The story goes that Warren Buffett once challenged Bill Gates to a game of dice. Each would choose one of Buffett’s four dice before rolling, with the greater number winning.
These weren’t your typical dice; instead of the regular 1 through 6, they contained a distinct mix of numbers. In randomly selected dice, mathematicians have discovered a surprisingly large number of patterns resembling rock-paper-scissors. More than 50 years ago, mathematicians came up with the first examples of intransitive dice and later shown that as you take dice with increasing numbers of sides, it is possible to construct intransitive cycles of any length. Up until recently, mathematicians were unaware of the prevalence of intransitive dice.
