How many people until a match?
A shared birthday can occur between any two people. At 23 people there are 253 pairs, and the probability of at least one match is about 50.7% under a uniform 365-day model.
Inside this model
Exact probability = 1 − product of (365 − i)/365 for i = 0 through n − 1. The sample draws 1,000 independent rooms; the displayed room highlights repeated day numbers. Pair count is n(n − 1)/2.
Out in the world
A practical use
The same collision logic helps explain why duplicate short identifiers can appear surprisingly early in a growing database.
A useful lens. Not a universal law.
- Real birthdays are seasonal and not independent for every group; leap days are excluded. A match with your own birthday is a different question.
Further reading
Explore the original research or the teaching reference behind this experiment.
Grinstead & Snell — The birthday problem, Section 3.1 ↗