martingale

mathematics

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June 30, 2026

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In mathematics, a martingale is a type of stochastic process, which is a collection of random variables indexed by time. Specifically, a martingale is a process where the expected value of the next value, given all past values, is equal to the current value. This concept is often illustrated with games of chance, where a martingale represents a "fair game" because the gambler's expected fortune in the next step remains the same, regardless of past outcomes.1

The term "martingale" also has a different meaning in horsemanship, referring to a strap used to steady a horse's head or control its upward movement. Additionally, it can describe a betting system where stakes are increased after each loss, typically by doubling.23

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probability theory
Martingale theory
As a final example, it seems appropriate to mention one of the dominant ideas of modern probability theory, which at the same time springs directly from the relation of probability to games of chance. Suppose that X₁, X₂,… is any stochastic process and,…
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As a final example, it seems appropriate to mention one of the dominant ideas of modern probability theory, which at the same time springs directly from the relation of probability to games of chance. Suppose that X₁, X₂,… is any stochastic process and,…
Read More