Canonical · Logic & Mathematics · Theorem

The Law of Large Numbers

Jacob Bernoulli / Andrey Kolmogorov · 1713

"As you take more independent draws from the same process, the average of what you see converges to the true underlying expectation — which is why small samples routinely mislead and large samples quietly correct."

The idea

Bernoulli proved in 1713 why your gut misreads streaks: flip a fair coin ten times and 70% heads is common; flip it ten thousand times and 51% heads is rare. Large numbers pull the average back to its true center.

Why it works

The takeaway — recall it first

Bayes' Theorem

"Belief should update in proportion to evidence — Bayes' theorem is the exact math for how much a new piece of evidence should move your confidence."

Thomas Bayes (published by Richard Price) · ModelContinue→