> Unless I'm mistaken, in the 5e6-from-1e9 sampling, the probability
> that a sampling contains exactly one number from a given 200-numbers
> interval is 200.0*(1/200)*(199.0/200)**199 = 0.3688. The probability
> that this happens for 20 such 200-numbers intervals is
> 0.3688**20 = 2.1e-09.

I think you are wrong. A rough estimates of this probability gives me
1e-2171438.
Actually, it should be a bit smaller, but at least the order of
magnitude of the order of magnitude is right :)
Quite impressive...

Paolo