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Chance not in the News
In current probability a Martingale is A stochastic process s(0),s(1),s(2),.... with E(s(n+1) = s(n), ie. if it be considered a fair game. With this definition the coin tossing model discussed by Jordon two Martingales, one when you have a finite amount of money and another when you have and unlimited amount of money. . Doob proved that if the values s(0), (1),s(2), ... are bound by a number B then for for any stopping rule
If s)0),.. is a bounded martingale then and T is a stopping time then the expeked value of S(T) - S(0)
Additional Reading
Slate piece on martingales, expected value, and the bailout.