∴chance lab
A little randomness. A bigger picture.
THE LAW OF LARGE NUMBERS

Let chance reveal
the pattern.

Small samples can surprise you. Run an experiment and watch the results approach their expected probabilities.

0Ready when you are
—Observed vs. expected
—One random draw at a time

Expected meets observed

Ready to explore
Observed countExpected count

Bar heights share the same count scale. Exact values appear in the table below.

The bigger picture

Running proportions

Solid lines: observed proportions · Dashed lines: expected probabilities · Horizontal axis: trials

↗
More trials. A clearer picture.

As independent trials accumulate, relative frequencies tend to approach the probabilities you set. The gap can still grow temporarily; convergence is a long-run tendency, not a guarantee at every step.

Your results, in detail

OutcomeExpectedSelectedObservedGap