paradox · counting
Birthday paradox
How full before two people share a day?
How full does the room get before two people share a day?
Fill a room and look for a shared day. The day number sits on each matching pair.
Lock a share, then run the rooms.
—This room
—Rooms with a shared day
—Long-run share for this size
Each birthday is one of 365 days, spread evenly. Leap day is left out.
A shared day is any two people in the room, not a match with you alone.
With 23 people there are 253 pairs. A shared birthday shows up in about half of rooms.