Abstract
Two questions were addressed: 1) What are the exact values of the c2 statistic critical values? 2. Does a dice tower offer improved fairness of dice rolls? Critical values of the statistic asymptotically approach those given by the continuous chi-square distribution, but the exact distribution is discrete. The exact distributions only asymptotically approach the chi-square distribution, and the convergence is slow (1/number of rolls). Th exact distributions are a function of the number of rolls, the chi-square distribution is not a function of the number of rolls. Exact values of c2 at the 90, 95, and 99 percent confidence levels were calculated. To address question 2, the ten diameters of a cubic zirconia D20 die were measured and the die weighed. From this, the principal mass moments of inertia were calculated. The die was rolled 3000 times and the c2 statistic calculated as 45.37. In addition, dice dynamic simulations of rolls of this die on a flat surface and in a dice tower were simulated. Three thousand rolls were simulated and then repeated 1000 times. This was to determine if a dice tower provided any fairness advantage. The result of this test was inconclusive.
Disciplines
Civil and Environmental Engineering | Physical Sciences and Mathematics | Statistical Models | Statistics and Probability
Recommended Citation
Campbell, Warren, "Exact x2 Statistic Critical Values for Dice Fairness Testing" (2026). SEAS Faculty Publications. Paper 25.
https://digitalcommons.wku.edu/seas_faculty_pubs/25