In a game two players $A$ and $B$ take turns in throwing a pair of fair dice starting with player $A$ and the total of scores on the two dice, in each throw, is noted. $A$ wins the game if he throws a total of $6$ before $B$ throws a total of $7$, and $B$ wins the game if he throws a total of $7$ before $A$ throws a total of $6$. The game stops as soon as either of the players wins. The probability of $A$ winning the game is: