Question

You are going to roll four twenty-sided dice. If the rolls total to 20 or less, roll two more twenty-sided dice and add that to the total. For instance, if the total of my four die rolls is 32, then that is the score of the game. If the total is 17, then I roll two more dice and add that to the total. If these two bonus dice total 20, then the score of that game is 37. Of ten thousand games, what is the average score?