SJS: We also played that game! It was lots of fun! The story we did with Right and Left was the Chanukah story, written in an adorable script that featured the words right and left again and again, in different context each time!
We had e/o write their name and birthday (Hebrew) on a paper, and folded up the papers. Then we passed those around, and at the end, each person was left with a paper with s/o birthday. When the time of year came, you had to remember the birthday and do/give/send s/t special. It worked! Many of us got cute cards, cakes…etc.