Solved: A fair 20-sided die is rolled repeatedly, until a gambler decides to stop. The

Chapter 9, Problem 5

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A fair 20-sided die is rolled repeatedly, until a gambler decides to stop. The gambler pays $1 per roll, and receives the amount shown on the die when the gambler stops (e.g., if the die is rolled 7 times and the gambler decides to stop then, with an 18 as the value of the last roll, then the net payo is $18 $7 = $11). Suppose the gambler uses the following strategy: keep rolling until a value of m or greater is obtained, and then stop (where m is a fixed integer between 1 and 20). (a) What is the expected net payo? Hint: The average of consecutive integers a, a + 1,...,a + n is the same as the average of the first and last of these. See the math appendix for more information about series. (b) Use R or other software to find the optimal value of m.