Question
Suppose $0 < p < 1$. Alice and Bob play game. The game consists of $3$ points. For the first point of each game, Alice has probability $p$ of winning, while Bob has probability $1-p$ of winning. For the other two points of the game, the winner of the previous round has probability $p$ of winning, while the loser has probability $1-p$ of winning. A winner is declared when someone wins two consecutive points. If neither player wins two consecutive points, the entire game replayed under the same rules until a winner is declared. Find the probability that Bob wins when $p = 1/3$.