Even then, 29,998 of 30,000 people (assuming it was exactly that many at p(.5)) chose a unique galaxy. That’s still pretty likely.

That's the chance of someone having a collision.

The chance of you having a collision at that point is still about 2^-15.

And how many people do you expect to follow these directions, anyway?

This seems like one of those probabilistic phenomena that's completely counter intuitive so my brain doesn't know how to comprehend it.

Could you elaborate?

It’s completely unintuitive. See https://en.wikipedia.org/wiki/Birthday_problem

The basic idea is simple enough: if you have a random collection of people, and keep adding more, eventually 2 of them will have the same birthday. If you run that experiment a bunch of times, eventually you’ll get the average number of people where there’s a 50% chance of having a “collision”. The surprising part is that the number is so small: in this case, it’s 23.

It's intuitive if you do it visually. Connect each person to every other person with a piece of string. 10 people each have about 10 connections. 50 people each have about 50 connections. 1000 people each have about 1000 connections.

When you're handing out 250 pieces of string it's easy to tell that something with a 1/365 chance per string is likely.

For this situation, if you put 50 thousand people in a room then they each have 50 thousand ways to pair up, so you're looking at over a billion opportunities to have a one-in-a-billion coincidence. (50k * 50k / 2 = 1.25 billion)

That's a great visualization, thanks!