Cool math problem for those that like such things

[maustin]

So, I was out to dinner with sunshine__girl, browascension, and lightling. We were going to play a game and we decided to play paper-scissors-rock to see who would go first. Instead of pairing off, we decided to keep playing until it was unambiguous (i.e. if two people did scissors, and two did rocks, the two scissors would be eliminated, but if there were one of each we'd all go again).

The math question that this prompted is: given N people, what is the average number of rounds before the game terminates?