The Introduction of the Concept of Expectation Comments on Pascal (1654)

The notion of the expected value of a gamble or of an insurance is as old as those activities themselves, so that in seeking the origin of “expectation” as it is nowadays understood it is important to be clear about what is being sought. Straightforward enumeration of the fundamental probability set suffices to establish the expected value of a throw at dice, for example, and Renaissance gamblers were familiar enough with the notion of a fair game, in which the expectation of each player is the same so that each should stake the same amount. But when more complicated gambles were considered, as in the Problem of Points, no one was quite sure how to compute the expectation. As is often the case in the development of a new concept, the interest lies not so much in the first stirrings which hindsight reveals but in the way its potential came to be realized and its power exploited. In the case of expectation, Pascal clarified the basic notion and used it to solve the Problem of Points.