Reversing Polarity -- Voodoo or Easy Tweak?

In a recent thread I noticed a comment about reversing polarity of speaker wires on both speakers which sparked one of my earliest audiophile memories.

On the liner or cover notes of Dave Grusin: Discovered Again on direct to disc vinyl, circa 1977, it too recommended reversing the polarity on BOTH speakers, for best sound.

Although my first system was a 25 WPC Technics receiver with Infinity Qa's and lousy speaker wire, I still remember getting very enthusiastic about reversing the polarity and wondering if it did anything.

Can anyone explain this and/or recommend if this is even worth the experiment?