Choosing who gets the first turn is usually one of the quickest parts of setting up a board game. Pick someone, roll a die, draw straws, and get on with it!
But one mathematician decided that this simple problem deserved a much more complicated solution. Nearly 15 years of research later, Eric Harshbarger and a team of mathematicians and programmers had created a set of dice that can decide who goes first without ever producing a tie!
A simple question
The idea started at a gaming convention, where Harshbarger was chatting with a board game designer over dinner. The designer asked whether it was possible to create dice that would allow players to roll simultaneously, with the highest number always winning and nobody ever tying. There was another catch. Every player needed to have the same chance of winning.
That made things considerably harder!
For example, if eight people each take a die, everyone needs a one-in-eight chance of rolling the highest result. If only five people are playing, those same dice need to give everyone a one-in-five chance. Suddenly, deciding who goes first had become a serious mathematical puzzle.
Rolling into trouble!
Harshbarger teamed up with mathematician Robert Ford to investigate the problem. They found a solution for three players using ordinary dice, before eventually developing a set of four 12-sided dice that worked for four players. The research then became much more ambitious. Computer programs were used to search through enormous numbers of possible combinations, while mathematical techniques helped researchers narrow down which arrangements were worth testing. According to Harshbarger, the number of possibilities became so enormous that the search could be compared to the number of atoms in the universe! Over the years, researchers from the United States, Canada, and Australia contributed to the project.
The 60-sided solution!
Five-player sets proved particularly tricky. A five-player solution using 120-sided dice was eventually discovered, but researchers wanted something more practical. Then, around 2023, Canadian researcher Paul Meyer contacted Harshbarger with a breakthrough: five identical 60-sided dice! The dice use carefully arranged numbers so that every player has an equal chance of rolling the highest result, while ties are mathematically impossible. After around 15 years of research, the problem had finally been cracked!
From game night to giant sculpture
Harshbarger didn't stop at solving the puzzle. He also turned the discovery into a giant mathematical artwork for Auburn University's College of Sciences and Mathematics. Five enormous 60-sided wooden dice were created, each measuring around 3.5 feet across. The sculpture is designed to get students and visitors thinking about the mathematics hiding inside something as familiar as a board game die. It might be the most unnecessarily complicated way to decide who goes first, but there's something brilliant about taking an everyday gaming question and turning it into a worldwide mathematical challenge!
Next time your group spends ten minutes arguing about who should start, just remember: somewhere out there, mathematicians spent 15 years making sure the dice could settle it properly!
