Consider the 2-player, zero-sum game "Rock, Paper, Scissors". Each player choosesone of 3 strategies: rock, paper, or scissors. Then, both players reveal their choices.The outcome is determined as follows. If both players choose the same strategy,neither player wins or loses anything. Otherwise:• "paper covers rock": if one player chooses paper and the other chooses rock,the player who chose paper wins and is paid 1 by the other player.• "scissors cut paper": if one player chooses scissors and the other chooses paper,the player who chose scissors wins and is paid 1 by the other player."rock breaks scissors": if one player chooses rock and the other player choosesscissors, the player who chose rock wins and is paid 1 by the other player.We can write the payoff matrix for this game as follows:scissorsrock paperrock 0 -1paper 10scissors -1 1Week 10 Coursework Questions2. Suppose now we alter the game so that whenever Colin chooses "paper" the loserpays the winner 3 instead of 1:-10rock paper scissors0-30rock1paperscissors -11-10MTH5114 (Spring 2023)(b) Formulate a linear program that can be used to calculate a mixed strategyx = A(R) that maximises Rosemary's security level for this modified game.

We consider the 2-player, zero-sum game "Rock, Paper, Scissors". Each player chooses one of 3…

Answered: Consider the 2-player, zero-sum game…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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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: fip 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 $20. 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 () is this game fair? Yes ONO
To raise money for the local Veterans Affairs hospital, your friend organizes a fundraiser, inviting you to play a two-stage game where you pay $8 to play. The game works as follows: a fair 8-sided die is rolled, noting the number shown, and a spinner divided into 4 equal regions of different colors (blue, red, green, orange) is spun, noting the color. If the die shows 3 or the spinner shows orange, then you win $21. If the die shows an even number and the spinner does not show orange, 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. $ (c) Is this game fair? Yes No
Sessa, an ancient wise man, visited the king of his nation and showed him a new game. The board was 8 squares by 8 squares. Two players would be given 16 pieces each, lined up on either side of the board. The pieces moved in set ways, and the purpose of the game was to move your pieces to trap the King piece of the other player. As you have probably figured out, Sessa invented chess. His king was utterly delighted at the game - war without bloodshed! - and asked Sessa what he would like in return. In the ancient bombastic style, the King said the request could include up to half of his kingdom. (That was not meant literally.) Sessa asked for the game board to be brought before him. "Highness," he said, "I ask for a grain of rice on the first square. Tomorrow, two grains of rice on the second square. The day after, 4 grains of rice on the third square. On the fourth day, 8 grains of rice. And so on, until the board is full in two months." The king and his ministers laughed…
I have 7 friends, 2 tickets to the concert of the century, and I can’t go!I could give the tickets to friend #1 and #2, or #1 and #3, etc. How many different options are there? I've decided to make them vie for the tickets using a single elimination knock-out ping pong tournament. How many matches will I need to have?
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.
You need to borrow money for gas, so you ask your mother and your sister. You can only borrow money from one of them. Before giving you money, they each say they will make you play a game. Your sister says she wants you to roll a six-sided die. She will give you $⁢4 times the number that appears on the die. Your mother says she wants you to spin a spinner with two outcomes, blue and red, on it. She will give you $⁢5 if the spinner lands on blue and $⁢15 if the spinner lands on red. Determine the expected value of each game and decide which offer you should take. The expected value for your sister's game: $$ The expected value for your mother's game: $$ Which offer should you take?
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.

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