a. If you bet $1 on each hand, what is the expected value to you of a single game? What is the house edge? b. If you played 150 games of blackjack in an evening, betting $1 on each hand, how much should you expect to win or lose? c. If you played 150 games of blackjack in an evening, betting $3 on each hand, how much should you expect to win or lose? d. If patrons bet $7,000,000 on blackjack in one evening, how much should the casino expect to earn? a. The expected value to you of a single game is $ (Type an integer or a decimal.)

a. If you bet $1 on each hand, what is the expected value to you of a single game? What is the house edge? b. If you played 150 games of blackjack in an evening, betting $1 on each hand, how much should you expect to win or lose? c. If you played 150 games of blackjack in an evening, betting $3 on each hand, how much should you expect to win or lose? d. If patrons bet $7,000,000 on blackjack in one evening, how much should the casino expect to earn? a. The expected value to you of a single game is $ (Type an integer or a decimal.)

Microeconomics: Principles & Policy

14th Edition

ISBN:9781337794992

Author:William J. Baumol, Alan S. Blinder, John L. Solow

Publisher:William J. Baumol, Alan S. Blinder, John L. Solow

Chapter13: Between Competition And Monopoly

Section: Chapter Questions

Problem 10DQ

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In the final round of a TV game show, contestantshave a chance to increase their current winnings of$1 million to $2 million. If they are wrong, theirprize is decreased to $500,000. A contestant thinkshis guess will be right 50% of the time. Should heplay? What is the lowest probability of a correctguess that would make playing profitable?
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3:51 9 M 23 The mixed strategy Nash equilibrium of the following * game is Player 2 R. L Player 1 U 2,2 3,1 D 3.-1 0.0 U with 3/4 probability and D with 1/4 probability for player 1; L with1/2 probability and probability for player 2 with 1/2 U with 1/2 probability and D with 1/2 probability for player 1; L with1/4 probability and R with 3/4 probability for player 2 U with 1/4 probability and D with 3/4 probability for player 1; L with1/2 probability and R with 1/2 probability for player 2 O None of the above. U with 1/2 probability and D with 1/2 probability for player 1; L with3/4 probability and R with 1/4 probability for player 2
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3. Suppose we play the following game. I give you $100 for your initial bankroll. At each time n, you decide how much of your current wealth to bet. You cannot borrow money. You can only play with the money I gave you in the beginning or any money that you have won so far. The game is simple. At each time n ≥ 1, you decide the amount to bet. I will roll a fair die. If the die comes up 1,2,3,..., or 5, you win; if the die comes up 6, then you lose. IOW, if you bet $10 on the first roll, you will either have $90 or $110 after the first roll. (a) Suppose you wish to maximize your profit on the first roll. How much should you bet? (Most of you will get this wrong.) (b) What is the expected profit on the first roll if your bet is b with 0 ≤ b ≤ 100? (c) Suppose you wish to maximize your expected profit on the first roll. How much should you bet? (d) Suppose you wish to maximize your expected profit betting on the nth roll. How much of your current wealth do you bet? (e) Let X₂, be your…
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