This chapter introduces some basic concepts pertaining to the interplay between probability and risk, as outlined in the earliest, albeit not always systematic, studies of the subject. In order to define the field of inquiry, the chapter illustrates the insights of Blaise Pascal and Daniel Bernoulli, who were among the first to apply mathematical analysis to games of chance, introducing expected utility maximization. These insights are presented alongside with the analyses of William Stanley Jevons and Alfred Marshall, who objected to its use.