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 1 X, two fingers with probability , and three fingers with probability , and three fingers with probability , two fingers with probability Player B should show one finger 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 1 X, two fingers with probability , and three fingers with probability , and three fingers with probability , two fingers with probability Player B should show one finger with probability Find the expected value of the game. The expected outcome is the player A will win points per round, on average.
A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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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 1
two fingers with probability
Player B should show one finger with probability
Find the expected value of the game.
The expected outcome is the player A will win
I
two fingers with probability
points per round, on average.
I
and three fingers with probability
and three fingers with probability](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5bca9fbe-c7b8-42a8-9abb-1ab27e9c4208%2Fccdb30df-4315-48bb-a414-894ce17c2626%2Fyp72dv_processed.png&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 1
two fingers with probability
Player B should show one finger with probability
Find the expected value of the game.
The expected outcome is the player A will win
I
two fingers with probability
points per round, on average.
I
and three fingers with probability
and three fingers with probability
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