This fascinating look at combinatorial games, that is, games not involving chance or hidden information, offers updates on standard games such as Go and Hex, on impartial games such as Chomp and Wythoff’s Nim, and on aspects of games with infinitesimal values, plus analyses of the complexity of some games and puzzles and surveys on algorithmic game theory, on playing to lose, and on coping with cycles. The volume is rounded out with an up-to-date bibliography by Fraenkel and, for readers eager to get their hands dirty, a list of unsolved problems by Guy and Nowakowski. Highlights include some of Siegel’s groundbreaking work on loopy games, the unveiling by Friedman and Landsberg of the use of renormalization to give very intriguing results about Chomp, and Nakamura’s “Counting Liberties in Capturing Races of Go.” Like its predecessors, this book should be on the shelf of all serious games enthusiasts.
Part I. Surveys: 1. Playing games with algorithms: algorithmic combinatorial game theory Erik D. Demaine and Robert A. Hearn; 2. Advances in losing Thane E. Plambeck; 3. Coping with cycles Aaron N. Siegel; 4. On day N David Wolfe; Part II. Standards: 5. Goal threats, temperature and Monte-Carlo Go Tristan Cazenave; 6. A puzzling hex primer Ryan B. Hayward; 7. Tigers and goats is a draw Lim Yew Jin and Jurg Nievergelt; 8. Counting liberties in Go capturing races Teigo Nakamura; 9. Backsliding toads and frogs Aaron N. Siegel; 10. Loopy games Aaron N. Siegel; 11. A library of eyes in Go, I: a life-and-death definition consistent with bent-4 Thomas Wolf; 12. A library of eyes in Go, II: monolithic eyes Thomas Wolf and Matthew Pratola; Part III. Complexity: 13. The complexity of Dyson telescopes Erik D. Demaine, Martin L. Demaine, Rudolf Fleischer, Robert A. Hearn and Timo von Oertzen; 14. Amazons, konane, and cross purposes are PSPACE-complete Robert A. Hearn; Part IV. Impartial: 15. Monotonic sequence games M. H. Albert, R. E. L. Aldred, M. D. Atkinson, C. C. Handley, D. A. Holton, D. J. Mccaughan and B. E. Sagan; 16. The game of End-Wythoff Aviezri S. Fraenkel and Elnatan Reisner; 17. On the geometry of combinatorial games: a renormalization approach Eric J. Friedman and Adam S. Landsberg; 18. More on the Sprague–Grundy function for Wythoff's game Gabriel Nivasch; Part V. Theory of the Small: 19. Yellow-brown hackenbush Elwyn Berlekamp; 20. Ordinal partizan end Nim Adam Duffy, Garrett Kolpin and David Wolfe; 21. Reductions of partizan games J. P. Grossman and Aaron N. Siegel; 22. Partizan Splittles G. A. Mesdal III; Part VI. Columns: 23. Unsolved problems in combinatorial games Richard K. Guy and Richard J. Nowakowski; 24. Bibliography of combinatorial games Aviezri S. Fraenkel.
"The authors succeed in, first, getting readers interested in this fascinating subject and, then, providing them with an overview of current research results and future research opportunities. Hence, the book is suited for the curious and interested novice, as well as the expert who is looking for new challenges. It is a must-read for anyone interested in the current state of the theory of combinatorial games."
Burkhard Englert, reviews.com