Rock paper scissors is an intransitive hand game, usually played between two people, in which each player simultaneously forms one of three shapes with an outstretched hand. These shapes are “rock” (a closed fist), “paper” (a flat hand), and “scissors” (a fist with the index finger and middle finger extended, forming a V). It has three possible outcomes: a draw, a win or a loss. A player who decides to play rock will beat another player who has chosen scissors (“rock crushes scissors”) but will lose to one who has played paper (“paper covers rock”); a play of paper will lose to a play of scissors (“scissors cuts paper”). If both players choose the same shape, the game is tied and is usually replayed to break the tie. Two players A and B play rock-paper-scissors continuously until player A wins 2 consecutive games. Suppose each player is equally likely to use each hand-sign in every game. What is the expected number of games they will play?