Cuboidal Dice and Gibbs Distributions

TL;DR

This paper models the face-probabilities of cuboidal dice using a Gibbs distribution, supported by experimental data, and shows how physical conditions influence these probabilities through a single adjustable parameter.

Contribution

Introduces a Gibbs distribution model for cuboidal die face-probabilities, incorporating physical condition effects with a single parameter.

Findings

Gibbs model aligns well with experimental data

Physical surface quality affects face-probabilities

A single parameter captures physical condition variations

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.