Cube Handling In Backgammon Money Games Under a Jump Model

TL;DR

This paper introduces a novel jump model for cube handling in backgammon money games, replacing traditional diffusion models with a stochastic jump process to improve decision accuracy.

Contribution

It develops a new cubeful equity model based on a jump process, providing closed-form approximations for better cube decision-making in backgammon.

Findings

Model captures jump dynamics with small volatility

Closed-form solutions enable precise doubling decisions

Local jump volatility improves decision accuracy

Abstract

A variation on Janowski's cubeful equity model is proposed for cube handling in backgammon money games. Instead of approximating the cubeful take point as an interpolation between the dead and live cube limits, a new model is developed where the cubeless probability of win evolves through a series of random jumps instead of continuous diffusion. Each jump is drawn from a distribution with zero mean and an expected absolute jump size called the "jump volatility" that can be a function of game state but is assumed to be small compared to the market window. Closed form approximations for cubeful equities and cube decision points are developed as a function of local and remote jump volatility. The local jump volatility can be calculated for specific game states, leading to crisper doubling decisions.