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Problem 8. You play the following game with a friend. You each have a fair six sided die. Your friend rolls the die. You then roll the die at most two times. When you stop rolling, if you rolled a number higher than your friend's roll on your final roll, then you earn in dollars the difference between the die rolls. When you stop rolling, if you rolled a number lower than your friend's roll on your final roll, then you pay your friend in dollars the difference between the die rolls. When you stop rolling, if you rolled the same number that your friend rolled, then neither of you pay the other. What is the expected amount you earn per game if you optimally play a large number of games?

Problem 8. You play the following game with a friend. You each have a fair six sided die. Your friend rolls the die. You then roll the die at most two times. When you stop rolling, if you rolled a number higher than your friend's roll on your final roll, then you earn in dollars the difference between the die rolls. When you stop rolling, if you rolled a number lower than your friend's roll on your final roll, then you pay your friend in dollars the difference between the die rolls. When you stop rolling, if you rolled the same number that your friend rolled, then neither of you pay the other. What is the expected amount you earn per game if you optimally play a large number of games?

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Problem 8. You play the following game with a friend. You each have a fair six sided die. Your friend rolls the die. You then roll the die at most two times. When you stop rolling, if you rolled a number higher than your friend's roll on your final roll, then you earn in dollars the difference between the die rolls. When you stop rolling, if you rolled a number lower than your friend's roll on your final roll, then you pay your friend in dollars the difference between the die rolls. When you stop rolling, if you rolled the same number that your friend rolled, then neither of you pay the other. What is the expected amount you earn per game if you optimally play a large number of games?
Transcribed Image Text:Problem 8. You play the following game with a friend. You each have a fair six sided die. Your friend rolls the die. You then roll the die at most two times. When you stop rolling, if you rolled a number higher than your friend's roll on your final roll, then you earn in dollars the difference between the die rolls. When you stop rolling, if you rolled a number lower than your friend's roll on your final roll, then you pay your friend in dollars the difference between the die rolls. When you stop rolling, if you rolled the same number that your friend rolled, then neither of you pay the other. What is the expected amount you earn per game if you optimally play a large number of games?
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