You can use this to work out how many people you need for a good chance of a match for any characteristic.
Suppose that any two people have a 1 in C chance of matching — for example, for an exact birthday match, C = 365. Then to have a 50 per cent chance of a match in a group of N people, N needs to be around 1.2√C. For a birthday match, this means that we need around 1.2√365 = 23 people, as claimed above. For a 95 per cent chance of a match, we need to approximately double this number, to 2.5√C. So if we have N = 2.5√365 = 48 people in a room, it is very likely indeed that two will have the same birthday.
This makes it tempting to try to make money off people.
Suppose you have 30 people at your Huntrodds party (you couldn't count). Bet the group that two have a birthday within one day of each other. What are the chances you will win? First, consider the chance that any two people (say Me and You) match in this way: if My birthday is 19th September, like the Huntrodds, then a match would happen if You were born on the 18th, 19th or 20th, which is 3 out of 365 days, or a 1 in 122 chance, so C = 122. So for a 50% per cent chance of a match we only need 1.2√122 = 13 people, and for a 95 per cent chance we need 2.5√122 = 28 people. So with 30 people at your Huntrodds party, you have an excellent chance of winning. (But still a chance of losing. That's chance for you).