Consider the following game: I will roll a single die no more than three times. You can stop me immediately after the first roll, or immediately after the second roll, or you can wait for the third roll. Your payoff is equal to the number of dots on the single upturned face on the dice when you decide to stop the game (for example, if you choose to stop after the first roll, then your payoff is equal to the number of dots on the upturned face of the die on the first roll). What is your optimal playing strategy? What is the expected payoff of this optimal strategy? Provide an analytic solution