A set of dice is nontransitive if it contains three dice, A, B, and C, with the property that A rolls higher than B more than half the time, and B rolls higher than C more than half the time, but it's not true that A rolls higher than C more than half the time. In other words, a set of dice is nontransitive if its "rolls a higher number than more than half the time" relation is not transitive.
It is possible to find sets of dice with the even stronger property that, for each die in the set, there is another die that rolls a higher number than it more than half the time. Using such a set of dice, one can invent games which are biased in ways that people used to transitive dice might not expect (see Example).
Read more about Nontransitive Dice: Example, Freivalds's Investigation, Warren Buffett, Nontransitive Dice Set For Three Players, Nontransitive Dodecahedrons, Nontransitive Prime-numbers-dodecahedrons, See Also
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“Gods dice always have a lucky roll.”
—Sophocles (497406/5 B.C.)