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==Chance not in the News== | ==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=== | |||
[http://quomodocumque.wordpress.com/2008/10/02/slate-piece-on-martingales-expected-value-and-the-bailout/ Slate piece on martingales, expected value, and the bailout.] | |||
[http://wizardofodds.com/gambling/bettingsystems.html The Wizard of Oz] | |||
[http://www.iansharpe.com/art_martingale.php Ian Sharpe] | |||
Revision as of 02:22, 21 December 2008
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.