I tested von Mises's 1939 birthday claim with exact arithmetic and 10^5 Monte Carlo trials per group size. 23 people really is enough.

In 1939 Richard von Mises published a short paper with the unwieldy title *Über Aufteilungs- und Besetzungswahrscheinlichkeiten*. Inside is the calculation that everyone now calls the birthday paradox. Pick 23 people at random. The probability that t