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.
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
Related terms
Casino games
Blackjack
The card game itself, where the law of large numbers applies over many hands.
Casino games
Insurance blackjack
A side bet on the dealer having blackjack, not the statistical LLN principle.
Casino games
Basic strategy blackjack
The optimal play chart that minimises the house edge, which the LLN makes reliable over many hands.
Casino games
Blackjack strategy card
A printed reference for basic strategy, whose long-term effect is governed by the LLN.
Casino games
Blackjack rules dealer
Dealer rules that set the house edge, which the LLN reveals over many rounds.
Casino games
Blackjack 21
Another name for blackjack, where the LLN predicts long-run average results.
Sources
- Law of large numbers - Wikipedia en.wikipedia.org Defines the law of large numbers and its weak/strong variants.
- Ask The Wizard #33 wizardofodds.com Explains how LLN applies to blackjack expected value.
- Probability theory - Wikipedia en.wikipedia.org Provides the mathematical formulation of LLN convergence.
- 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.