# Shared Birthdays

Famously, in a group of 23 randomly chosen people, the chance is slightly higher than 50 percent that two will share a birthday.

In 2014, James Fletcher considered the birth dates of players in the World Cup, who were conveniently organized into squads of 23 people each. He found that 16 of the 32 squads had at least one shared birthday. If data from 2010 World Cup was included, 31 of 64 squads had shared birthdays, still quite close to 50 percent.

If a group numbers 366 people, the probability of a shared birthday is 100 percent (neglecting leap years). But to reach 99 percent certainty we need only 55 people. “It is almost unbelievable that such a small difference between the probabilities 99% and 100% can lead to such a big difference between the numbers of people,” writes Gabor Szekely in Paradoxes in Probability Theory and Mathematical Statistics (1986). “This paradoxical phenomenon is one of the main reasons why probability theory is so wide-ranging in its application.”