The Role of Roguery in the History of Probability

Abstract

The English literature on gambling is examined from the early sixteenth to the mid-eighteenth centuries to try to discover the relationship between gambling and the development of the probability calculus. Throughout this entire time period, there is an overwhelming preoccupation in the literature with cheating at games of chance. The acts of cheating remain constant through time. However, the methods of cheating take various forms: for example false dice, legerdemain at cards and dice, perfect shuffles and card counting. Some probability calculations begin to creep into this literature near the end of the seventeenth century. What is demonstrated in this paper is that, contrary to the accepted folklore and even though there is some evidence that gamblers did have a concept of probability, gambling itself provided very little stimulus to the development of probability theory. In the other direction, the development of the probability calculus had a profound effect on gambling, namely in the formulation of a strategy of play. These strategies, first devised by Edmond Hoyle in the mid-eighteenth century and applied initially to the card game of whist, used very simple results in probability. As a result of this historical analysis, it is necessary to reanalyze the events surrounding the emergence of probability in the seventeenth century.