Arbitrary example: If you're using SHA256 you're emitting 256bit hashes. Hopefully the distribution of SHA256 outputs is indistinguishable from random (or close enough) or else we've got big problems in other domains.
If you're drawing at random from a pool of size k you need approximately sqrt(k) draws until you reach a ~50% chance of a collision[0].
With 256 bits, there are 2^256 possibilities, so following the rule-of-thumb you'd need 2^128 draws until you had a 50% chance of a collision.
2^128 > # of atoms in the universe.
If you adjust your risk tolerance you'll have different numbers come out, but the chance of a collision in any realistic scenario is negligible.
If you're drawing at random from a pool of size k you need approximately sqrt(k) draws until you reach a ~50% chance of a collision[0].
With 256 bits, there are 2^256 possibilities, so following the rule-of-thumb you'd need 2^128 draws until you had a 50% chance of a collision.
2^128 > # of atoms in the universe.
If you adjust your risk tolerance you'll have different numbers come out, but the chance of a collision in any realistic scenario is negligible.
[0]: https://en.wikipedia.org/wiki/Birthday_problem