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.

Name: A three-finger Morra game is a game in which two players simultaneous
Uploaded: 2024-03-20T07:07:26.000Z
Channel: Bartleby
Description: 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 ona predetermined set of rules. Here is an interesting example: If the numbers of fingers shown by A and B dif

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Q: 2. Three friends pooled their money to purchase a new game system that costs $196. Friend #2…

Q: You need to borrow money for gas, so you ask your mother and your sister. You can only borrow money…

A: Given Information: Your sister says she wants you to spin a spinner with six outcomes, numbered 1…

Q: Suppose you play a game with a (fair) six sided die, with sides 1, 2, 3, 4, 5, 6. The first time you…

A: The probability of winning on the first roll is 1/6 since you need to roll a 6 to set it as the mark…

Q: Players A and B take turns taking one or two pennies from a pile of pennies. The player to takes the…

Q: Suppose a game requires a player to roll three 6-sided number cubes. In order to determine if the…

A: Given that: Sample size, n=200 Observed frequencies for each category: 70, 80, 40, 10 Expected…

Q: A casino offers the following game, which costs 10 dollars to play. Two cards are selected at…

A: Considering the provided information, if both of the cards are kings, then you win = 220+10-10 =…

Q: A bag contains an unknown number of red and black marbles, but you do know that there are more black…

A: X1,X2,..,XNare random samples with same mean μ and standard deviation σ . The sampling distribution…

Q: (a) If you have a chance of getting each question right, what is the distribution of Q: the total…

Q: This problem is courtesy of Mr. Lange’s friend Paul. The Queen of Hearts is a card game played at a…

A: Solution: From the given information, Mr. Lange wishes to purchase 400 of the 1600 tickets sold.

Q: Imagine that Ehsaan and TJ play a game, in which Ehsaan flips 2 fair coins, and TJ flips 3 fair…

A: Sample space foe 2 fair coins and 3 fair coins are obained

Q: Traditionally, the game of Rock, Paper, Scissors is played with two people. Each of the two people,…

A: **Step 1: Understand the Outcomes**Each player can choose among three options (rock, paper,…

Q: Suppose a friend of yours decides to play a game. He shows you three cards, one is white on both…

Q: You pay $11 to play a game where you draw a numbered ball from a bucket containing 12 identical…

A: Here the given information is ,You pay $11 to play a game where you draw a numbered ball from a…

Q: Hangman is a paper and pencil guessing game for two players. One player thinks of a word, phrase or…

A: a)Only seven guesses are allowed for the player, Hence the word length can be from 4,5,6,7. If the…

Q: There are four medals (Gold, Silver, Bronze and Wood) on a table, but they are all wrapped with dark…

A: Given that, There are four medals (Gold, Silver, Bronze and Wood) on a table, but they are all…

Q: You and two friends (Adam and Alana) will only play a game if it is fair for all three of you. The…

A: Given that two dice are thrown. We have to solve this using probability.

Q: You are playing the new Lemon Game at Vegas. There are 3 windows in the slot machine. Window 1…

Q: The game Capture is played by two players, First and Second, who take turns to move towards one…

A: The generalized problem involves two players, First and Second, positioned at opposite ends of a…

Q: You need to borrow money for gas, so you ask your mother and your sister. You can only borrow money…

Q: In a bridge game, a hand consists of 13 cards taken from a deck of 52 cards. (i) A hand is balanced…

A: Total number of cards in the deck = 52 Number of suits = 4 Number of cards for each suit = 13

Q: You are using cash to pay a $20 parking ticket. In your wallet you have one $5-dollar bill, two…

A: Given that there are 1- 5$ bill 2-10$ bills 3-20$ bills

Q: A casino is offering a gamble to customers. A single, fair six-sided die is rolled. If a player…

A: Given, A single, fair six-sided die is rolled. If a player rolls 1,2, or 3, the payoff is the number…

Q: At a back-to-school party, one of your friends lets you play a two-stage game where you pay $3 to…

A: Given Information: You pay $3 to play the game. A fair coin is flipped, noting the side shown and a…

Q: Andy and Marjorie are playing tennis. The points system is as follows: there are two conditions for…

A: Given information: The points system for the tennis game played between Andy and Marjorie is as…

Topic Video

Question

100%

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.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step 5

Step 6

Step 7

Trending now

This is a popular solution!

