Uniform distribution

The uniform distribution is the distribution in which all possible outcomes have exactly the same probability. It is the mathematical translation of equiprobability: no value is favored or penalized, and chance shows no preference.

The mental image is that of a cake cut into rigorously identical slices: whichever slice you get, they are all worth the same. A fair die, a wheel with equal-sized sectors, or drawing a number between 1 and 100 all embody this same idea of perfect fairness.

The calculation is immediate in the discrete case: if there are n possible outcomes, each receives the probability 1/n. For a six-faced die, each face is worth 1/6, that is about 0.167. For drawing an integer between 1 and 100, each number is worth 1/100, that is 0.01. The sum of all these equal parts always gives 1.

A common trap is to believe that "uniform" means "unpredictable" or "without regularity." The opposite is true: the uniform distribution is very regular, because over a large number of draws each value comes up roughly as often as the others. What remains unpredictable is only the next single result.

We must also distinguish the discrete case, where we count a finite number of values, from the continuous case, where the uniform distribution spreads over an interval, like an instant taken at random within a minute. The site's tools fall under the discrete case.

The uniform distribution is the explicit target of all the fair draws offered: number generator, drawing a name from a list, virtual die, equal-part wheel. Guaranteeing this uniformity guarantees that no participant and no option is secretly favored.