These 60-sided dice never have to be rolled twice
A standard six-sided die has one simple shortcoming: You’ve got a 1 in 6 chance of getting the same number as your opponent when you’re rolling to go 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 embarked on a journey to create a set of five dice that would be unimpeachably fair.
Their parameters?
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 iterations, they finally came up with a design that works.
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 + Agricultural Sciences Complex.
The pieces of the sculpture are fashioned from different types of wood—pine, poplar, red oak, walnut, and mahogany.
Each weighs more than 100 pounds and is about three-and-a-half feet in diameter.
The idea for the dice came from a conversation Harshbarger had with James Ernest, founder of Cheapass Games, at a gaming convention in 2010.
Ernest wondered if it was possible to create no-tie dice.
Harshbarger found the question to be an intriguing math problem to solve.
“I don’t think he [Ernest] had any idea so much research would be thrown at the question,” Harshbarger says. “There are plenty of much easier ways to fairly decide who goes first in a https://www.fastcompany.com/90478874/the-11-best-family-friendly-board-games" rel="noreferrer noopener" target="_blank">board game, but the mathematics behind the question fascinated me, and the quest for sets of ‘Go First Dice’ began.”
Harshbarger began working on the problem with Robert Ford, a mathematician, and they soon found a solution with https://www.theguardian.com/science/alexs-adventures-in-numberland/2012/sep/18/puzzler-go-first-dice" rel="noreferrer noopener" target="_blank">four 12-sided dice that used 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 lots of math to determine the right numbers to include on each die. “We’re talking numbers way greater than the number of atoms in the universe—that kind of thing,” Harshbarger tells Fast Company.
Harder yet was ensuring the dice could roll.
An early attempt with a 120-sided die they designed was about the size of a baseball.
Harshbarger’s project to design the dice took more than a decade, work from a core group of about six researchers, and contributions from even more.
The Canadian researcher and software engineer Paul Meyer finally found the solution for the 60-sided dice in 2023 that arranged the numbers in just the right way so each piece had an equal chance of rolling the highest number, regardless of where two, three, four, or all five of dice in the set are used.
The group’s work, including 60- and 12-sided dice sets, is available at the website https://mathartfun.com/dSpecial.html" rel="noreferrer noopener" target="_blank">Math Art Fun.
Having to roll dice only once saves players seconds.
Figuring out how to do it fairly took researchers years, and the new sculpture memorializes the work it took to figure it all out.