Willful Ignorance: The Mismeasure of Uncertainty

CHAPTER 7 CLASSICAL PROBABILITY

In a letter written in September 1749 to Frederick the Great, the King of Prussia, the great mathematician Leonhard Euler (1707–1783) wrote:

My researches on the hydraulic machine occupying me again for some days, I take the liberty to render account of the examination of the Italian Lottery, for which it has pleased Your Majesty to charge me so graciously. First I have determined by the calculus of probabilities, how much each player ought to pay in order that the advantage were so much equal for him as for the bank.¹

This is one of the first clear references to the calculus of probabilities. Before 1750, the mathematical analysis pertaining to games of chance had almost always been known as the doctrine of chances. After that, this subject was more frequently termed the calculus of probabilities or sometimes the theory of probability.

This change in terminology reflected a major shift in thinking. From this point on we can find several writers referring to the calculus of probabilities in addition to, or in place of, the doctrine of chances. Moreover, the mathematical expositions became increasingly framed in terms of probability directly, although references to chances, odds, and expectations still occurred as well. By the 1760s, the idea of mathematical probability seems to have become so established that these earlier concepts were rarely mentioned explicitly.

During this critical transitional period, the concept of probability, defined ...