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You roll a die and keep a separate running total for each face value. The game ends when any of the six totals passes 100. What is the expected sum of all rolls?

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You keep rolling a die and keep six running sums: the total of all 1s rolled, the total of all 2s, and so on up to the total of all 6s. The game ends when any of these six sums exceeds 100. What is the expected sum of all the dice rolled?

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Keep rolling a die and count how many times each face has appeared; stop when any face's count is greater than 100. What is the expected sum of all the rolls?You roll a fair 10-sided die with faces 0 to 9 again and again, adding each roll to a running total, but a 0 wipes out the total and ends the game. When should you stop?You roll a die repeatedly. An even roll is added to a sequence, a 3 or 5 wipes the sequence, and a 1 is added and ends the game. What is the expected length of the final sequence?

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