# Maths Toys

## 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.

GAME 1
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.