$A$ and $B$ play a series of games. Each game is independently won by $A$ with probability $p$ and by $B$ with probability $1−p$. They stop when the total number of wins of one of the players is two greater than that of the other player. The player with the greater number of total wins is declared the winner of the series.
Q:Find the probability that A is the winner of the series.
Could anyone please help me out with this question and let me know how to approach it? BTW, I've already seen the answer from the book, but I don't know how to get it. Thanks.