The Role of Dice in the Emergence of the Probability Calculus

Abstract

The early development of the probability calculus was clearly influenced by the roll of dice. However, while dice have been cast since time immemorial, documented calculations on the frequency of various dice throws date back only to the mid-13th century. This paper examines the conceptual changes that took place between the ancient and medieval worlds regarding dice rolls. Archaeological data and written source material are used to explore various notions around tesseræ, or six-sided dice, and tali, which are four-sided dice made from the anklebones of goat or sheep. Given this evidence, it appears that dice rolls provided little or no incentive in Roman society to carry out numerical probability calculations. The first documented frequency computations on dice appeared circa 1260 in the manuscript De vetula, likely written by the English polymath Roger Bacon. In the same period, King Alfonso X of Castile, León and Galicia commissioned a book on games, Libro de los juegos. It is argued that the conceptual changes present in these publications reflect the emerging empiricism, related to dice, and mathematical interests of Bacon and his Islamic predecessors.