Mittagsseminar (in cooperation with J. Lengler, A. Steger, and D. Steurer)

Date and Time: Tuesday, December 01, 2009, 12:15 pm

Duration: This information is not available in the database

Location: OAT S15/S16/S17

Speaker: Gabriel Nivasch

On the Sprague-Grundy function for Wythoff's game

Wythoff's game is the following two-player game: There are two piles of tokens. On each turn, a player takes either any number of tokens from one pile, or the same number of tokens from both piles. The last player to move is the winner. The winning strategy for this game is well-known (Wythoff, 1907).

The Sprague-Grundy function (Sprague, 1936; Grundy, 1939) is something that allows one to play "sums" of impartial games. The Sprague-Grundy function for Wythoff's game looks quite chaotic, but we prove the following simple property: For every fixed g, the n-th g-value is always within a bounded distance of the n-th 0-value.

We also briefly describe a recursive algorithm for finding the n-th g-value in time O(log n), but which depends on an unproven "convergence" conjecture.

At the end we will mention an open problem regarding 3-row Chomp (another game) of very similar flavor.

This work is based on the speaker's Master's thesis (Weizmann Institute of Science, 2005).

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