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.

Author Bio

Rulon Olmstead was born and raised in Ogden, Utah. Always had an interest in mathematics and as a young fourth grader wanted to be a math professor. Finished his undergraduate career in late 2017.

DonEliezer Baize was born and raised in Kahuku, Hawaii. Don was a 2 time John Hopkins Talent Search Finalist in math and spatial ability in both 2014 and 2015.