A retrograde approximation algorithm for one-player can't stop

Authors:
James Glenn;Haw-Ren Fang;Clyde P. Kruskal
Affiliations:
Department of Computer Science, Loyola College in Maryland, Baltimore, MD;Department of Computer Science and Engineering, University of Minnesota, Minneapolis, MN;Department of Computer Science, University of Maryland, College Park, MD
Venue:
CG'06 Proceedings of the 5th international conference on Computers and games
Year:
2006

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Abstract

A one-player, finite, probabilistic game with perfect information can be presented as a bipartite graph. For one-player Can't Stop, the graph is cyclic and the challenge is to determine the game-theoretical values of the positions in the cycles. In this contribution we prove the existence and uniqueness of the solution to one-player Can't Stop, and give an efficient approximation algorithm to solve it by incorporating Newton's method with retrograde analysis. We give results of applying this method to small versions of one-player Can't Stop.