A year has 365 days, so meeting two people who share a birthday feels like it should take a huge crowd, right? But with just 23 people in a room, the probability that two of them share a birthday already passes 50%. It clashes so sharply with intuition that it's called a "paradox."
It's easy to get this wrong because people usually think of "someone who shares my birthday." But what we're actually finding is "the probability that any two people among the 23 share a birthday." With 23 people, the number of possible pairs is 23×22/2 = 253 pairs. That's 253 separate chances to ask "might these two match?" — which is exactly why the probability climbs so much higher than intuition suggests.
Change the number of people with the slider and see the probability that two of them share a birthday.
Compare the probability at different group sizes on a bar chart, and see at a glance just how steeply it climbs around 23 people.
Pick a group size and press the button to draw actual random birthdays. Draw several times and check how often a match really happens.