Count me as another one that didn't know about sitting in the middle. We played it the way LadyBears describes it, only growing up in Minnesota, we called it "Duck, Duck, Grey Duck".
It was very creative - as you tapped the other kids on the head going around the circle, you'd say things like "purple duck, blue duck, grrr...een duck, pink duck, spotted duck, silly duck, ggg...oofy duck, GREY DUCK! And then take off running. With a little luck, you'd have distracted the Grey Duck kid with all the other names and get a good head start on getting back to your seat.