"Pass the Buck" on a Rooted Tree

TL;DR

This paper introduces a new technique to predict outcomes in the game "Pass the Buck" on rooted trees, overcoming computational challenges posed by the stochastic abacus method.

Contribution

A novel anticipatory method is developed for estimating game outcomes on rooted trees, improving upon the computational limitations of the stochastic abacus.

Findings

The technique effectively predicts winning probabilities in complex trees.

It reduces computational complexity compared to the stochastic abacus.

The method is applicable to various tree structures.

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.