The Law of Large Numbers

How randomness is averaged out in the long run

The Law of Large Numbers is one of the most frequently misunderstood concepts of probability and statistics.

You’ve probably fallen into the gambler’s fallacy a few times already: just because you lost ten blackjack games in a row, it doesn’t mean that you’ll be more likely to be lucky next time because of the law of large numbers.

Games (and other phenomena) of chance don’t have memories. The cards, coins, and dice don’t care what happened previously, they’ll behave the same each time. On the other hand, randomness is averaged out in the long run. If you toss a coin a million times, it’ll land on its heads approximately half the time.

What is the law of large numbers, then? Let’s answer this question.

Tossing coins

The strength of probability theory lies in its ability to translate complex random phenomena into coin tosses, dice rolls, and o…