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