Saturday, 4 July 2009

Sicherman Dice

An unusual pair of dice. One has sides 1,3,4,5,6,8. The other has sides 1,2,2,3,3,4. Martin Gardner reported on the discovery of these dice by a certain Colonel George Sicherman, of Buffalo, New York, in a 1978 article in Scientific American.

What is special about these dice? When you roll a normal set of two dice, and add up the total of the two faces, you get scores ranging from 2 (when you throw two 1's) up to 12 (when you throw two 6's). However there is also a certain probability of each score. Throwing a total of 2 has a 1 in 36 chance of happening, as does throwing a 12. Some scores are much more likely. Throwing a total of 6 has a 5 in 36 chance of happening, and can involve throwing two 3's, a 4 and a 2, or a 5 and a 1.

Sicherman Dice behave just like a normal set of dice, in that the chance of throwing a combined total of 2 is 1 in 36, and of throwing a total of 6 has a 5 in 36 chance of happening. There is no other arrangement of numbers on 2 dice that will replicate the behaviour of normal dice (excluding dice with blank or zero faces, or negative numbers!)

So any game that you can play with a normal set of 2 dice can also be played with a set of Sicherman Dice, with no difference in the outcome!

However the odds of throwing a double are not the same as a normal pair of dice. You might like to work that one out for yourself!


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