There are guests at a party and they are making groups for a game. To do this they each write their name on a piece of paper and put it into a hat. One by one, each guest picks a name from the hat. Each guest will be a part of a group with the guest they pulled the name out of from the hat. If a guest pulls out their own name, they are in a group all by themselves. If Guest A pulls out Guest B's name, Guest B pulls out Guest C's name, and Guest C pulls out Guest A's name, they are all a part of the same closed group and no one else will be able to join them. What is the average size of a group? Round your answer to the nearest tenth.