That's not the definition of a cryptographic hash. One of the four requirements of a function being a cryptographic hash function is that "it is infeasible to find two different messages with the same hash."

Then a cryptographic hash is not what you need.

Exactly, it's be interesting to have the average number of hashes needed before you hit a collision.

Crypto hashes are made so that collisions are as rare as possible.

Sometimes, you need something very, very fast, with as little collisions are possible (aka it "never" happen, like crypto hashes) yet those are not hashes of passwords and the like, so if it would happen it wouldn't be a security issue.

For that reason, this question is in fact interesting. Not that I have the answer to that :-)