"Pass the Buck" on a Rooted Tree

Abstract

The Stochastic Abacus is can employed to compute winning probabilities for each vertex of a rooted tree in the game "Pass the Buck", with the starting vertex being the root of the tree. For all but the simplest trees, the abacus can't really be implemented due to the large number of steps needed for completion. In this paper, a technique for anticipating the outcome is introduced.