# Mathematicians Create Unique 60-Sided 'Go First Dice' for Fair Turn Order Auburn University displays sculpture of permutation-fair dice solving game night's first-move dilemma. - **Source:** [Scientific American Content: Global](https://brifing.si/source/4f066134-e06d-4415-87ef-305e3dc2aba6) - **Published:** 2026-09-11 - **Topic:** [Career Growth](https://brifing.si/c/growth) - **Original article:** - **On Brifing:** https://brifing.si/s/c371c9fd-8526-4fb9-a29d-18b2d7206cc3 ## The Problem of First Moves Deciding who goes first in games often involves arbitrary methods or repeated dice rolls when ties occur. Traditional solutions create inefficiencies in gameplay. Auburn University lecturer Eric Harshbarger identified this common frustration and sought a mathematical solution that would eliminate the need for rerolls while ensuring complete fairness in player order determination. ## Mathematical Breakthrough Harshbarger and collaborators developed Go First Dice that guarantee random turn order with single rolls. The dice use permutation fairness - ensuring equal probability for all possible player orderings. For five players, this required five unique 60-sided dice displaying numbers 1-300 collectively. Each die's numbering was carefully tiled to maintain statistical fairness across all possible outcomes. ## Physical Implementation The team faced manufacturing challenges creating functional five-player dice sets. Early prototypes used 120-sided dice that proved too unwieldy. The final 60-sided version balances mathematical requirements with physical practicality. Harshbarger hand-carved three-foot wooden replicas from five different wood types for Auburn University's STEM complex display, drawing on his sculpture background. ## Permutation Fairness Explained True permutation fairness means each player has equal chance to go first, and remaining players have equal chances for subsequent positions. For five players, this requires satisfying nested probability conditions - exponentially more complex than two-player solutions. The dice maintain fairness even when fewer than five players participate by allowing random die selection. ## Collaborative Solution After years of stagnation, Google engineer Paul Meyer advanced the project in 2023. Combining math expertise with software engineering skills, Meyer developed algorithms to find viable five-player solutions. His contribution bridged the gap between theoretical mathematics and practical implementation, enabling the creation of manufacturable dice sets. ## Design Challenges Creating fair dice required overcoming geometric constraints. Not all face counts form regular polyhedrons suitable for rolling. The team balanced mathematical requirements with physical manufacturability, ensuring the dice would actually roll properly. This dual focus on theory and practicality distinguishes the project from purely academic exercises. ## Educational Impact Auburn University's decision to display the dice as sculpture highlights their educational value. The installation demonstrates applied mathematics solving real-world problems. It serves as a tangible example of STEM principles for students, showing how abstract concepts can yield practical innovations that improve everyday experiences like game nights. ## Broader Applications While designed for games, the permutation fairness concept has potential applications in randomized decision-making systems. The mathematical framework could inform fair selection processes in various contexts. The project exemplifies how solving niche problems can yield insights transferable to broader domains requiring verifiably random yet constrained outcomes. ## Sources covering this story - https://www.scientificamerican.com/article/unique-mathematical-60-sided-go-first-dice-go-on-display/ — --- _Summary written by Brifing from the original reporting. Copyright in the original article belongs to its publisher; read the full piece at the link above._