Superstitious discussion of fair and unfair dice has pervaded the tabletop gaming industry since its inception. Many of these are not based on any quantitative data or studies. Consequently, misconceptions have been spread widely. One dice float test video on Youtube currently has 925,000 views (Fisher, 2015a). To combat the flood of misconceptions we investigated the following questions: 1) Are dice cursed? 2) Are D20s (20-sided dice) less fair than D6s (6-sided dice)? 3) Do float tests tell anything about the fairness of dice? 4) Are some dice systems inherently fairer than others? 5) Are density differences or dimensions more critical to dice fairness? 6) What is the best way to test your dice for fairness? 7) How many rolls are needed to detect unfair dice? 8) Are metal dice fairer than plastic dice? Based on tens of thousands of physical dice rolls, billions of simulated dice rolls, and analysis our answer to these questions are as follows. 1) Probably plastic dice are cursed. 2) Yes, D6s are fairer than D20s. 3) Float tests tell you nothing about which side of a die will come up more often. 4) Yes, some dice systems are fairer. 5) Usually dimensions are more important except for large, off-center bubbles. 6) The running chi square goodness of fit test is the best way to test dice that we found. 7) 100 rolls are not enough except possible for loaded dice. 8) Our preliminary conclusion based on limited tests is that metal dice are not fairer than plastic dice.
Engineering | Probability | Statistics and Probability
Campbell, Warren and Dolan, William P., "Dice Questions Answered" (2020). SEAS Faculty Publications. Paper 2.