We didn’t play this one. Our version was “one potato, two potato …” All of these were elimination rounds to some subsequent game of tag, I think and the words varied depending on where you were born and raised. New York had a particular set of chants and games, many of which included Dutch words missing elsewhere because the Dutch preceded the English in settling the region … and they left some of their language behind.
My cousin was born and raised in northern Virginia, right outside of Washington D.C. I was always surprised at the differences in words between us. Simple stuff, lots of the time. I called it “potsy,” and she called it “hopscotch.” I sat on the couch. She lounged on the sofa. We ate supper. She sat down for dinner. It was the subject of some humor and teasing as the years rolled along.
So this game — duck, duck, goose — is not a New York game, or at least, not a Queens, New York game. I don’t know if it is a New England game, either. But Wikipedia says it is universal, which means it must be true. Of course!