We could make many other fun examples to illustrate the same counterintuitive phenomenon (thread).
Do it 16 times, and your chances are over 90%. Try it!
With more than 250 people, its >95%.
Ditto for ATM pin codes.
How many hands would you think you'd have to draw before you've likely had the same *exact* hand twice?
It's about 100.
It's actually around 1,900 hands that it becomes more likely than not to have held the same hand twice. That's just 19 evenings with 100 hands each. Many (most?) of you reading this have held the same exact poker hand twice!
In the phone numbers example, sqrt(10,000) = 100, and the 50% point happens with 118 people.
In the card example, sqrt(52) = 7.2, and it took 9 draws.