Grew-up-in-and-around-New-York-City-area:

I've heard it both ways - "blind man's buff" and "blind man's bluff." I always assumed one was originally the "right" way, the other an innocent mispronunciation on the part of some child many years ago, maybe several hundred. The meaning wasn't altered any; ultimately the change diffused out and was incorporated into the the common parlance as totally equivalent. By now the two are interchangeable.

(Note the scrupulous avoidance of suggesting which one is "correct" ! )