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.)

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.)

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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Morra is a hand game that dates back thousands of years to ancient Roman and Greek times. Two people called Even (E) and Odd (O) simultaneously reveal a number of fingers. Each one can choose the number of fingers (or more simply, they want to show even or odd number of fingers). If the total number of fingers is even, E wins two dollar from O: Ifthe total number of fingers is odd, O wins one dollar from E. For example, if E chooses three fingers andO chooses two fingers, then O wins one dollars from E. 1. Write down the payoff matrix of the game. 2. What is the optimal strategy for E and O? Formulate the problem as a LP and solve for the optimal strategies by the Simplex Method.
Introduction: Here's the game: there are two boxes with four balls each. To play, you put on a blindfold and then pick one ball at random from each box. There are two red, one blue and one green ball in the box on the left. There are two blue, one red and one green ball in the box on the right. Payouts: • So if the balls are different colors, • S0.50 if they are both red, • Sl if they are both blue, and • $16 if they are both green. Question: If the game costs $1 to play, would you expect to gain or lose money on average? And how much? In your solution, you must show: • How you compute the probability that payout is $0. • How you compute the probability that payout is $0.50. • How you compute the probability that payout is S1. • How you compute the probability that payout is $16. Summarize the data into a probability table. • Compute the expected value. Remember to account for the $1 you pay to play the game. • Your conclusion.
Can you do question 2? I didn't get it. Thanks
Chang is playing a game in which he spins a spinner with 6 equal-sized slices numbered 1 through 6. The spinner stops on a numbered slice at random. This game is this: Chang spins the spinner once. He wins $1 if the spinner stops on the number 1, $3 if the spinner stops on the number 2, $5 if the spinner stops on the number 3, and $7 if the spinner stops on the number 4. He loses $1.25 if the spinner stops on 5 or 6. (a) Find the expected value of playing the game.___ dollars (b) What can Chang expect in the long run, after playing the game many times?
at a casino, you throw a fair 4 sided dice whose sides are labeled 1, 2, 3 and 4. If you land on a one, you get thirty dollars. If you land on a two, you get ten dollars. If you land on either a three or four, you owe the casino eight dollars. If you repeatedly play this game, what would your "winnings" be on average, in dollars?
Given question is A basket of fruit is being assembled from apples, bananas, and oranges. What is the fewest number of fruit pieces that should be placed in the basket to ensure that there are at least 8 apples, 6 bananas, or 9 oranges?Your answer: The question is asking you to prepare for a worst-case scenario, not a best-case scenario. Imagine a game where you're not the one in charge of choosing the fruits - your opponent is in charge, and they don't want you to win. The opponent can get away with choosing 20 fruits (7 apples, 5 bananas, and 8 oranges) before the 21st fruit finally forces your condition to be satisfied. Therefore total required the fewest number of fruit pieces =(7+5+8)+1=21.My question:Why did you add 7+5+8 , instead of 8 apples, 6 bananas, or 9 oranges? The given is 8+6+9 not 7+5+8. Also why did you add +1? Here, you add 1: (7+5+8) +1 =21. Also, Is it pigeonhole formula? The pigeonhole is ⌈n/m⌉ not like this as far as i know. Thank you
A certain game involves tossing 3 fair coins, and it pays 23¢ for 3 heads, 10¢ for 2 heads, and 2¢ for 1 head. Is 10¢ a fair price to pay to play this game? That is, does the 10¢ cost to play make the game fair? The 10¢ cost to play a fair price to pay because the expected winnings are (Type an integer or a fraction. Simplify your answer.)
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A game consists of spinning a wheel that is divided into 8 differently colored sectors (red, blue, yellow, violet, orange, green, black, and white). The amount to pay to play is P12. The prizes for each color are as follows: Red, Blue, P5 Yellow 31-35. Is the game fair? Show your computation to support your claim. P15 Purple, Orange. Green White Black P20 No prize
In roulette, the numbers from 1 to 36 are evenly distributed between red and black. A player who bets $1 on black wins $1 (and gets the $1 bet back) if the ball comes to rest on black; otherwise (if the ball lands on red, 0, or 00), the $1 bet is lost. One option in a roulette game is to bet$ 3on red. If the ball lands on red, you get to keep the $ 3you paid to play the game, and you are awarded$4.If the ball lands elsewhere, you are awarded nothing, and the$ 3 that you bet is collected. What is the expected value of the game?
A bag contains 5 gold marbles, 9 silver marbles, and 21 black marbles. The rules of the game are as follows: You randomly select one marble from the bag. If it is gold, you win $4, if it is silver, you win $2. If it costs $1 to play, what is your expected profit or loss if you play this game?
Hangman is a paper and pencil guessing game for two players. One player thinks of a word, phrase or sentence and the other tries to guess it by suggesting letters within a certain number of guesses. The word to guess is represented by a row of dashes, representing each letter of the word. If the guessing player suggests a letter which occurs in the word, the other player writes it in all its correct positions. If the suggested letter does not occur in the word, the dashes remain as they were and one guess of the player is wasted. The first player can choose as long or as short a word as they wish. The second player is allowed seven guesses. a) If the word length is from 4 to 8 and any letter is allowed except the letter 'X' and a maximum of two vowels are allowed, then how many words can be formed? b) If it is known that only one vowel comes in the word and that if 'e' is that vowel then it comes as 'ee' and the word length is exactly 6, how many words can be formed? c) Player B…