Games of No Chance 4

Presents the mathematical structure of old games and new: Hex, Go, Toppling Dominoes, Maze, plus a tutorial on analysing misère games.

Richard J. Nowakowski (Edited by)

9781107011038, Cambridge University Press

Hardback, published 16 April 2015

350 pages, 70 b/w illus. 23 tables
23.4 x 15.6 x 2.1 cm, 0.6 kg

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.

1. Peeking at partizan misère quotients Meghan R. Allen
2. A survey about solitaire clobber Laurent Beaudou, Eric Duchene and Sylvain Gravier
3. Monte-Carlo approximation of temperature Tristan Cazenave
4. Retrograde analysis of woodpush Tristan Cazenave and Richard J. Nowakowski
5. Narrow misère dots-and-boxes Sebastien Collette, Erik D. Demaine, Martin L. Demaine and Stefan Langerman
6. Toppling conjectures Alex Fink, Richard J. Nowakowski, Aaron Siegel and David Wolfe
7. Harnessing the unwieldy MEX function Aviezri Fraenkel and Udi Peled
8. The rat game and the mouse game Aviezri Fraenkel
9. A ruler regularity in hexadecimal games J. P. Grossman and Richard J. Nowakowski
10. A handicap strategy for hex Philip Henderson and Ryan Hayward
11. Restrictions of m-wythoff nim and p-complementary Beatty sequences Urban Larsson
12. Computer analysis of sprouts with nimbers Julien Lemoine and Simon Viennot
13. Navigating the MAZE Neil McKay, Richard J. Nowakowski and Angela Siegel
14. Evaluating territories of Go positions with capturing races Teigo Nakamura
15. Artificial intelligence for bidding Hex Sam Payne and Elina Robeva
16. Nimbers in partizan games Carlos Pereira Dos Santos and Jorge Nuno Silva
17. Misère canonical forms of partizan games Aaron Siegel
18. The structure and classification of misère quotients Aaron Siegel
19. An algorithm for computing indistinguishability quotients in misére impartial combinatorial games Mike Weimerskirch
20. Unsolved problems in combinatorial games Richard J. Nowakowski
21. Combinatorial games: selected short bibliography with a succinct gourmet introduction Aviezri Fraenkel and Richard J. Nowakowski.

Subject Areas: Combinatorics & graph theory [PBV], Mathematics [PB]