Monday, November 22, 2010

Dice Statistics

Observation -- The standard deviation of a normal polyhedral die (i.e., a discrete uniform distribution 1..N with small N) is approximately one-half of the mean. For the case of a 7-sided die, the standard deviation is exactly equal to one-half of the mean. For dice with fewer sides it is less, and for more sides it is greater.

The d7 coincidentally also has the property that the variance exactly equals the mean. However, the two are not generally close for other sorts of dice (although still less for smaller dice, and more for bigger dice).