Suppose two teams play a series of games, each producing a winner and a loser, until one team has won two more games than the other. Let Y be the total number of games played. Assume each team has a chance of 0.5 to win each game, independent of results of the previous games. Find the probability distribution of Y. 3. The attempt at a solution At first I thought I'd say that given that team A has had X games and team B has Z games, then Y=X+Z, and since it takes two more games for the winner to get, then Z=X+2, so Y=2x+2. Probability function would be then P(Y<=y)=P(Y<=2x+2) but I am not sure where to go from here...Also, was thinking that it may be a binomial, with (Y choose 2x+2)(0.5)^(2x+2)(0.5)^y where x=1,2,3....y. Any input is appreciated!