Gambling terms, explained straight

Casino & Table Games

Law of large numbers blackjack

In blackjack, the law of large numbers means that over many independent hands, the average result tends toward the game's expected value—typically the house edge.

Also called
Weak law of large numbers, strong law of large numbers, or LLN13
Applies to
Repeated play in blackjack and other random wagers in gambling mathematics42

Key points

  • Each hand is random, but as the number of hands grows, short-term swings average out toward the game's expected value12.
  • The sample mean of independent, identically distributed variables converges to the common expectation for finite expectations3.

Where this term is used

Sources

  1. Law of large numbers - Wikipedia en.wikipedia.org Defines the law of large numbers and its weak/strong variants.
  2. Ask The Wizard #33 wizardofodds.com Explains how LLN applies to blackjack expected value.
  3. Probability theory - Wikipedia en.wikipedia.org Provides the mathematical formulation of LLN convergence.
  4. Gambling mathematics en.wikipedia.org Covers LLN in gambling mathematics context.

Sources are drawn from regulators, universities and published research, and each one is labelled with what it actually is — a preprint is not called a paper. Bookmaker and affiliate pages are never cited here, because a page that sells betting is not a neutral authority on it.