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Probability in Games
The focus of this chapter so far has been on the macro-level of uncertainty inherent in all games. Now we turn to a more specific examination of the micro-operations of chance. The study of mathematical uncertainty is called probability. According to Richard Epstein, "The word 'probability' stems from the Latin probabilis, meaning 'truth-resembling'; thus the word itself literally invites semantic misinterpretation." [1]What Epstein means by "semantic misinterpretation" is that if something is "truthresembling," then it isn't actually truthful; at the same time, the truth is exactly what the something does resemble. It is appropriate that probability would have at its etymological roots such a paradoxical meaning. We have seen that macro-uncertainty has its own paradoxes, such as a feeling of randomness when formal randomness does not exist. The micro-study of uncertainty—exhibited in the form of probability —has its own paradoxes as well. For example, the role that probability can play in a game is twofold. On the one hand, chance elements in a game introduce randomness and chaos, leading to uncertainty. On the other hand, a thorough study of the mathematics of probability reduces wild unknowns to known risk values, increasing the overall certainty of a game. Appropriately enough, the mathematical study of probability has its origin in games. In the Seventeenth Century, a French nobleman, the Chevalier de Méré (who in contemporary society might be considered a professional gambler), brought a problem to his friend Blaise Pascal, the mathematician. De Méré wanted to know a logical way to divide the stakes in a dice game when the game had to be terminated before it was completed. In working out the solution to this problem, Pascal developed a new branch of mathematics, the theory of probability. De Méré's problem amounted to determining the probability that each player had of winning the game, at a given stage in the game.[2]
The study of probability has evolved into an important field of mathematics that goes far beyond simple percentages and betting odds. In fact, for the mathematically inclined, Epstein's book offers a wonderful overview of the field. However, for the purposes of this volume, we will keep the math extremely simple and straightforward. [1]Richard Epstein, The Theory of Gambling and Statistical Logic (San Diego: Academic Press, 1995), p. 43.
[2]Elliott Avedon and Brian Sutton-Smith, The Study of Games (New York: John Wiley & Sons, 1971), p. 383.
