Ah yes, I did misunderstand, apologies. Based on the approximation listed on wikipedia of 0.5sqrt(.25-252!*ln(.5)) it is about 10^34 to have a better than 50-50 chance of two shuffled decks landing on the same permutation. The original source of that approximation is at: A Generalized Birthday Problem on JSTOR
Though, it might be useful to note that if you have your own shuffled deck, the probability that any other shuffled deck so far matching your particular deck is actually lower than any two randomly chosen shufflings having already occurred. The approximation for that seems to break down for a very large sample space such as 52!. I went from p(d) = 1-(d-1/d)^n => -.5=-(d-1/d)^n => ln(.5)=nln(d-1/d) => n=ln(.5)/ln(d-1/d)
