There's 12 random numbers, and I assume banks reject some numbers based on obviousness (e.g. all 0, all 1s, 1234, all 3 groups are identical etc.) so I'd assume there's actually less probability space than what we'd expect.
Sorry I think I'm missing it, does that page explain somewhere how the 12 digits that are not set by the MII/IIN and check digit rules are not random ?
It says the first six digits are the IIN (and the first one of those is the MII).
So if you have fourteen digits, one of which is a check digit and up to six of which are non-random, that leaves only seven truly random digits per issuer, i.e. a pool of 10'000'000 (10^7) numbers rather than the 1'000'000'000'000 (10^12) possible numbers claimed elsewhere.
Of course the actual pool is different as the number of fixed digits seems to vary per issuer and for some it seems to be only one.
Even if it's still a pretty huge space.