Cuboidal Dice and Gibbs Distributions

Abstract

What are the face-probabilities of a cuboidal die, i.e. a die with different side-lengths? This paper introduces a model for these probabilities based on a Gibbs distribution. Experimental data produced in this work and drawn from the literature support the Gibbs model. The experiments also reveal that the physical conditions, such as the quality of the surface onto which the dice are dropped, can affect the face-probabilities. In the Gibbs model, those variations are condensed in a single parameter, adjustable to the physical conditions.