At first glance, a die seems simple: roll it, get a number, keep the game going. But for mathematicians, it turned into a 15-year problem.
Eric Harshbarger of Auburn University and his colleagues wanted to create ideal dice for determining turn order: each player rolls their own die and gets an equal chance to go first — and to take any other place as well. No ties and no rerolls.
The main challenge was arranging the numbers correctly. Simply giving the dice different values was not enough — it had to be proven that any combination of players and dice would remain equally fair.
In the end, they created five 60-sided dice with numbers from 1 to 300, with no repeats. They work for any group of two to five players: every possible order of play has the same probability.
So even randomness sometimes has to be carefully calculated first.
