Numerically Balanced Dice
Robert Bosch, Robert W. Fathauer, Henry Segerman · Princeton University Press eBooks · 2017
This chapter uses integer programming to find numerically balanced, twenty-sided dice (d20s). On most commercially available d20s, the numbers on opposite sides sum to 21. The chapter begins with a brief thought experiment in an attempt to explain why do die manufacturers do this. It then suggests that the opposite numbers convention is a form of “numerical balancing” that serves to promote fairness, giving die manufacturers a way of hedging against the possibility that their d20s are not perfectly formed regular isocahedra. Are there additional measures that they could take? Is it possible to make d20s that are even more numerically balanced?