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Repeating Dice
You roll a single die. For each roll, you are paid the face value. If a roll gives 1, 2 or 3, you can roll the die again. Once you get 4, 5 or 6, the game stops. What is the expected payoff of this game?
Solution
E[X] is the expected payoff of this game. Then we have
(1) 
(2) 
(3) 
(4) 
(5) 
(6) 
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