1. (10 marks) (Dynamic Programming) Consider the following game. You are given a fair six sided die, with faces {1,2,3,4,5,6}. You can roll the die, and obtain a payoff equal to the value shown on the die, or you can choose to roll again. Note that if you choose to roll again, you can only get the new payoff or roll again. You can roll the die up to four times. What is your expected gain, assuming you follow the optimal strategy? Note: Do not write Matlab code to solve this problem, this is a pencil and paper exercise.