When Raymond Smullyan was teaching probability at Princeton, he told one class about the birthday paradox - the fact that if there are 23 or more people in a room, the chances are greater than 50 percent that at least two of them share a birthday.
There were only 19 students in the class, so the chances of sharing a birthday were quite small.
One boy said: “I’ll bet you a quarter that two of us here have the same birthday.
I give you my word that I don’t know the birthday of anyone here other than my own.
Nevertheless I’ll bet you as I have said.”
Smulllyan took the bet and lost.

Why?

Source: A mixed bag by R.S. 2016