Dice Design Solves Board Gaming's Most Surprisingly Complex Problem: Who Goes First?

Every board game night starts with the same ritual: deciding who takes the opening turn. Usually, everyone grabs a die, rolls, and the highest number wins. But what happens when two players roll a six? Cue the awkward silence, followed by a tie-breaking re-roll.

It sounds like a minor annoyance, but it sparked a 15-year mathematical puzzle that recently found an ingenious solution thanks to Eric Harshbarger, a senior lecturer at Auburn University's College of Sciences and Mathematics (COSAM). 

The journey began at a gaming convention. Harshbarger was chatting with a board game designer friend who posed a deceptively simple question: "Could you design a set of dice that completely eliminates ties while giving every player an equal chance of winning?"

The criteria were strict:

• No ties allowed: A single roll must definitively crown a single highest number.

• Scalable fairness: If an eight-player set exists, and only five people choose to play, each of those five participants must still have an exact one-in-five chance of rolling the highest number.

What started as a casual dinner conversation quickly evolved into a phenomenal computational and combinatorial challenge.

Intrigued by the abstract beauty of the problem, Harshbarger teamed up with longtime friend Robert Ford, an Auburn mathematics alumnus. Together—with help from researchers around the world and heavy computing power—they set out to map a universe of mathematical possibilities.

Initially, Ford cracked a solution for three players using standard dice, figuring out how to distribute the numbers 1 through 18 across the dice to banish ties entirely while preserving fair odds. From there, scaling the concept up to accommodate larger groups required advanced geometry, combinatorial logic, and brute-force computer algorithms to sort through millions of potential face-value arrangements.

While there are plenty of everyday ways to decide who goes first—like drawing straws or pointing fingers—Harshbarger admits that practicality took a backseat to pure mathematical curiosity. "Mathematically, this is a pretty interesting question," he noted.

The project ultimately bridged abstract theory and physical reality. Harshbarger even brought the math to life by designing a giant wooden sculpture for Auburn’s STEM + Agricultural Sciences Complex, celebrating the intersection of probability, geometry, and human play.

The next time you sit down for a tabletop game night and face a tie-breaking roll, remember that behind that simple plastic cube lies a deep universe of mathematical research waiting to be solved.  Let me know what you think, I'd love to hear. Have fun.