Optimal Doubling Thresholds in Backgammon-like Stochastic Games

TL;DR

This paper analyzes optimal doubling strategies in backgammon-like stochastic games with various proposal options and multipliers, providing analytic solutions and exploring a new three-player variant with simulations.

Contribution

It introduces a comprehensive analysis of optimal doubling thresholds in multiple game variants and extends the model to a three-player version with initial theoretical results.

Findings

Analytic solutions for optimal doubling thresholds in several variants.

Introduction of a three-player generalization and basic behavioral results.

Simulation data supporting the theoretical findings.

Abstract

We study variants of a stochastic game inspired by backgammon where players may propose to double the stake, with the game state dictated by a one-dimensional random walk. Our variants allow for different numbers of proposals and different multipliers to the stake. We determine the optimal game state for proposing and accepting, giving analytic solutions in many variants. We also introduce a 3-player generalization of the game and prove basic results about its behavior, in addition to providing a simulation.