Probability Analysis for Rolls of a Square Cuboidal Die
Abstract
Consider a six-sided die in which two opposite faces are squares of sides yand the other four faces are rectangles of sides x and y, as sketched in Figure 1.One can think of it as an ordinary cubical die that has been stretched or compressed along one axis. There is some probability that one of the two square faces will show uppermost after such a die is randomly tossed, and a probability that one of the four rectangular faces will show. For example, in the limit that y becomes equal to so that the die is cubical, then the probability that theoriginal square faces come up is p= 1/3 . Over 30 years ago, the question wasasked [1] what is p if y is not equal to x? The author of that article cut 15 such diceout of a steel bar and had his students roll each of them N times to experimentally determine p. His results are listed in Table 1. A simple explanation was subsequently hypothesized in which is proportional to the solid angle subtended by a square face [2], but it does not match the data well. In the present paper, an alternative simple model is proposed that better fits the measurements.
Document Details
- Document Type
- Technical Report
- Publication Date
- Mar 01, 2013
- Accession Number
- AD1016860
Entities
People
- Carl Mungan
- Trevor Lipscombe
Organizations
- United States Naval Academy