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 ________ .
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 ________ .
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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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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