Birthday Paradox

Put 23 people in a room and it is a coin flip that two of them share a birthday. Nobody believes it. So: fill a room, watch where everyone lands on the calendar, then run a thousand rooms and see whether reality agrees with the arithmetic.

READY

One room on the calendar ring23 PEOPLE

←→ step through the room · Esc clear

Chance of a shared birthday, 2 to 100 peoplen = 23 → 50.73%

theory measured runs click or arrow-key the chart to move the group size

1000 rooms, one square eachn = 23

shared birthdayall different

Rooms with a match—
Measured—
Theory50.73%
Gap—
Run a thousand rooms to test the number on the left.

The odds right now

50.73%

chance that at least two of the 23 people share a birthday


Pairs in the room253
Matches your day5.86%

Controls

23

Why 23 is the surprise

Ask around and most people guess about 180 — half of 365. That answers a different question: how many strangers you need before one matches your birthday. In this room that chance is only 5.86%.

Nobody is the reference point. Every pair counts, and 23 people quietly make 253 pairs — each one its own little chance to collide. That is why the answer is 23 and not 180.