There are 365 birthdays and only 23 people. It feels like a lottery you should lose. Make a guess, then fill the room yourself.
Assume 365 equally likely birthdays and no leap days. Drag to your guess.
Why so few? Count pairs, not people. Each new person can match everyone already there, so the number of pairs grows with the square: n(n-1)/2.
Each dot is one person's birthday. Red days have two or more people.
The curve is the exact formula, 1 minus the product of (365-k)/365 for k from 0 to n-1. The tally counts your own random rooms.
| People | Pairs | Chance |
|---|
Real birthdays are uneven (more in some months), but unevenness only raises the chance, and the 50% threshold stays at 23.
Wikipedia, Birthday problem (opened 19 Oct 2026): 23 people give 50.7297%; 70 people give 99.9%; uniform birthdays minimise the match chance, and the real-world threshold is still 23, citing Cortina Borja and Haigh, "The Birthday Problem", Significance 4(3), 2007. All other figures on this page are computed live from the formula in your browser.