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Published online by Cambridge University Press: 29 May 2025
This volume arose from the second Combinatorial Games Theory Workshop and Conference, held at MSRI from July 24 to 28, 2000. The first such conference at MSRI, which took place in 1994, gave a boost to the relatively new field of Combinatorial Game Theory (CGT); its excitement is captured in Games of No Chance (Cambridge University Press, 1996), which includes an introduction to CGT and a brief history of the subject. In this volume we pick up where Games of No Chance left off.
Although Game Theory overlaps many disciplines, the majority of the researchers are in mathematics and computer science. This was the first time that the practioners from both camps were brought together deliberately, and the results are impressive. This bringing together seems to have formed a critical mass. There has already been a follow-up workshop at Dagstuhl (February 2002) and more are planned.
This conference greatly expanded upon the accomplishments of and questions posed at the first conference. What is missing from this volume are the reports of games that were played and analyzed at the conference; of Grossman's Dotsand- Boxes program beating everyone in sight, except for the top four humans who had it beat by the fifth move.
This volume is divided into five parts. The first deals with new theoretical developments. Calistrate, Paulhus, and Wolfe correct a mistake about the ordering of the set of game values, a mistake that has been around for three decades or more. Not only do they show that the ordering is much richer than previously thought, they open up a whole new avenue of investigations. Conway echoes this theme of fantastic and weird structures in CGT (2 being the cube root of), and he introduces the smallest infinite games.
The classical games are well represented. Elkies continues his investigations in Chess. There are many new results and tantalizing hints about the deep structure of Go. Moore and Eppstein turn one-dimensional solitaire into a twoplayer game, and conjecture that the S—values are unbounded. (In attempting to solve this, Albert, Grossman and Nowakowski defined Clobber, a big hit at the Dagstuhl conference.)
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