Expected value multiplies each outcome by its probability, which is how casinos and insurers set long-term prices.

The longer version

Take every possible outcome, multiply it by how likely it is, and add the products. A fair six sided die gives three point five, a value no single roll can ever show, because it is a long run average rather than a prediction. Add a cost to play and the same arithmetic turns positive or negative.

Any business built on repeatable bets lives off this number. A game with a small negative expected value for the player still pays out often, but over thousands of rounds the average dominates and the operator's income becomes predictable. Insurers apply the same logic to premiums, spreading risk across many policies instead of one.

Where this entry sits

This section collects odd corners of mathematics, from stubborn prime numbers to counting systems older than modern schools. Expect famous constants, probability puzzles, shapes that break everyday intuition, and numbers far too large to picture. The full list sits on the Numbers and Math page, where every entry is listed in order.