This article has been reviewed according to Science X's editorial process and policies. Editors have highlighted the following attributes while ensuring the content's credibility: It took nearly 15 years, researchers around the world and enough computing power to search through a universe of possibilities to answer one question: Who goes first? Eric Harshbarger was at a gaming convention with a friend, who was a board game designer, when a dinner conversation turned to one of the simplest parts of playing a game: deciding who gets the first turn.
Usually, everyone rolls a die. The highest number goes first. If two people roll the same number, they roll again.
His friend wondered whether he could eliminate that last step. "He said, 'Hey Eric, you study math. Can you come up with a set of dice?'" said Harshbarger, a senior lecturer in Auburn University's College of Sciences and Mathematics (COSAM).
"Everyone can just arbitrarily grab one of the dice and roll to see who goes first. Highest will go first, but they will never tie." Cool, Harshbarger thought. But eliminating ties was only half the challenge.
No matter how many dice were being used, each player still needed an exactly equal chance of winning. "If all eight of them are rolling, they have exactly one-eighth chance of getting the highest number," Harshbarger said. "But if only five people grab a die [from the eight-person set], they each have a one-in-five chance of rolling the highest number." In other words, his friend had managed to turn one of the easiest decisions in a board game into a trivial yet phenomenally complicated math problem.
"You draw matchsticks or you just point at someone," Harshbarger said. "There are plenty of ways to decide who goes first." Still, once the question was out there, Harshbarger wanted an answer. "As with many, many math problems, who cares about the practicality?" he said.
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