Law of Large Numbers

The law of large numbers says that as you collect more and more independent observations, their average gets closer and closer to the true expected value. Flip a fair coin ten times and you might see 70% heads, but flip it a million times and you will be extremely close to 50%.

It is the reason sampling works at all: a large enough sample reliably reveals the population's average. A crucial caveat is that it governs the average, not the individual: it does not promise that a streak will “balance out,” and a small sample can still be wildly misleading.