Mathematicians Roll the Dice and Get Rock-Paper-Scissors

In their paper, posted online in late November 2022, a key part of the proof involves showing that, for the most part, it doesn’t make sense to talk about whether a single die is strong or weak. Buffett’s dice, none of which is the strongest of the pack, are not that unusual: If you pick a die at random, the Polymath project showed, it’s likely to beat about half of the other dice and lose to the other half. “Almost every die is pretty average,” Gowers said.

The project diverged from the AIM team’s original model in one respect: To simplify some

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