Question

Two players play each other in a pool tournament of "Solids and Stripes". The first player 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) one-half of the balls are solids and the other half are stripes, 2) the two players have the same skill: each with a 0.5 probability of winning, 3) there are no ties, and 4) the tournament is concluded once a player has won two games. What is the expected number of games played in the tournament?

Answer 1

Let us say two players A and B are playing the game. Both of them have same chances of winning a game = 0.5

P( A wins ) = P( B wins) = 0.5

We consider 2 cases- a tournament with 2 games and a tournament with 3 games (in this case we will definitely have a winner)

P(tournament lasts 2 games) = (a particular player wins both the games) = 2 x 0.5 x 0.5 = 0.5

P(tournament lasts 3 games) = (a particular player wins 1 of first 2 games and 3rd game) = 2 x (2x0.5x0.5) x 0.5 = 0.5

Expected number of games = 2 x 0.5 + 3 x 0.5 = 1.5