A Brief History of Risk

The human fascination with games of chance was a major driving force behind the emergence of probability theory.   There is evidence that ancient civilizations had developed games similar in concept to modern-day games that are based on throwing dice.   The “dice” used in these ancient games were often the heel bones or “astragali” of animals.   When thrown, these bones could come to rest on one of four differently shaped sides, each of which counted for a certain number of points[1].   The absence in these societies of a basic understanding of odds or probabilities was apparent in the scoring system they used.   For example, the astragali had two narrow sides and two wider sides.   You might expect that a higher number of points would be awarded to the more difficult task of landing the bone on one of the narrow sides. But studies of classical writings suggest that the wider sides scored either three or four points while the narrower sides scored one or six.   Obviously, the points awarded did not accurately reflect the odds of achieving a particular outcome.  They had no real understanding of either probability or risk.

It was not until the Renaissance that any systematic effort was made to analyze these games within some sort of a theoretical structure.   Many reasons have been put forward to explain the long delay in developing laws of probability.   One argument points to the emphasis placed by the Greeks on theoretical proofs and their consequent lack of interest in the empirical experimentation needed to understand gambling odds[2].   Another argument focuses on the use of dice or lotteries to consult the gods.   Efforts to try to compute in any way what the gods might have to say could be considered improper.   The most widely accepted explanation for the delay was the absence of basic tools of arithmetic to easily carry out probability calculations.   The Greeks and Romans traditionally used letters for counting and calculating.  And importantly, these early civilizations did not have the number we call zero, which severely restricted the development of their mathematics. It was not until the 13^th century that the Hindu-Arabic numbering system came to the Western world, which facilitated calculations that were unmanageable under the letter-based systems[3].  

The 17^th century mathematician Blaise Pascal is generally credited with the invention of the theory of probability.[4]   Pascal, together with the mathematician Pierre de Fermat, laid the foundations for modern probability theory, before abandoning mathematics for a quieter life in a Parisian monastery.

 While Pascal’s contribution to probability theory was undoubtedly substantial, it was just the beginning.   Importantly, his analysis was limited to cases in which a finite number of equally likely possible outcomes could be enumerated.  As a result, the analysis is only useful for studying dice, cards and other games of chance.  More realistic situations, such as examining the likely future course of the weather, require other tools.[5]  

Jacob Bernoulli, who stressed the role of statistical sampling in dealing with uncertainty, moved things forward by examining problems with a potentially infinite number of outcomes in the early 18th century.   Through his law of large numbers, Bernoulli sought to provide a formal proof of the idea that uncertainty decreased as the number of observations increased.   Another other key development of that century was the discovery by Abraham De Moivre of the normal curve – the fact that random drawings would distribute themselves in a bell shape around their average value.   Although theories relating to risk and uncertainty have continued to develop, the contributions of Pascal, Bernoulli and De Moivre remain pivotal to our understanding of risk.