How the Dice Fall: Investigating the Final State Probabilities of Bevelled Versus Non-bevelled Dice

Abstract Many of the household board games people play use bevelled dice, with rounded corners, and are one of the most common examples of chance. However, casinos are not allowed to use them due to their supposed unbalanced and imperfect rolls. They are required to use non-bevelled dice with sharp corners and flush sides. When asked, it is safe to assume that the average person would say that each face of any dice have a 1/6 chance of turning up when rolled. So why is there a difference between bevelled and non-bevelled in casinos? There is a huge gap in the research of probability and fairness of different types of dice. This lack of research was our motivation. Many people have looked into the true randomness of dice and there is no lack of research there; the lack of research comes with comparing the difference between bevelled and non-bevelled dice. Our research will investigate whether bevelled or non-bevelled dice are more random or fair and attempt to create a mathematical model. By rolling a large sample size of both types of dice under the same conditions and recording the final-state-the side that was facing up when the dice settled during each of our many rolls-we will be able to show the differences between the two types and determine an explanation. This research will explore our findings and their implications in a practical setting, specifically casinos.