This trend continues up to around twenty-three people, where the curve hits 50% odds, and the rate of increase starts going down.
It practically flattens out when fifty-seven people are considered, and the odds rest at about 99%.
Though it may not be intuitive, the numbers follow the pattern quite faithfully.
But over time I have come to the realization that I’m not the source of the problem. Consider the following example: Assuming for a moment that birthdays are evenly distributed throughout the year, if you’re sitting in a room with forty people in it, what are the chances that two of those people have the same birthday? A reasonable, intelligent person might point out that the odds don’t reach 100% until there are 366 people in the room (the number of days in a year + 1)… so such a person might conclude that the odds of two people in forty sharing a birthday are about 11%.
In reality, due to Math’s convoluted reasoning, the odds are about 90%.
This phenomenon is known as the If the set of people is increased to sixty, the odds climb to above 99%.
But that doesn’t really satisfy the question for me, it just feels marginally less screwy.
So I did something quite out of character: I crunched the numbers.
The values rapidly become unmanageable, but the trend is clear: possible combinations of birthdays the group has, 7.4% of cases— or about one in thirteen— result in two of them having the same birthday.As each person is added, the odds do not increase linearly, but rather they curve upwards rapidly.This means that with only sixty people in a room, even though there are 365 possible birthdays, it is almost certain that two people have a birthday on the same day.After making these preposterous assertions, Math then goes on to rationalize its claims by recruiting its bastard offspring: numbers and formulas.It’s tricky to explain the phenomenon in a way that feels intuitive.You can consider the fact that forty people can be paired up in 780 unique ways, and it follows that there would be a good chance that at least one of those pairs would share a birthday.