A quest that began at a gaming convention around 2010 has finally reached its resolution. Board game designer James Ernest posed a deceptively simple challenge to his friend Eric Harshbarger, a mathematician at Auburn University: create a dice set that allows any number of players to roll for the starting position with absolutely equal probability and zero ties.<\/p>\n
For Harshbarger, the difficulty lay not in avoiding ties, but in distributing numbers such that fairness is maintained across every possible subset of players. If three, five, or eight people played, each die had to offer identical odds of winning regardless of the total group size.<\/p>\n
Harshbarger enlisted childhood friend Robert Ford, a mathematician at Dalton State College, to help tackle the problem. The pair quickly devised a solution for three players using standard six-sided dice, and Ford later calculated a fair configuration for four players using 12-sided dice. By 2012, the four-player set had gained international attention, leading Harshbarger to mass-produce and ship handmade sets from his home workshop.<\/p>\n
As the research progressed, the team discovered that these dice possessed “permutation fairness,” meaning they determine the entire turn order among players, not just who goes first. Every possible sequence of finishing positions was equally likely.<\/p>\n
Extending this logic to five players proved exponentially more difficult. The mathematical space of possible number arrangements was estimated at 10 to the 128th power\u2014more combinations than atoms in the observable universe. Brute-force computing was impossible, and previous attempts resulted in theoretical designs involving dice with 180 sides, which were too large to manufacture or hold.<\/p>\n
The breakthrough arrived in mid-2023 when Paul Meyer, a Canadian software engineer, contacted Harshbarger. Meyer had analyzed patterns in the existing four-player data and wrote a program to exploit them. His algorithm successfully identified a valid configuration of five 60-sided dice, known as hexecontahedrons, each engraved with unique numbers from 1 to 300.<\/p>\n
To commemorate the achievement, Harshbarger constructed five giant wooden replicas of the dice, each carved from a different species: pine, poplar, oak, walnut, and mahogany. The sculptures are now permanently displayed in Auburn University\u2019s new mathematics building, which opened this fall. For Harshbarger, the project highlights the accessibility of complex mathematical concepts, turning an abstract puzzle into a tangible display that invites public fascination.<\/p>\n","protected":false},"excerpt":{"rendered":"
After 15 years, mathematicians designed a set of five 60-sided dice that ensures fair play for any number of players, solving the elusive ‘go first dice’ problem.<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[5],"tags":[2096,2095,2097,2098,2094,162],"class_list":["post-961","post","type-post","status-publish","format-standard","hentry","category-science","tag-auburn-university","tag-dice","tag-game-theory","tag-geometry","tag-mathematics","tag-science"],"_links":{"self":[{"href":"https:\/\/yovao.com\/index.php\/wp-json\/wp\/v2\/posts\/961","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/yovao.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/yovao.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/yovao.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/yovao.com\/index.php\/wp-json\/wp\/v2\/comments?post=961"}],"version-history":[{"count":0,"href":"https:\/\/yovao.com\/index.php\/wp-json\/wp\/v2\/posts\/961\/revisions"}],"wp:attachment":[{"href":"https:\/\/yovao.com\/index.php\/wp-json\/wp\/v2\/media?parent=961"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/yovao.com\/index.php\/wp-json\/wp\/v2\/categories?post=961"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/yovao.com\/index.php\/wp-json\/wp\/v2\/tags?post=961"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}