At a gaming convention around 2010, board game designer James Ernest posed a deceptively simple challenge to his friend Eric Harshbarger: could a set of dice be built so that any number of players, each taking one die, would have exactly the same chance of rolling the highest number, with no ties or rerolls? That question launched a long, collaborative effort led by Eric Harshbarger, a mathematician at Auburn University, and supported by colleagues including Robert Ford. Over roughly 15 years they sought configurations that deliver equal odds not only for who goes first but for the full ordering of players.
The project produced smaller, practical solutions along the way. The team found a three-player arrangement distributed numbers 1–18 across three standard six-sided dice, and a four-player set using four 12-sided dice. In testing these designs the researchers uncovered a stronger property they call permutation fairness: every possible sequence of players is equally likely. During this phase Harshbarger produced and sold handcrafted sets and numerical patterns drew wider interest from hobbyists and educators. The work also connected with the mathematics and board games communities exploring fair randomization methods.
The five-player problem proved far more demanding because the space of possible number assignments explodes to astronomically large proportions. Brute-force search was infeasible, so the team looked for symmetries and structural shortcuts. In mid-2023 Canadian software engineer Paul Meyer identified a workable configuration: five 60-sided dice whose faces collectively carry the integers 1 through 300 with no repeats. Harshbarger verified the result; the arrangement satisfies the no-tie, no-reroll condition and preserves permutation fairness for any subset of players.
Beyond the mathematical achievement, the set meets practical aims: the dice are small enough to manufacture and usable in ordinary play. To celebrate the discovery and to draw public attention to abstract ideas, Harshbarger also carved five oversized wooden replicas from different woods; these sculptures are now installed in Auburn’s new math building. The team frames the project as an instance where an accessible puzzle led to deeper combinatorial structure, and where tangible objects help invite curiosity about dice and mathematical design.
