How Rare Is My Hash?

Human pattern recognition gets the best of us when we look at long strings. Practical randomness tests look at exactly this kind of thing: bit frequencies, runs, longest runs, and repeated templates (statistical randomness). If we pick enough axes to measure your hash along, eventually it will be absurdly unique in at least one.

For a fun read on how badly humans handle randomness, see Ben Torvaney's How to pick a random number from 1-10 — asked to pick “at random” between 1 and 10, people pick 7 about a third of the time.