Games of No Chance 5

Surveys the state-of-the-art in combinatorial game theory, that is games not involving chance or hidden information.

Urban Larsson (Edited by)

9781108485807, Cambridge University Press

Hardback, published 9 May 2019

498 pages
24.1 x 16 x 3 cm, 0.85 kg

'Those with a strong interest in combinatorial game theory may want to add this book to their library.' David Bevan, The Mathematical Gazette

This book surveys the state-of-the-art in the theory of combinatorial games, that is games not involving chance or hidden information. Enthusiasts will find a wide variety of exciting topics, from a trailblazing presentation of scoring to solutions of three piece ending positions of bidding chess. Theories and techniques in many subfields are covered, such as universality, Wythoff Nim variations, misère play, partizan bidding (a.k.a. Richman games), loopy games, and the algebra of placement games. Also included are an updated list of unsolved problems, extremely efficient algorithms for taking and breaking games, a historical exposition of binary numbers and games by David Singmaster, chromatic Nim variations, renormalization for combinatorial games, and a survey of temperature theory by Elwyn Berlekamp, one of the founders of the field. The volume was initiated at the Combinatorial Game Theory Workshop, January 2011, held at the Banff International Research Station.

1. About this book Urban Larsson
2. Temperatures of games and coupons Elwyn Berlekamp
3. Wythoff visions Eric Duchêne, Aviezri Fraenkel, Vladimir Gurvich, Nhan Ho, Clark Kimberling and Urban Larsson
4. Scoring games: the state of play Urban Larsson, Richard Nowakowski and Carlos Pereira dos Santos
5. Restricted developments in partizan misère game theory Rebecca Milley and Gabriel Renault
6. Unsolved problems in combinatorial games Richard Nowakowski
7. Misère games and misère quotients Aaron Siegel
8. An historical tour of binary and tours David Singmaster
9. A note on polynomial profiles of placement games J. I. Brown, D. Cox, A. Hoefel, Neil McKay, Rebecca Milley, Richard Nowakowski and Angela A. Siegel
10. A PSPACE-complete Graph Nim Kyle Burke and Olivia George
11. A nontrivial surjective map onto the short Conway group Alda Carvalho and Carlos Pereira dos Santos
12. Games and complexes I: transformation via ideals Sara Faridi, Svenja Huntemann and Richard Nowakowski
13. Games and complexes II: weight games and Kruskal-Katona type bounds Sara Faridi, Svenja Huntemann and Richard Nowakowski
14. Chromatic Nim finds a game for your solution Mike Fisher and Urban Larsson
15. Take-away games on Beatty's theorem and the notion of k-invariance Aviezri Fraenkel and Urban Larsson
16. Geometric analysis of a generalized Wythoff game Eric Friedman, Scott M. Garrabrant, Ilona Phipps-Morgan, Adam S. Landsberg and Urban Larsson
17. Searching for periodicity in officers J. P. Grossman
18. Good pass moves in no-draw HyperHex: two proverbs Ryan Hayward
19. Conjoined games: Go-Cut and Sno-Go Melissa Huggan and Richard Nowakowski
20. Impartial games whose rulesets produce continued fractions Urban Larsson and Mike Weimerskirch
21. Endgames in bidding chess Urban Larsson and Johan Wastlund
22. Phutball draws Sucharit Sarkar
23. Scoring play combinatorial games Fraser Stewart
24. Generalized misère play Mike Weimerskirch.

Subject Areas: Algorithms & data structures [UMB], Combinatorics & graph theory [PBV], Game theory [PBUD], Discrete mathematics [PBD], Mathematics [PB], Information theory [GPF]