oh derp
It should be 1/4 then, because the sledgehammer takes care of another one of the 8 EO cases.
EDIT: Wait no, give me a minute.
Hmm.
7/8 cases don't have solved EO. If you have a solved pair, then sledgehammer will solve one of those 7. But if you don't ever have a solved pair (R U R' insert), then you'll never get solved EO for any of those 7.
So the answer is somewhere between 1/8 and 1/4, but I think it actually depends on how you solve the various F2L cases.