IIUC it's just (N/4294967296)**4

I believe the figure I should have provided is:
(1 - ((4294967295/4294967296) ** N)) ** 4

And if that's not right, I give up.

Update: The logic is simple. (Danger, Will Robinson ;-)
If you're picking numbers at random in the range (1 .. 4294967296), then the probability that the N+1th pick has already come up is:
1 minus the probability that it has *not* already come up
and the probability that it has *not* already come up is (4294967295/4294967296) ** N

So that gives us the
1 - ((4294967295/4294967296) ** N)

But because we're looking for the case where all *4* numbers have already come up, that probability needs to be raised to the 4th power ... which yields the final figure.

Cheers,
Rob