Optional stopping theorem

In probability theory, the optional stopping theorem (or sometimes Doob's optional sampling theorem, for American probabilist Joseph Doob) says that, under certain conditions, the expected value of a martingale at a stopping time is equal to its initial expected value. The concept can be understood through the following key principles: Since martingales can be used to model the wealth of a gambler participating in a fair game, the optional stopping theorem implies that, on average, nothing can be gained by stopping play based on the information obtainable so far (i.e., without looking into the future).

Source: Wikipedia — Optional stopping theorem (CC BY-SA 4.0)

Optional stopping theorem

In probability theory, the optional stopping theorem (or sometimes Doob's optional sampling theorem, for American probabilist Joseph Doob) says that, under certain conditions, the expected value of a martingale at a stopping time is equal to its initial expected value. The concept can be understood through the following key principles: Since martingales can be used to model the wealth of a gambler participating in a fair game, the optional stopping theorem implies that, on average, nothing can be gained by stopping play based on the information obtainable so far (i.e., without looking into the future).

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Source: Wikipedia "Optional stopping theorem" · CC BY-SA 4.0

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