The goal is to be able to calculate probabilities involving irregular shaped dice rolls. Here it is attempted to model the probabilities of rolling standard tri-rectangular tetrahedral dice on a hard surface, such as a table top. The vertices and edges of a tetrahedron were projected onto the surface of a sphere centered at the center of mass of the tetrahedron. By calculating the surface areas bounded by the resultant geodesics, baseline probabilities were achieved. Using a 3D printer, dice were constructed of uniform density and the results of rolling them were recorded. After calculating the corresponding confidence intervals, the results were significantly different from the original calculated probabilities. Possible reasons for the discrepancy are noted, but further research is needed to better understand what is going on.
Paul R. Hurst Ph.D
Olmstead, Rulon and Baize, DonEliezer
"Probabilities Involving Standard Trirectangular Tetrahedral Dice Rolls,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 19
, Article 4.
Available at: https://scholar.rose-hulman.edu/rhumj/vol19/iss1/4