Consider the following version of the game of craps: The player rolls two dice. If the sum on the first roll is 7 or 11, the player wins the game immediately. If the sum on the first roll is 2, 3, or 12, the player loses the game immediately. However, if the sum on the first roll is 4, 5, 6, 8, 9, or 10, then the two dice are rolled again and again until the sum is either 7 or 11 or the original value. If the original value is obtained a second time before either 7 or 11 is obtained, then the player wins. If either 7 or 11 is obtained before the original value is obtained a second time, then the player loses. Determine the probability that the player will win this game.
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