# The Center of Math Blog

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## Thursday, November 6, 2014

### Throwback Fact of the Week - Sicherman Dice - 11/06/14

Sicherman dice are not your typical board game dice, but you could use them in almost any board game without changing the outcomes. How can this be?

The faces on the Sicherman dice (pictured below) are numbered 1, 2, 2, 3, 3, 4 and 1, 3, 4, 5, 6, 8. Sicherman dice are very unique; they are the only pair of 6-sided cubic dice with positive integers that have the same odds as your standard cubic dice. Note, if negative numbers are allowed there are an infinite number of such dice.
 Image credit: Grand Illusions (dice can also be purchased from their site)
What does this mean? As you know, with regular dice there is a fixed probability of rolling a given sum (you can roll between 2 and 12) when both dice are thrown. The same holds true for Sicherman dice; you can roll a sum between 2 and 12 and the odds of a particular sum occuring is the same as for a regular pair of dice.

For example, regular dice have a 1/9 chance of rolling a sum of 5. With Sicherman dice, there is also a 1/9 chance of rolling a sum of 5.

We mention you could play almost any game with these. The reason for almost is because some games have certain rules when doubles are rolled and these dice have different odds of doubles being rolled. The reader is left with the exercise of calculating the odds of rolling doubles using Sicherman dice!