical approach Vadim V. Anshelevich
13. Hypercube tic-tac-toe Solomon W. Golomb and Alfred W. Hales
14. Transfinite chomp Scott Huddleston and Jerry Shurman
15. A memory efficient retrograde algorithm and its application to Chinese chess endgames Ren Wu and Donald F. Beal
Part III. The New Classics: 16: The 4G4G4G4G4 problems and solutions Elwyn Berlekamp
17. Experiments in computer amazons Martin Müller and Theodore Tegos
18. Exhaustive search in amazons Raymond Georg Snatzke
19. Two-player games on cellular automata Aviezri S. Fraenkel
20. Who wins domineering on rectangular boards? Michael Lachmann, Christopher Moore and Ivan Rapaport
21. Forcing your opponent to stay in control of a loony dot-and-boxes endgame Elwyn Berlekamp and Katherine Scott
22. 1 x n Konane: a summary of results Alice Chan and Alice Tsai
23. 1-dimensional peg solitaire, and duotaire Christopher Moore and David Eppstein
24. Phutball endgames are hard Erik D. Demaine, Martin L. Demaine and David Eppstein
25. One-dimensional phutball J. P. Grossman and Richard J. Nowakowski
26. A symmetric strategy in graph avoidance games Frank Harary, Wolfgang Slany and Oleg Verbitsky
27. A simple FSM-based proof of the additive periodicity of the Sprague-Grundy function of Wythoff's games Howard Landman
Part IV. Puzzles and Life: 28. The complexity of clickomania Therese C. Biedl, Erik D. Demaine, Martin L. Demaine, Rudolf Fleischer, Lars Jacobsen and Ian Munro
29. Coin-moving puzzles Erik D. Demaine, Martin L. Demaine and Helena A. Verrill
30. Searching for spaceships David Eppstein
Part V: Surveys: 31. Unsolved puzzles in combinatorial game theory: updated Richard K. Guy and Richard J. Nowakowski
Bibliography of combinatorial games: updated Aviezri S. Fraenkel.

Subject Areas: Combinatorics & graph theory [PBV]