You are going to play the 7-11 game, which has the following rules: You roll two dice. If the total value of the two dice is 7 or 11, you immediately win the game. If the total value is 2, 3, or 12, you immediately lose. If the total value is 4, 5, 6, 8, 9, or 10, you keep this value as a referenced point. Then, you continue rolling the dice until you obtain the same value as the referenced point then you win the game. However, if you obtain the value of 7 before the referenced point, then you lose. For example, you obtain 4 in the first time of rolling, you keep rolling the dice until you get 4 (before 7) then you win. Similarly, you obtain 4 in the first time of rolling, you keep rolling the dice but you get 7 (before 4) then you lose. What is the probability to win this game? You can solve this question either by - a simulation - in this case you have to answer one more question, i.e., on average how many times do you roll the dice for each game? (for a submission, you will need to present the code); - or treating this problem as a probability problem.

Answer the question by breaking the problem down into: assumptions, model and solution/discussion.