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I'd better present my logic to see if anyone disagrees.
(n*(n-1))/(2*52!) = P; solve for P, where P = probability of 2 or more matching shuffled decks in n shuffles.
(n-1)^2 < n*(n-1) < n^2, so
(n-1)^2/(2*52!) < n*(n-1)/(2*52!) < n^2/(2*52!),
so the first equation can be simplified (for large values of n) as
n^2 ~= P*2*52!
n = square_root(P*2*52!)
If P = 0.5 (50%), n = 8.98e33
If P = 0.1 (10%), n = 4.0e33
If P = 0.01 (1%), n = 1.27e33
I just noticed a flaw in this logic. Can you see it?
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