Could you please give a dp solution written by yourself (presucode),including the base condition and the running time.

And also pls provide the detailed explain.

Thank you

Suppose two teams, A and B, are playing a match to see who is the first to win n games (for some particular n), we can suppose that A and B are equally competent, so each has a 50% chance of winning any particular game. Suppose they have already played i +j games, of which A has won i and B has won j. Give an efficient algorithm to compute the probability that A will go on to win the match. For example, if n-1 and j = n-3 then the probability that A will win the match is 7/8, since it must win any of the next three games