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Because you watch SciShow, Brilliant is offering you a 30-day free trial and 20% off an annual premium subscription at Brilliant.org/SciShow. There’s something so fun about finding out you have the same birthday as someone else.

It feels like a statistical marvel to hear that you and a buddy were born on the same day, and think of how much you can save on birthday cakes by going Dutch! But have you ever wondered what those odds really are? Like, how likely is it that you’ve got a birthday twin living on your street, or working in your office?

As it turns out, the odds of two people having the same birthday are way higher than many would guess. How about you? How many people do you think need to gather for the odds of a birthday match to be better than 50 percent?

Comment below with your best guess now, and see if you got it right in just a sec. [♪ INTRO] Okay, comments in? Good. Here’s the big reveal.

The number of people you need for it to be probable that at least two of them will share a birthday is just 23. I know, that sounds crazy. With 365 possible birthdays in a year, surely you’d need way more people before you find a match.

And yes, for perfect, 100 percent odds of a match, you would need 367 people. But just 23 people gives you more than a 50% chance of finding two people with the same birthday. If your mind is blown right now, you’re not alone.

This fact has been puzzling people for decades, so much so that it’s earned names like “The Birthday Problem” and even “The Birthday Paradox.” So why does it take so few people to get a match? The answer lies in probability. When you think about the Birthday Problem, you might picture each person in the room just shouting their birthdays all at once.

That would be the equivalent of one big comparison of all 23 dates. But to wrap your brain around this so-called paradox, it’s actually better to picture everyone in the room standing on their birthday on a giant calendar, one at a time. The first person has a 100 percent chance of standing on an empty date.

The second person has a 364 in 365 chance, since only one box is occupied. Which means the third person has a 363 in 365 chance, and so on. By the time it’s person 23’s turn, they have a 343 in 365 chance of standing in an empty box — that still seems likely!

But that’s not the end of the story. We can think of each person moving onto a box as a sort of pairwise comparison, with each pair having 1/365 odds of being a match. Person A, the first onto the calendar, has nobody to compare themselves to, and person B compares themselves only to A.

Person C compares to both A and B, person D compares to A, B, and C, and so on. So 23 people is really 253 pairs of people, each of which has 1/365 odds of being a match. And hey, listen.

This is a lot of tedious math to do, so we’re just not gonna bother showing you all that here. But please, trust us, if you do all that multiplying, you’re left with about 50.7 percent odds of a match!. And it gets even more brain-hurty as you add more people into the room and those odds get higher.

With 32 people, there’s a 75 percent chance of a match. With 41 people, there’s a 90 percent chance. And when you have just 70 people in a room together, there’s a 99.9 percent chance that two of those people share a birthday.

Now, some of you may have been shouting at your computers about a slight flaw in this logic. This problem assumes that any person has perfectly equal odds of their birthday being any of the days on the calendar– that birthdays are randomly distributed. But the real world is more complicated, and there are some factors that might alter the probability of a birthday match.

Obviously, we haven’t taken into account any leap year birthdays. Sorry to everyone out there born on February 29th, but even if we did include you, it wouldn’t change the odds all that much. A bigger factor is that there isn’t an even chance that people are born on any day of the year.

There are times of the year when more babies are born, and they vary around the world. For example, in the U. S., the month with the most babies born is August, while in the U.

K., it’s July. The most popular birthday in the U. S. is September 9th, while in England and Wales, it’s September 25th.

But the best birthday is mine, which is a secret. As interesting as all of these statistical calculations are, the Birthday Problem isn’t just a fun fact that you can pull out at parties. It has practical applications, too!

After all, birthdays aren’t the only thing that can overlap. Take medical studies, for example. A lot of the time, data collected in studies is anonymized, meaning all identifying information like names, birthdays, addresses, and phone numbers, is removed from the data.

This is done to protect people’s safety and privacy. If data isn’t anonymized, then people’s private health information may not be so private anymore. Once you anonymize the data, there’s no way of telling who participated in what studies, which is great for anyone in witness protection - which, hey, why are you answering surveys?

But this anonymized data can present its own kind of problem - double counting. Let’s say we want to find out how many people in Nebraska had a diagnosis of heart disease in a ten year span. We could just ask each hospital in Nebraska for the number of patients they had with heart disease and add them all up, and we’d get a solid number.

But we’d have no way of telling how many of those people had been to multiple hospitals and were in both hospitals’ numbers - they’d be double counted. Thankfully, math based on the Birthday Problem can help us out here. Using the same math of probabilities, researchers who are combining multiple datasets can find out the chances that someone is being counted twice, and skewing their results.

Unfortunately that doesn’t mean we can pick out those double-counts. It’s more to calculate the risk of overlaps and provide a margin of error around your study results. Here’s another example where the birthday problem can also give us birthday solutions.

In computer science, data is kept secure by something called a hash function, which assigns each datapoint a new value called a hash value. The problem is, every possible hash function can only produce a finite number of hash values, so sometimes, two inputs will result in the same output value, which is called a collision. And basically, if two data points have the same hash value, it means that a hacker can get the right result with the wrong answer.

It makes the whole dataset vulnerable to attacks. Using the math behind the Birthday Problem, computer scientists can calculate the risks of collisions in their hash functions, which could help point at ways to minimize the chances of them happening. In some commonly used methods, a hacker would need a thousand trillion attempts to cause a collision.

So what started as a quirky thought experiment ends up having real-world applications! And that, like any birthday, is something worth celebrating. And in this video, we’d like to celebrate our sponsor: Brilliant!

Brilliant is an interactive online learning platform offering an ever-growing catalog of lessons in math, science, and engineering. Like their course in Creative Coding! This course develops your programming skills with variables and loops in just eight lessons.

Then you’ll be ready to move onto one of Brilliant’s 17 other computer science courses. So one day soon, you could be one of those computer scientists protecting data against attacks with the birthday problem. To get started with your first 30 days free, you can go to Brilliant.org/SciShow or click the link in the description down below.

That link also gives you 20% off an annual premium Brilliant subscription. Thanks to Brilliant for supporting this SciShow video! And happy birthday to whoever is watching this video on their special day!

Sound off in the comments so we can see the birthday problem in our own community. [♪ OUTRO]