Game Theory Talks

Many major new results were reported at the workshop on Combinatorial Game Theory held at Banff in June 2005. Here are a few of my favorites:

Teigo Nakamura presented his methodology for applying combinatorial game theory to capturing races in Go. His paper includes some brilliant problem compositions, whose solutions seem well beyond the capabilities of most experienced Go players but well within the grasp of combinatorial game theorists. In Nakamura's theory, liberties behave rather like classical atomic weights: when they are integers, your best move is to reduce your opponent's assets by one. But in the more interesting problems, the proper values of liberties are combinatorial games rather than simply integers. Although capturing races in which the liberties can be decomposed into sums of disjoint values seem to occur more rarely in actual games than the endgame analyses we have been studying for the past decade, the stakes (in terms of points in the Go game) are so much larger that there seems good reasons to hope that Nakamura's work may attract more Go players to study combinatorial game theory.

Aaron Siegel presented his recent discovery of the unique nontrivial automorphism of the lattice of games born by Day n. He also presented his recent work on loopy games. Using his very powerful, publicly available and continually improving program, cgsuite, he revealed the intricate structure of loopiness in some positions of one-dimensional Phutball.

Thane Plambeck explained his discovery that the solutions of many, perhaps all, misere octal games can be expressed elegantly and concisely in terms of monoids. He presented several explicit examples, including his elegant reformulation of the Siebert-Conway solution of misere Kayles. He explained the conditions which the semigroup must satisfy. I consider this the biggest advance in misere theory in the past 50 years. Plambeck also offered prizes to the first finder of the solution of each of ten more specific misere games which he identified as challenging but now potentially computable(?).

Several weeks after of conference, Aaron Siegel improved Plambeck's algorithms to hunt for the Plambeck monoids, programmed them, applied them to Plambeck's challenge problems, and claimed most of the prizes which Plambeck had offered. Plambeck and Siegel are now jointly working on further extensions...

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