Which of the following gambles has the largest objective risk? 20% chance of winning $100 and 80% chance of losing $100 50% chance of winning $10,000 and 50% chance of losing $10,000 50% chance of winning nothing and 50% chance of losing $100 50% chance of winning $100 and 50% chance of winning nothing

Which of the following gambles has the largest objective risk? 20% chance of winning $100 and 80% chance of losing $100 50% chance of winning $10,000 and 50% chance of losing $10,000 50% chance of winning nothing and 50% chance of losing $100 50% chance of winning $100 and 50% chance of winning nothing

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter11: Simulation Models

Section: Chapter Questions

Problem 44P: You now have 5000. You will toss a fair coin four times. Before each toss you can bet any amount of...

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A martingale betting strategy works as follows. You begin with a certain amount of money and repeatedly play a game in which you have a 40% chance of winning any bet. In the first game, you bet 1. From then on, every time you win a bet, you bet 1 the next time. Each time you lose, you double your previous bet. Currently you have 63. Assuming you have unlimited credit, so that you can bet more money than you have, use simulation to estimate the profit or loss you will have after playing the game 50 times.
You now have 5000. You will toss a fair coin four times. Before each toss you can bet any amount of your money (including none) on the outcome of the toss. If heads comes up, you win the amount you bet. If tails comes up, you lose the amount you bet. Your goal is to reach 15,000. It turns out that you can maximize your chance of reaching 15,000 by betting either the money you have on hand or 15,000 minus the money you have on hand, whichever is smaller. Use simulation to estimate the probability that you will reach your goal with this betting strategy.
In this version of dice blackjack, you toss a single die repeatedly and add up the sum of your dice tosses. Your goal is to come as close as possible to a total of 7 without going over. You may stop at any time. If your total is 8 or more, you lose. If your total is 7 or less, the house then tosses the die repeatedly. The house stops as soon as its total is 4 or more. If the house totals 8 or more, you win. Otherwise, the higher total wins. If there is a tie, the house wins. Consider the following strategies: Keep tossing until your total is 3 or more. Keep tossing until your total is 4 or more. Keep tossing until your total is 5 or more. Keep tossing until your total is 6 or more. Keep tossing until your total is 7 or more. For example, suppose you keep tossing until your total is 4 or more. Here are some examples of how the game might go: You toss a 2 and then a 3 and stop for total of 5. The house tosses a 3 and then a 2. You lose because a tie goes to the house. You toss a 3 and then a 6. You lose. You toss a 6 and stop. The house tosses a 3 and then a 2. You win. You toss a 3 and then a 4 for total of 7. The house tosses a 3 and then a 5. You win. Note that only 4 tosses need to be generated for the house, but more tosses might need to be generated for you, depending on your strategy. Develop a simulation and run it for at least 1000 iterations for each of the strategies listed previously. For each strategy, what are the two values so that you are 95% sure that your probability of winning is between these two values? Which of the five strategies appears to be best?
You now have 10,000, all of which is invested in a sports team. Each year there is a 60% chance that the value of the team will increase by 60% and a 40% chance that the value of the team will decrease by 60%. Estimate the mean and median value of your investment after 50 years. Explain the large difference between the estimated mean and median.
You have 5 and your opponent has 10. You flip a fair coin and if heads comes up, your opponent pays you 1. If tails comes up, you pay your opponent 1. The game is finished when one player has all the money or after 100 tosses, whichever comes first. Use simulation to estimate the probability that you end up with all the money and the probability that neither of you goes broke in 100 tosses.
The game of Chuck-a-Luck is played as follows: You pick a number between 1 and 6 and toss three dice. If your number does not appear, you lose 1. If your number appears x times, you win x. On the average, use simulation to find the average amount of money you will win or lose on each play of the game.
Anand Publishing Company received a six-chapter manuscript for a new college textbook. The editor of the college division is familiar with the manuscript and estimated a 0.6513 probability that the textbook will be successful. If successful, a profit of $950,000 will be realized. If the company decides to publish the textbook and it is unsuccessful, a loss of $150,000 will occur. Before making the decision to accept or reject the manuscript, the editor is considering sending the manuscript out for review. A review process provides either a favorable (F) or an unfavorable (U) evaluation of the manuscript. Past experience with the review process suggests probabilities P(F) = 0.7 and P(U) = 0.3 apply. Let s₁ = the textbook is successful, and $₂ = the textbook is unsuccessful. The editor's initial probabilities of s₁ and s₂ will be revised based on whether the review is favorable or unfavorable. The revised probabilities are as follows: P(S₁IF): = 0.75 P(S₂IF): = 0.25 P(S₁IU) = 0.421…
A NY Times best-selling author wants to write a new book as either volume II of her earlier successful book or an autobiography. She believes that by writing the volume II, given her previous success, she will have a 50% chance of placing it with a major publisher where it should ultimately sell about 40,000 copies. However, the worst-case scenario, if she can’t get a major publisher to take it, then she thinks there is 80% chance of placing it with a smaller publisher, with sales of 30,000 copies. On the other hand, if she writes an autobiography, considering the potential interest in her journey as successful writer, she thinks there will be 40% chance of placing it with a major publisher, and it should result in ultimate sales of about 50,000 copies. If she can’t get a major publisher to take it, the worst-case scenario, she thinks there is a 50% chance of placing it with a smaller publisher, with ultimate sales of 35,000 copies. Construct a decision tree to help this author…