In the dice game called craps^ the player tosses two (fair) dice simultaneously. If the sum of the two numbers that show up is equal to 7 or 11, the player wins. If the sum is equal to 2, 3, or 12, he loses. When the sum is a number x different from the preceding numbers, the player must toss the two dice again until he gets a sum equal to x or 7. If x is obtained first, the player wins; otherwise, he loses. What is the probability that the player wins?