Expected Value
The probability-weighted average of all possible values. For example, the expected value in rolling a six-sided die is 3.5, because the average of all the numbers that come up in an extremely large number of rolls is close to 3.5.
Origin
The concept emerged from correspondence between Blaise Pascal and Pierre de Fermat in 1654, solving the "problem of points"—a gambling question about fairly dividing stakes in an interrupted game. Pascal's "method of expectations" provided the first systematic reasoning about expected value, using what became Pascal's triangle. Fermat used complete outcome enumeration. Their work founded probability theory and influenced Christiaan Huygens' 1657 treatise De Ratiociniis in Ludo Aleae, the first systematic probability text.