Every year, hundreds of millions of dice are manufactured and sold. Because of the impossibility of precise dimensional control and nonuniform density, none of these dice are fair. Polyhedral dice manufactured for role-playing games like Dungeons and Dragons typically contain 4-sided, 6-sided, 8-sided, 10-sided, 12-sided, and 20-sided dice (D4, D6, D8, D10, D12, and D20). D20s are especially problematic. In 3000-roll tests of several D20s, only about one-quarter tested fair. In light of the inherent unfairness of most dice, we explored the possibility of using dice mechanics involving multiple dice to obtain fairer results. For D20s, summing three dice gave promising results. Even using dice that tested highly unfair individually, sums of three dice tested fair. We also considered Fate or Fudge dice mechanics which effectively use the sum of 4 D3s. With one exception, these dice tested fair. In our tests, three D20s tested fairer than four Fate dice.
Campbell, Warren; Miller, Cameron; and Simpson, Xavier, "Dice: Blessed or Cursed?" (2023). SEAS Faculty Publications. Paper 9.