Optimal Doubling Thresholds in Backgammon-like Stochastic Games
Optimization and Control
2024-10-28 v1 Probability
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.
Cite
@article{arxiv.2410.19178,
title = {Optimal Doubling Thresholds in Backgammon-like Stochastic Games},
author = {Haoru Ju and Daniel Leifer and Steven J. Miller and Sooraj A. Padmanabhan and Chenyang Sun and Luke Tichi and Benjamin Tocher and Kiley Wallace},
journal= {arXiv preprint arXiv:2410.19178},
year = {2024}
}