# martingales

Published articles for martingales.

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## Martingales and the Optional Stopping Theorem

DevFeed: [Martingales and the Optional Stopping Theorem](<https://devfeed.tech/articles/martingales-and-the-optional-stopping-theorem-40349.md>)

Original publisher: [Read original article](<https://www.jeremykun.com/2014/03/03/martingales-and-the-optional-stopping-theorem/>)

Published: 2014-03-03T10:00:38Z

Content type: tutorial

Language: en

Sources: [Jeremy Kun](<https://devfeed.tech/sources/jeremy-kun.md>)

Topics: [math](<https://devfeed.tech/topics/math.md>)

Tags: [2-sat](<https://devfeed.tech/tags/2-sat.md>), [conditional-probability](<https://devfeed.tech/tags/conditional-probability.md>), [expectation](<https://devfeed.tech/tags/expectation.md>), [gambling](<https://devfeed.tech/tags/gambling.md>), [martingales](<https://devfeed.tech/tags/martingales.md>), [mathematics](<https://devfeed.tech/tags/mathematics.md>), [optional-stopping-theorem](<https://devfeed.tech/tags/optional-stopping-theorem.md>), [primer](<https://devfeed.tech/tags/primer.md>), [probability-theory](<https://devfeed.tech/tags/probability-theory.md>), [random](<https://devfeed.tech/tags/random.md>), [random-variables](<https://devfeed.tech/tags/random-variables.md>), [randomized-algorithm](<https://devfeed.tech/tags/randomized-algorithm.md>), [stochastic-processes](<https://devfeed.tech/tags/stochastic-processes.md>), [theory](<https://devfeed.tech/tags/theory.md>)

### AI overview

This primer introduces martingales as models of fair betting games and explains their connection to probability theory. It begins with a geometric-distribution exercise involving repeated die throws, then introduces the ABRACADABRA problem using a monkey typing random letters.

### Source excerpt

This is a guest post by my colleague Adam Lelkes. The goal of this primer is to introduce an important and beautiful tool from probability theory, a model of fair betting games called martingales. In this post I will assume that the reader is familiar with the basics of probability theory. For those that need to refresh their knowledge, Jeremy's excellent primers (1, 2) are a good place to start.