Pass the Buck on a Complete Binary Tree

TL;DR

This paper uses the Stochastic Abacus to calculate winning probabilities in the game Pass the Buck on complete binary and k-ary trees, providing a probabilistic analysis framework for such tree-based games.

Contribution

It introduces a novel application of the Stochastic Abacus to analyze game outcomes on complete k-ary trees, extending previous binary tree results.

Findings

Winning probabilities computed for each level of the game

Generalization from binary to k-ary trees

Framework for probabilistic analysis of tree-based games

Abstract

The Stochastic Abacus is employed to compute winning probabilities at each level of the game Pass the Buck on a complete binary tree with the starting vertex being the root of the tree. The derivation is also generalized to play on complete k-ary trees.