Dynamic programming algorithm? World series game problem

There are two teams A and B playing against each other to see who will win n games first. A and B are equally competent. Therefore, each team has a 50% chance of winning any particular game. Suppose they have already played x + y games, of which A has won x and B has won y games, respectively. Give an algorithm to compute the probability that A will go on to win the match. What's the worst-case time complexity of your algorithm? For instance, if x = n - 1 and y = n - 3 then the probability that A will win the match is 7/8, since it must win any of the next three games