Games of No Chance 5 Mathematical Sciences Research Institute Publications Series

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.

Urban Larsson is a postdoctoral fellow at the Industrial Engineering and Management department at Technion – Israel Institute of Technology, Haifa. Prior to this he was a Killam postdoctoral fellow at Dalhousie University, Canada 2014-2016, and before that he was a Lecturer 2013–2014 and a Ph.D. student (ending 2013) at Chalmers tekniska högskola and Göteborgs universitet, Sweden. His main research areas are game theory, number theory, computer science and algorithms.