Two players play each other in a pool tournament of Solids and Stripes. The first play to win two games wins the tournament.

Two players play each other in a pool tournament of "Solids and Stripes". The first play to win two games wins the tournament. In the game of Solids and Stripes, it is equally likely that a player will be assigned solid balls or striped balls. Assume that 1) 1/2 of the balls are solids and the other half are stripes. 2) the two players have the same skill and each with a 0.5 probability of winning; 3) there are no ties; 4) the tournament is concluded once a player has won two games. So, what is the expected number of games played in the tournament?