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MENTAL MODEL · M3819

Gambler's Ruin

Gambler's Ruin
TechnicalHigh supportProbability Theory
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Version 1.0.0 · Updated 2026-07-28

CORE DEFINITION

In statistics, gambler's ruin is the fact that a gambler playing a game with non-positive expected value will eventually go bankrupt, regardless of their betting system.

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In statistics, gambler's ruin is the fact that a gambler playing a game with non-positive expected value will eventually go bankrupt, regardless of their betting system.

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The gambler's ruin theorem proves that in a fair game against an opponent with unlimited (or greater) capital, a player with finite capital will eventually go bankrupt with probability 1; even in a fair game, over time they are certain to lose all their money.

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Source support: Explicit

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    en.wikipedia.orghttps://en.wikipedia.org/wiki/Gambler%27s_ruinZH · Explicit
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