Maths Toys

Non Transitive Dice - Set 1

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Non Transitive Dice - Set 1

An amusing new game to trick and baffle your friends, based on a recent discovery made at Stanford University, USA. These so-called 'Non Transitive Dice' (Magic Dice) demonstrate a probability that violates common sense and traps the unwary.

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 that throw. In a game of 'The 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.

The secret
Turn up the highest faces on each of the four dice and arrange them in a circle, as shown in the diagram.

Proceeding clockwise around the circle, the dice with the 6's and 2's on it, called the 6-2, will beat the 5-1, the next in the circle, which in turn beats 4-0, which beats 3-3... WHICH IN TURN BEATS 6-2! Your advantage is that you will win 24 times out of 36 - that is 2 times out of 3, or a 66% advantage. So whichever dice your opponent selects - and asking someone to choose first is part of the strategy - you take the next dice backwards in the circle.

Made in UK

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