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Intransitive dice #math

The introduction to the Quanta Magazine article "Mathematicians Roll Dice and Get Rock-Paper-Scissors" is fun:

As Bill Gates tells the story, Warren Buffett once challenged him to a game of dice. Each would select one of four dice belonging to Buffett, and then they’d roll, with the higher number winning. These weren’t standard dice — they had a different assortment of numbers than the usual 1 through 6. Buffett offered to let Gates choose first, so he could pick the strongest die. But after Gates examined the dice, he returned a counterproposal: Buffett should pick first.

Gates had recognized that Buffett’s dice exhibited a curious property: No one of them was the strongest. If Gates had chosen first, then whichever die he chose, Buffett would have been able to find another die that could beat it (that is, one with more than a 50% chance of winning).

Seemingly simple things can be so very complicated.