I posted the next draft of my new model for calculating cube decision points to the preprint site arxiv.org, so now it has a proper stable link:
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.
Simple closed form approximations for the market window and doubling points are developed as a function of local and average jump volatility. The local jump volatility can be calculated for specific game states, leading to crisper doubling decisions.
Cube Handling In Backgammon Money Games Under a Jump Model
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.
Simple closed form approximations for the market window and doubling points are developed as a function of local and average jump volatility. The local jump volatility can be calculated for specific game states, leading to crisper doubling decisions.
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