A three-finger Morra game is a game in which two players simultaneously show one, two, or three fingers at each round. The outcome depends on a predetermined set of rules. Here is an interesting example: If the numbers of fingers shown by A and B differ by 1, then A loses one point. If they differ by more than 1, the round is a draw. If they show the same number of fingers, A wins an amount equal to the sum of the fingers shown. Determine the optimal strategy for each player. (Enter your probabilities as fractions.) Player A should show one finger with probability , two fingers with probability , and three fingers with probability Player B should show one finger with probability , two fingers with probability , and three fingers with probability Find the expected value of the game. The expected outcome is the player A will win points per round, on average.
A three-finger Morra game is a game in which two players simultaneously show one, two, or three fingers at each round. The outcome depends on a predetermined set of rules. Here is an interesting example: If the numbers of fingers shown by A and B differ by 1, then A loses one point. If they differ by more than 1, the round is a draw. If they show the same number of fingers, A wins an amount equal to the sum of the fingers shown. Determine the optimal strategy for each player. (Enter your probabilities as fractions.) Player A should show one finger with probability , two fingers with probability , and three fingers with probability Player B should show one finger with probability , two fingers with probability , and three fingers with probability Find the expected value of the game. The expected outcome is the player A will win points per round, on average.
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter12: Probability
Section12.CR: Chapter 12 Review
Problem 68CR
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![A three-finger Morra game is a game in which two players simultaneously show one, two, or three fingers at each round. The outcome depends on
a predetermined set of rules. Here is an interesting example: If the numbers of fingers shown by A and B differ by 1, then A loses one point. If they
differ by more than 1, the round is a draw. If they show the same number of fingers, A wins an amount equal to the sum of the fingers shown.
Determine the optimal strategy for each player. (Enter your probabilities as fractions.)
Player A should show one finger with probability
, two fingers with probability
and three fingers with
probability
Player B should show one finger with probability
, two fingers with probability
, and three fingers with
probability
Find the expected value of the game.
The expected outcome is the player A will win
points per round, on average.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1a81ee51-9f92-459d-87ff-587deeba4e19%2F515076ba-8e4b-4708-829b-7a9f6ac9b7b2%2Fgb7ev1t_processed.jpeg&w=3840&q=75)
Transcribed Image Text:A three-finger Morra game is a game in which two players simultaneously show one, two, or three fingers at each round. The outcome depends on
a predetermined set of rules. Here is an interesting example: If the numbers of fingers shown by A and B differ by 1, then A loses one point. If they
differ by more than 1, the round is a draw. If they show the same number of fingers, A wins an amount equal to the sum of the fingers shown.
Determine the optimal strategy for each player. (Enter your probabilities as fractions.)
Player A should show one finger with probability
, two fingers with probability
and three fingers with
probability
Player B should show one finger with probability
, two fingers with probability
, and three fingers with
probability
Find the expected value of the game.
The expected outcome is the player A will win
points per round, on average.
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