When is your birthday? The math behind hash collisions (opens in new tab)

> What is the probability that you are sharing the same birthday with people around you?

> What if I told you that in a room with only 23 people there’s already a 50% chance for two of them to have matching birthdays?

I guess it's the subject shift from _you_ to _any two people from a group_ that creates the surprise in the birthday paradox. You definitely need way more than 23 randomly sampled people to get to a high probability that _you_ specifically share a birthday with one of them, and the result does not contradict that notion.

This is also an easy way to detect RNGs that are not truncated (i.e. return the entire state (or any 1-to-1 permutation of their entire state):

https://www.pcg-random.org/posts/birthday-test.html

Example:

Any RNG with a period 2**32 that can output every 32-bit value at least once must have zero collisions for the first 2**32 outputs, but we would expect to see about 100 collisions after just 200k outputs.

> What is the probability that you are sharing the same birthday with people around you?

If you're a twin and your twin sibling is standing next to you, nearly 100%. But not exactly 100%: there have been cases of twins born on either side of midnight ending up with birthdays that differ by a day. (I don't personally know of any twins born on either side of midnight between Dec 31st and Jan 1st, who would then have different calendar years in their birthdays, but odds are very good that it has happened at least once in human history).

And what are the odds of your birthday being exactly at the center of the (non-leap) year? That's my B'day. Cool!

Related today:

Ask HN: We just had an actual UUID v4 collision...

https://news.ycombinator.com/item?id=48060054