Hvornår gælder det store antal love?
Law of large numbers
LLN er vigtig, fordi den garanterer stabile langsigtede resultater for gennemsnittene af nogle tilfældige begivenheder. Selv om et kasino f.eks. kan tabe penge ved et enkelt spin på rouletten, vil dets indtjening have en tendens til en forudsigelig procentdel over et stort antal spins. Enhver gevinststrejke hos en spiller vil i sidste ende blive overvundet af spillets parametre. Det er vigtigt at huske, at loven kun gælder (som navnet antyder), når der tages hensyn til et stort antal observationer. Der er ikke noget princip om, at et lille antal observationer vil falde sammen med den forventede værdi, eller at en stribe af en værdi straks vil blive "opvejet" af de andre (se gambler's fallacy).
Law of large numbers
The LLN is important because it guarantees stable long-term results for the averages of some random events. For example, while a casino may lose money in a single spin of the roulette wheel, its earnings will tend towards a predictable percentage over a large number of spins. Any winning streak by a player will eventually be overcome by the parameters of the game. It is important to remember that the law only applies (as the name indicates) when a large number of observations is considered. There is no principle that a small number of observations will coincide with the expected value or that a streak of one value will immediately be "balanced" by the others (see the gambler's fallacy).
Law of large numbers