I had never taught Lilly "duck duck goose." We sing a whole lot of songs, play lots of games, find lots of creative ways to fill our time; but the only "circle" game we play is "ring around the rosy."
I think they must be playing "duck duck goose" regularly at school though, as Lilly has been coming home for the past week or two begging to play it with us. The first time I was shocked that she knew exactly how to play it - she set me and Jon on the carpet, with her monkey and a baby in between us, and started patting our heads as she walked around the circle: "Duck, duck, duck, duck, GOOSE!" Then she would pick up the monkey and have him chase her around the circle as she shouted: "Gemegemegemegemegeme!" ("Get me get me get me"... but really fast.)
My mom said she's played it with Lilly in the past, so she's learned it there, but she definitely has perfected it at school as she's been obsessed with playing it all the time now. And it's so cute as we run around chasing each other, laughing and smiling. And it's a game she's definitely good at.
Yesterday when she came home from school, I showed her a bag of old "My Little Pony's" that were handed down from her cousin. It was her first time really playing with them, and she was excited. She pulled each one out of the bag, and named it. Their names were, in order: "Mom, Mom, Mommy, Mommy, Lilly, Daddy, Lilly, Lilly, and Mommy." She lined them all up as she told them their names. And then she moved the line of ponies into a circle. And she took one from the end and said "Duck, duck..." and started the ponies with playing "duck duck goose." And when the "pony" finally said "goose," she had the two ponies chase each other around the "circle" and she shouted "gemegemegemegemegeme!" Love it.