Problem 2: You go to the racetrack and are choosing between 2 horses: Belle and Jeb (you are at the racetrack, so you will bet on one of these two horses). Betting on either horse will cost you $1, and the payoffs are as follows: • Bet on Belle: you will be paid $2 if she wins (or a net profit of $1). You believe she has a 75% chance of winning. • Bet on Jeb: you will be paid $9 if he wins (for a net profit of $8). You believe that he has a 20% chance of winning. Prior to making your decision of which horse to bet on, someone comes and offers you gambler’s “insurance.” If you agree to the gamblers “insurance,” they pay you $1 immediately and you agree to pay them 50% of the profit on your winnings (that is, $0.50 if Belle wins, and $4 if Jeb wins). What should you do? Answer this question by: a) Creating a decision tree for this scenario, making sure you label all branches and include all probabilities and consequences. b) Solving the decision tree using EMV and stating the optimal decision strategy. c) While the problem stated that you will bet on a horse, if the problem allowed you to decide to not bet (you would have to decide this before agreeing to gambler’s insurance, if you accepted the insurance, you would have to bet), would you change your decision? Briefly explain; you do NOT need to draw a new tree but should explain based on your original tree.
Problem 2: You go to the racetrack and are choosing between 2 horses: Belle and Jeb (you are at the racetrack, so you will bet on one of these two horses). Betting on either horse will cost you $1, and the payoffs are as follows:
• Bet on Belle: you will be paid $2 if she wins (or a net profit of $1). You believe she has a 75% chance of winning.
• Bet on Jeb: you will be paid $9 if he wins (for a net profit of $8). You believe that he has a 20% chance of winning. Prior to making your decision of which horse to bet on, someone comes and offers you gambler’s “insurance.” If you agree to the gamblers “insurance,” they pay you $1 immediately and you agree to pay them 50% of the profit on your winnings (that is, $0.50 if Belle wins, and $4 if Jeb wins).
What should you do? Answer this question by:
a) Creating a decision tree for this scenario, making sure you label all branches and include all probabilities and consequences.
b) Solving the decision tree using EMV and stating the optimal decision strategy.
c) While the problem stated that you will bet on a horse, if the problem allowed you to decide to not bet (you would have to decide this before agreeing to gambler’s insurance, if you accepted the insurance, you would have to bet), would you change your decision? Briefly explain; you do NOT need to draw a new tree but should explain based on your original tree.
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