(1 point) Consider the following game of chance based on the spinner below: Each spin costs...
(1 point) Consider the following game of chance based on the spinner below: Each spin costs $2. If the spinner lands on the player wins a dime, if the spinner stops on A the player wins $8 otherwise the player wins nothing. Calculate the players expected winnings. Express your answer to at least three decimal places in dollar form.. Answer: $ 4/11 3/11 1/11 3/11
2. A game of chance costs $5 to play and consists of rolling a five fair dice. If at least four of the dice shows a number (strictly) greater than 2 then the player wins $10. (a) What is the expected net winnings from one game? (b) Suppose that a gambler plans to keep playing this game until he has lost a total of four games, what is his expected net loss or net winnings under this strategy?
Consider the following game: We spin the spinner. If the outcome is favorable for E, then we win 1 unit. If the outcome is not favorable for E, then we neither win nor lose anything. Compute the expected value, E.V., for this game and compare it to P(E), which is 60%. You should discover a coincidence that holds for this kind of game, but which is not true for every game.
Consider the following game. You choose a color on the spinning wheel to the right and pay a price of $3 to spin the wheel. If your color comes up, you get $3 back plus $3 additionally. Otherwise, you get nothing. a. What is the expected financial outcome from this game (in dollar amount)? nothing dollars. (Round up to 2 digits after the decimal point.) b. What price of the game would ensure that the expected financial outcome is positive?...
Chaps 1. Winnings and Losing. Suppose that a person wins a game of chance with probability 0.40. and loses otherwise. If he wins, he earns 5 dollars, and if he loses, then he loses 4 dollars. (a.) What is his expected gain or loss? boeqabat om llo onodg d 1d S a a(b.) What is the variance of his gain or loss? (c.) Find const ants a, b such that if X 0 when he loses and X = 1...
A game of chance offers the following odds and payoffs. Each play of the game costs $200, so the net profit per play is the payoff less $200. Probability 0.30 0.60 0.10 Payoff $600 200 Net Profit $400 0 -200 a-1. What is the expected cash payoff? (Round your answer to the nearest whole dollar amount.) a-2. What is the expected rate of return? (Enter your answer as a percent rounded to the nearest whole number.) b-1. What is the...
1. NIM game. This is a different version or easier version of NIM game Consider a pile of 5 matchsticks. Two people take turns removing 1 or 2 sticks each time from this pile. Suppose both players play smartly (nobody plays a fool move trying to let the opponent wins. But there is only one winner anyway) a)If the person getting the last stick wins, will the first player win? Why? Show the steps the first and second player will...
Question 1 (1 polnt) The following Information applies to questions 1 through 5. Consider a tennis match with 3 sets. The first player to win 2 sets wins the match. Let the probability of Player 1 winning a set be 0.7. The winner of the match gets $100, and the loser get nothing. Hint: draw the game tree will help answer the following questions. 1. This game is an example of a Simultaneous game in pure strategies Recursive Dynamic Progranm...
Question 1 (1 polnt) The following Information applies to questions 1 through 5. Consider a tennis match with 3 sets. The first player to win 2 sets wins the match. Let the probability of Player 1 winning a set be 0.7. The winner of the match gets $100, and the loser get nothing. Hint: draw the game tree will help answer the following questions. 1. This game is an example of a Simultaneous game in pure strategies Recursive Dynamic Progranm...
1. Consider the following normal form game: 112 LC R T10 102 12 0 13 M 12 25 5 0 0 В|13 010 0111 (a) (Level A) First suppose this game is played only once. What are the pure strategy Nash equilibria? b) (Level B) Now suppose this game is played twice. Players observe the actions chosen in the first period prior to the second period. Each player's total payoff is the sum of his/her payoff in the two periods....