Martin Gardner's nontransitive dice
Picture four unusually numbered dice, A, B, C, and D. They're built so that A beats B more often than not, B beats C more often than not, and C beats D more often than not - yet D beats A more often than not, closing the loop like rock-paper-scissors. If you let a friend inspect all four dice and choose whichever one they want first, are you at a disadvantage, or can you still come out ahead?
Reveal the answer
Let your friend choose first: for every die in Bradley Efron's set of four, there is always another die in the set that beats it with probability 2/3, so whichever one your opponent picks, you pick its 'predator' and become the long-run favorite. The paradox is that overall dominance behaves like rock-paper-scissors rather than ordinary numerical ranking. Efron devised the dice; Martin Gardner introduced them to a wide readership in his December 1970 'Mathematical Games' column in Scientific American.