Provide Solution with working note.

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 thefirst roll, then your payoff is equal to the number of dots on the upturned face of the die on the first roll). Suppose that you would like to maximize your expected payoff from playing the game.

(a) What is your optimal playing strategy? That is, when should you decide to stop the game?

(b) What is the expected payoff of this optimal strategy? Explain your reasoning clearly. What is the Expected Value of Perfect Information (EVPI) here? To answer this question, first consider the perfect hindsight problem, where we make decisions after the uncertainty is resolved (here, the uncertainty is on the outcomes of the three die rolls).

(c) As a warm up, suppose you knew that the outcomes on the three die rolls were 2, 4 and 1 respectively. What would your decision be? That is, when you would stop? What would be your payoff? (d) Find the expected value of the perfect hindsight problem and use this to determine the EVPI.

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