FWIW, doing Google searches that exclude 3 of these 4 possibilities at a time:
blind man's bluff = 180,000
blind man's buff = 29,800
blindman's buff = 15,800
blindman's bluff = 12,200

Similarly:
billy goats gruff = 173,000
billy goats guff = 57
billygoats gruff = 2,320
billygoats guff = 0

I have no idea what that all means... I just have not enough to do. (^_^)