Non-Transitive Dice (Efron Dice) by Bradley Efron

(c. 1970) (Submit Review) (Submit Update)

These first came to the public’s attention via Martin Gardner’s Mathematical Games column in Scientific American (December, 1970).  There, he discussed a set of four Efron Dice which were discovered by and named after, statistician Bradley Efron, for which: A > B > C > D > A … in the sense that each die beats the next one listed with a probability 2/3.

Effect: Ask your opponent to select any one of the four dice. You select another and both dice are thrown at the same time, a predetermined number of times, to see who gets the highest number on each throw, and hence wins the throw. In a game of “Best of Ten Throws” you will almost always have more wins. Invite the player to choose another dice – perhaps your “winner” – leaving you to select another for yourself and play again. Again you will win. Whichever die your opponent selects, your choice, in a longer run of ten or more throws, will always win.

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Approx. Price: $17.50 (2002) ***

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