Editing Principle of indifference (section)

===Dice===
A [[symmetry|symmetric]] [[dice|die]] has ''n'' faces, arbitrarily labeled from 1 to ''n''. An ordinary cubical die has ''n'' = 6 faces, although a symmetric die with different numbers of faces can be constructed; see [[Dice]]. We assume that the die will land with one face or another upward, and there are no other possible outcomes. Applying the principle of indifference, we assign each of the possible outcomes a probability of 1/''n''. As with coins, it is assumed that the initial conditions of throwing the dice are not known with enough precision to predict the outcome according to the laws of mechanics. Dice are typically thrown so as to bounce on a table or other surface(s). This interaction makes prediction of the outcome much more difficult.

The assumption of symmetry is crucial here. Suppose that we are asked to bet for or against the outcome "6". We might reason that there are two relevant outcomes here "6" or "not 6", and that these are mutually exclusive and exhaustive. A common fallacy is assigning the probability 1/2 to each of the two outcomes, when "not 6" is five times more likely than "6."