The law of large numbers says averages settle down as more trials are added to an experiment.

The longer version

Add more independent repetitions and the running average stops wandering. Each new observation is weighted the same as every earlier one, so a freak early result gets diluted rather than erased, and the running total drifts toward the underlying probability. Roughly, the typical error shrinks in step with the square root of the number of trials.

That statement says nothing about catching up. A coin that has landed heads fifty times in a row is not obliged to produce extra tails; the early imbalance simply becomes negligible against a huge denominator. Polls, quality checks, and insurance pools all depend on this stabilising behaviour, provided the trials really are independent.

Where this entry sits

This section collects odd corners of mathematics, from stubborn prime numbers to counting systems older than modern schools. Expect famous constants, probability puzzles, shapes that break everyday intuition, and numbers far too large to picture. The full list sits on the Numbers and Math page, where every entry is listed in order.