Possible Duplicate:
If a player is 50% as good as I am at a game, how many games will it be before she finally wins one game?
Can anyone help me solve the following problem:
Player A and Player B are playing a game with multiple rounds. The game stops once one of them wins $10$ rounds and is declared the winner. Player A's chances of winning in each round are $\frac13$. What are Player A's chances of winning the game?
Thank you!