Petals Around the Rose: Fraternity Register

I have to admit that this didn't make sense to me at all. I felt like I was playing a game without any rules. Roll the dice and guess the number?

I couldn't figure it out until I read someone else's web page about this "game." In the comments section there, somebody had called it "Polar Bears Around the Ice Hole." Finally it clicked. "Petals Around the Rose" seems too misleading of a name. Oh well.