Step by step

Solved in 7 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Optimization$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.

Similar questions

At a county fair, you pay $2 to play the following game: You are given a fair coin, and two bags standin front of you, labelled Bag A and Bag B. You flip a coin: If your coin lands Heads, you pick a ballfrom Bag A. If your coin lands tails, you pick a ball from Bag B. Each ball has a dollar value written onit, and you win the number of dollars shown on the ball. • Bag A contains four (4) balls in total: Three (3) balls show $1, and one (1) ball shows $5.• Bag B contains three (3) balls in total: Two (2) balls show $2, and one (1) ball shows $3.You WIN money if you leave with more money than you started with. You LOSE money if you leavewith less money than you started with. You BREAK EVEN if you leave with the same money that youstarted with.Let H denote the event that you flip heads, T denote the event that you flip tails, W the event that youwin, and L the event that you lose.(i) You pay to play exactly one game. What is the probability that you WIN given thatyou flipped a Heads?(ii)…
Zara and Sue play the following game. Each of them roll a fair six-sided die once. If Sue’s number is greater than or equal to Zara’s number, she wins the game. But if Sue rolled a number smaller than Zara’s number, then Zara rolls the die again. If Zara’s second roll gives a number that is less than or equal to Sue’s number, the game ends with a draw. If Zara’s second roll gives a number larger than Sue’s number, Zara wins the game. Find the probability that Zara wins the game and the probability that Sue wins the game. Note: Sue only rolls a die once. The second roll, if the game goes up to that point, is made only by Zara.
In a game, two coins are tossed. If either of the coins comes up heads, you have won a prize. To claim the prize, you must point to one of your coins that is a head and say 'look, that coin's a head, I've won'. You watch Fred play the game. He tosses the two coins, and he points to a coin and says 'look, that coin's a head, I've won'. What is the probability that the other coin is a head?
At a back-to-school party, one of your friends lets you play a two-stage game where you pay $3 to play. The game works as follows: flip a fair coin, noting the side showing, and roll a fair standard 4-sided die (numbered 1–4), noting the number showing. If the die shows a 3 and the coin shows tails, then you win $22. If the coin shows heads and the die shows an even number, then you win $9. Otherwise, you do not win anything. Let X be your net winnings. (a) Create a probability distribution for X. Enter the possible values of X in ascending order from left to right. All probabilities should be exact. X P(X) (b) Compute your expected net winnings for the game. Round your answer to the nearest cent.
Answer the following question. In a recent competition, each of three teams played each other team once. The results are given in the table below. What was the score of the A vs. C game? Give A's goals first. Team A B C Wins 1 1 0 Losses Ties 0 1 0 1 2 0 Goals For Goals Against 6 3 2 4 2 5 (Remember: Your solution must show appropriate work or reasoning.)
A favorite casino game of dice “craps” is played in the following manner: A player starts by rolling a pair of balanced dice. If the roll (the sum of two numbers showing on the dice) results in a 7 or 11, the player wins. If the roll results in a 2 or 3 (called “craps”) the player loses. For any other roll outcome, the player continues to throw the dice until the original roll outcome recurs (in which case the player wins) or until a 7 occurs (in which case the player loses). When answering the following questions, you can use this outcome chart for the roll of two dice: Provide the probability answers in fraction and in decimal forms rounded to 4 digits. A. List the possible outcomes (sample space) for winning on the first roll of the dice. B. What is the probability that a player wins the game on the first roll of the dice? C. List the possible outcomes (sample space) for losing on the first roll of the dice. D. What is the probability that a player loses the game on the…
2. The college's soccer team will play II games next fall. Each game can result in one of three outcomes: a win, a loss, or a tie. Find the total possible number of outcomes for the season record.
A father and his three children decide to hold a vote to select an after dinner activity. They will either see a play or a movie. If the majority of the family agrees on a preferred activity, then they will do that activity. If two family members vote to see a play and the other two family members vote to watch a movie, then (since the father will pay for the activity), the father's vote will be used to break the tie. (a) How many winning coalitions are there in this situation? (b) Find one of the children's Banzhaf power index.