Equiprobability

Equiprobability describes a situation in which no outcome is favored over the others: all possible outcomes share exactly the same probability. The randomness is perfectly flat, with no bias and no favored result. This is the implicit assumption behind most games designed to be fair.

The clearest mental image is that of a perfectly symmetrical object. A fair coin has no reason to lean toward heads rather than tails; an untampered die favors none of its faces; a wheel divided into identical sectors does not stop more readily on any one of them. The physical symmetry of the object produces equal chances.

When equiprobability holds, the calculation becomes very simple. If an experiment has a certain number of equally likely outcomes, each one has a probability equal to 1 divided by that number. For a six-sided die, each face is therefore worth 1 in 6, or about 0.17; for a coin, each side is worth 1 in 2, that is 0.5.

The probability of a compound event then comes down to counting. It is enough to count the outcomes that make the event happen, then divide by the total number of outcomes. Rolling an even number with a die amounts to 3 favorable outcomes out of 6, that is a probability of 0.5.

Equiprobability should not be confused with independence. The former concerns equal chances within a single experiment; the latter describes the absence of influence between several successive experiments. A common trap is also to assume equiprobability without checking that the object is genuinely symmetrical: a wheel with sectors of different sizes is not equiprobable.

On the site, equiprobability is the basic contract of the drawing tools. The coin flip, the die roll, the wheel with equal sectors, and the name draw from a list all aim to give each possibility the same chance of being selected.