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.
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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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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