On GoogleFacePlusBook, Jeff linked to an article about
dice—three dice where, on average (meaning—many rolls) die A will
win over die B, die B will win over die C, but die C will win over
die A (kind of like rock-paper-scissors).
Even weirder, if you double the dice, two A's against two B's against two
C's, the order reverses! (And the accompanying video shows a series of five
dice with an even weirder dual-non-transitive ordering).
This page remineded me of a set of “go-first-dice”—a
set of twelve sided dice where, say, four people each have a ¼ chance
of rolling the highest number, a ¼ chance of rolling the second
highest number, a ¼ chance of rolling the third highest number and a
¼ chance of rolling the lowest number. In this case, the dice form a
strict ordering (there is no chance of a tie).
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