NONTRANSITIVE DICE

The mathematical property of transitivity states that if A is T greater than B, and B is greater than C, then A is greater than C. But certain games appear to flout this logic. One common nontransitive game is “Rock, Paper, Scissors,” the children’s game that displays circular logic Scissors cut paper, paper wraps rock, rock breaks scissors.

A special set of dice, shown here, also displays this nontransitive logic. If you play a two-person betting game with these dice, always allow your opponent to select his or her die first. No matter which die your opponent chooses, you can select a die that will give you an advantage. Can you work out how?