
The Birthday Paradox - the_70x
https://en.wikipedia.org/wiki/Birthday_problem
======
FabHK
Rule of thumb (useful for cryptography, among other things):

If you draw randomly (with replacement) from N numbers, you'll need to draw
approximately sqrt(N) times until the probability of a collision (drawing the
same number again) rises to 1/2.

For example, if you generate random keys with 128 bits, then after generating
2^64 keys you have a good (50%) chance that you've reused a key.

See
[https://en.wikipedia.org/wiki/Birthday_attack](https://en.wikipedia.org/wiki/Birthday_attack)

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ColinWright
As FabHK[0] says[1], the rule of thumb is that you are 50% likely to get a
collision with about sqrt(N) selections from N objects.

We are, of course, more interested in much smaller probabilities of collision,
and that's why I wrote about this[2] some time ago, giving the derivation, and
the actual formula for those who just want the answer.

It's been submitted and discussed before[3][4], with some interesting
comments.

[0]
[https://news.ycombinator.com/user?id=FabHK](https://news.ycombinator.com/user?id=FabHK)

[1]
[https://news.ycombinator.com/item?id=21069837](https://news.ycombinator.com/item?id=21069837)

[2]
[https://www.solipsys.co.uk/new/TheBirthdayParadox.html?si25h...](https://www.solipsys.co.uk/new/TheBirthdayParadox.html?si25hn)

[3]
[https://news.ycombinator.com/item?id=19296265](https://news.ycombinator.com/item?id=19296265)

[4]
[https://news.ycombinator.com/item?id=4753014](https://news.ycombinator.com/item?id=4753014)

------
mcherm
I just recently published a blog post on this topic:
[https://www.mcherm.com/unique-ids.html](https://www.mcherm.com/unique-
ids.html)

Sadly, I am still getting pushback from others at my company who are either
not convinced by the math or for whom any such analysis doesn't matter. "Yes,
but there is still a chance of getting a duplicate, so I don't think this can
be safe."

~~~
FabHK
Yes, that is funny.

It feels a bit insane - how do you choose your secret private Bitcoin wallet
key? Easy, just pick one randomly! Oh no, but someone else could pick the same
key. Sure, but the probably is so vanishingly small, we really really really
don't have to worry about it...

It is a bit hard to wrap your head around it, but the maths is solid
(assuming, of course, that you have a good source of randomness).

------
rinchik
Related:
[https://en.wikipedia.org/wiki/Birthday_attack](https://en.wikipedia.org/wiki/Birthday_attack)

Also shameless plug: [https://blog.rinatussenov.com/collision-probability-and-
birt...](https://blog.rinatussenov.com/collision-probability-and-birthday-
paradox-ef98b84fe009)

