How did gambling and insurance contribute to the development of probability in the 17th century?
Swiss commemorative stamp of mathematician Jakob Bernoulli, issued 1994, displaying the formula and the graph for the law of large numbers, first proved by Bernoulli in 1713.
In the 17th century, the development of probability was deeply rooted in the practical challenges of gambling and the legal requirements of insurance.
Gambling and the Theory of Chances
The modern mathematics of chance emerged from a 1654 correspondence between Pierre de Fermat and Blaise Pascal, prompted by a problem regarding the fair division of stakes in an interrupted game of chance. These games provided model problems that allowed mathematicians to develop methods for calculating combinations and expectations. While earlier thinkers like Girolamo Cardano had calculated odds for games of luck, the 17th-century scientific revolution provided the necessary credibility for these calculations to flourish as a formal theory.1
Insurance and Fair Contracts
The theory of chances extended beyond gambling into the legal concept of a "fair contract," which required an equality of expectations between parties. This framework helped justify lending at interest by sharing risk, circumventing religious prohibitions against usury. By the 1660s and 1670s, mathematicians like Christiaan Huygens and statesmen like Jan de Wit began applying these probabilistic concepts to determine fair rates for annuities, laying the groundwork for the future of actuarial science.2