Why I use UUIDs for primary/foreign keys

[eluser]sl3dg3hamm3r[/eluser]
Well, I confess I am not able to write any mathematical proof for it. But if you imagine a finite range of 1 to 10. Now you generate the first id, the chance of hitting one you didn't use yet is 100%, and now we have a chance of 10% that we generate the same again.
Let's say we used now 9 out of 10 (we are up on 90% that we gonna hit one of the used ones), you have only a chance of 10% of hitting one of the unused ones (only one left), thus leveraging 90% again, to the maximum in fact.
The pool of unused ids decreases with time, thus the chance of hitting one of these gets smaller.

This leads me to my conclusion: the curve flattens.