How many people does it take before a shared birthday is more likely than not?
Most people guess somewhere near half of 365. Try 23.
It's about pairs, not dates. With 23 people there are 23×22÷2 = 253 different pairs of people. The number of possible pairs grows much faster than the number of people, so the chance of at least one match crosses 50% surprisingly quickly.
This same collision math turns up anywhere you're checking many pairs instead of one: pharmacy name-and-birthdate mix-ups, hash collisions in computing, and DNA database matches all run into it.
Where else are you checking many pairs instead of just one?
Explore other probability thresholds
| Odds of a shared birthday | People needed |
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It is the same species of trap as the Monty Hall problem: a result that keeps feeling wrong even after the math settles it, because gut instinct evaluates the choice in front of it and quietly ignores the information hiding in everything that did not happen.
How is this calculated?
This assumes birthdays are spread evenly across 365 days (no Feb 29 and no real-world seasonal clustering), the standard simplification used in the classic problem.
P(shared) = 1 − (365 × 364 × … × (365−n+1)) / 365ⁿ, computed exactly for each n.