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Roll a die repeatedly until the same number comes up twice in a row. Your payout is the total of every roll you made. What is the game's expected value?

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Roll a fair die repeatedly until you roll a number greater than 4. What is the expected sum of all the rolls, including the last?You roll a die twice and are paid the higher of the two numbers if they differ, nothing if they match. What is the expected payout?One die is numbered 1-6 and another 1-4. You pick one at random and roll it twice; the first roll is a 2. What is the expected value of the second roll?

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