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Wednesday, May 08, 2013

A Roll of the Dice... Probability "Explained"

Writing about "The Law of Errors," in his masterful work "The Metaphysical Club: The Story of Ideas in America," Louis Menand explains discrepancies in calculative mechanics this way (which I find brilliant, by the way): "The solution to this problem [the problem of not knowing what produces a discrepancy] was borrowed from probability theory--specifically, from a formula published in 1738 by a mathematician named Abraham De Moivre, a Huguenot who had emigrated to England, in the second edition of a work called The Doctrine of Chances.  When you roll two dice, you get one of thirty-six possible combinations (one and one, one and two, one and three, and so on, up to six and six).  These thirty-six combinations can produce eleven possible totals (two through twelve).  The total with the greatest likelihood of coming up is seven, since a seven can be produced by any of six different combinations (one and six, two and five, three and four, four and three, four and two, six and one).  Only five of the thirty-six combinations will produce an eight or a six, only four will produce a nine or a five, and so on, down to the two and the twelve.  If you chart on a graph the results of many rolls of the dice, with the totals (two through twelve) on the horizontal axis and the number of times each total comes up on the vertical axis, you will eventually get points that connect to form a bell-shaped curve.  The highest point on this curve will be at seven on the horizontal axis (approximately one-sixth of your throws will produce some combination of numbers adding up to seven), and the curve will slope downward symmetrically on either side to two and one end and twelve at the other."

What I find most fascinating about this is the fact that in gambling there are many ways of calculating risk this way, enabling experienced and knowledgeable gamblers to "beat" the house again and again.  Case in point: the mathematical genius that is card-counting. While its application to "real" life is hard to interpret right at this moment, I am going to take some time this summer to study this roll of the dice probability issue and come up with some results.  I don't know how the roll of the dice game works at casinos but my curiosity has been cracked and now there'll be hell to pay :-)

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