The game of Rock-Paper Scissors between two teams

We use a coin or the game of Rock-Paper Scissors before the main game to determine which team will begin first. And we can use effectively the game of Rock-Paper Scissors to choose one of the two or one of many. Two teams may consist of different number of players. In this paper we consider a rule that after each game if the winners consist of only one team then the team wins or the winners continue the next game till the winning team is decided. According to this rule we find the means and variances of the total number of games till the winning team is decided.