I hadn't heard of the "Birthday Paradox" before you mentioned it your comment, but your description of it isn't quite right. It's not that half the people in a group of 23 will share a birthday, it's that there is a 50-50 chance that two people in the group will have the same birthday. Still, very interesting and I learned something today!
That's how i understood GP's "half of such groups" statement - as a 50-50 chance (half of all groups, not half of the people in the group). But maybe I was biased because I heard of "Birthday Paradox" before.
