[gaming_mouse]

I just realized, you could also solve this using inclusion exlusion, solving P(A or B or C or D) where:

A= the chance that rank "a" of hearts is next to a rank "b"
B= "" of clubs ""
...etc

Getting an exact answer would still be a decent of amount work, but doing the first two terms would not be, and that would give you a pretty good approximation. More importantly, it would give you an exact bound on the error of the approx.

gm