> Your point is good, but there must be something wrong with your math.

No, with my eyes.

> Christian's point is (I assume) that with a number space of 2^36, when you
> select 2^19 random values you start running into a reasonable risk of two of
> those random values being the same.
> 
> Your equation (N^2/2^18) doesn't seem to take into account the 2^36 number,

It doesn't.  My eye seized upon the wrong number.  2^19 should have
been 2^38 throughout.  And then making private-space connections to
16 sites gives you a <= one-in-500-million chance of collision, and
connecting to 256 sites gives <= one-in-2-million.

> Am I not getting something?

Yes, presbyopia.  Lucky you.
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