A standard six-sided die has one simple shortcoming: you have a 1 in 6 chance of rolling the same number as your opponent when you roll to see who goes first in a game.
Eric Harshbarger has a solution for that.
More than a decade ago, Harshbarger, a senior lecturer at Auburn University's College of Sciences and Mathematics, and a group of mathematicians and computer scientists set out to create a set of five dice that would be completely fair. Their goal? Rolling the dice should never result in a tie, and every player should have a mathematically equal chance of rolling the highest number.
After many attempts, they finally came up with a design that worked. They created the Go First Dice, a set of five 60-sided dice, with the numbers 1 through 300 spread across their faces.
Their dice are now represented in a sculpture at Auburn University's new STEM and Agricultural Sciences Complex. The pieces of the sculpture are made from different types of wood — pine, poplar, red oak, walnut, and mahogany. Each piece weighs more than 100 pounds and is about three and a half feet across.
The idea for the dice came from a conversation Harshbarger had with James Ernest, a tabletop game designer, at a gaming convention in 2010. Ernest wondered if it was possible to create dice that never produced a tie. Harshbarger found the question to be an interesting math problem worth solving.
"I don't think he [Ernest] had any idea how much research would go into answering the question," Harshbarger says. "There are plenty of much easier ways to fairly decide who goes first in a board game, but the math behind the question fascinated me, and the search for sets of 'Go First Dice' began."
Harshbarger began working on the problem with Robert Ford, a mathematician, and they soon found a solution using four 12-sided dice with the numbers 1 through 48. Then came the bigger challenge: could they do it with five dice?
Creating five no-tie dice with an equal chance of rolling the highest number requires a great deal of math to work out the right numbers to put on each die. "We're talking about numbers far greater than the number of atoms in the universe — that kind of thing," Harshbarger says.
Even harder was making sure the dice could actually roll. An early attempt at a 120-sided die they designed ended up about the size of a baseball.
Harshbarger's project to design the dice took more than a decade, with work from a core group of about six researchers and contributions from many more. The Canadian researcher and software engineer Paul Meyer finally worked out the solution for the 60-sided dice in 2023, arranging the numbers in just the right way so that each die had an equal chance of rolling the highest number, no matter whether two, three, four, or all five dice in the set were used.
Rolling the dice just once saves players a few seconds. Working out how to do it fairly took researchers years, and the new sculpture stands as a record of the effort it took to solve the problem.