Combinatorial Game Theory

Speaker: Elwyn Berlekamp (University of California, Berkeley) Title: Report on the latest Coupon Go tournament Abstract: Late in 2010 a Coupon Go tournament was held in Korea. This talk will give an overview of the tournament and the results. Speaker: Kyle Burke (Wittenberg University) Title: Neighboring Nim: a PSPACE-complete NimG variant Abstract: Neighboring Nim is a version of Nim where heaps are embedded onto vertices of a graph. A turn consists of traversing an edge (adjacent to the last play) then removing sticks from the resulting vertex. Even with small heap sizes, the game is PSPACE-hard. Speaker: Tristan Cazenave (Paris-Dauphine University ) Title: Developments on the Monte-Carlo approximation of temperature Abstract: Speaker: Erik Demaine (MIT ) Title: Geometric Puzzles Abstract: Speaker: Aviezri Fraenkel (Weizmann Institute of Science) Title: Learn How To Beat Your Fractional Beatty Game Opponent Abstract: The P -positions of impartial take-away games on two piles usually split the positive integers into two nonintersecting sequences. Here we consider the case where the P -positions are given a priori as two sequences whose intersection has infinite cardinality. The challenge is to find appropriate succinct game rules for a game having the given P -positions. We present a solution in terms of two exotic numeration systems, for a seemingly first such problem. Speaker: JP Grossman (D. E. Shaw ) Title: Searching for Periodicity in .6 Abstract: .6 is the only unsolved single-digit octal game. In this take-and-break game, a move consists of removing a bean from a heap and leaving the remaining beans from that heap in exactly 1 or 2 non-empty heaps. It is conjectured that the nim-values for this game are eventually periodic; finding the period (if it exists) requires fast computation of the nim-values. We review the ”rare values” algorithm that effectively reduces the computation time for the first N nim-values from O(N2) to O(N). We present several low-level optimizations and show how to parallelize the computation, resulting in significant additional speedups. Speaker: Alan Guo & Mike Weimerskirch (Duke University; Macalester College) Title: Lattice point methods in misere games Abstract: Positions in normal play heap games with bounded heap size d can be thought of as elements of the lattice C = Nd. We imbed C in Zd, with Zd\C declared to be defeated positions. Misère play is treated similarly with gameboard C = Nd \ {(0, 0, . . . , 0)}. This can be generalized to arbitrary gameboards. A description of the optimal strategy of such games using Hilbert Series provides an alternative to Plambeck’s Quotient Monoid approach.