Suppose, hypothetically, that the Team A and Team B will be in this year’s World

Question

Suppose, hypothetically, that the Team A and Team B will be in this year’s World Series. You are betting on which team will win. Suppose Team A has a prior probability 0.6 of winning. Your net payoff contingent on which team you bet on and which one wins is:

Team A Win

probability = 0.60

Team B Win

probability = 0.40

a. Which team will you bet on without better information? What is your expected payoff?

b. Suppose an expert could give you a “tip” which is a perfect prediction of the outcome of the series, what would be the value of this information?

c. If the expert’s tip is 75% accurate, what will be the value of the information?

Team A Win

probability = 0.60

Team B Win

probability = 0.40

Explanation / Answer

a. Total profit when Bet on Team A = Winning probability * Bet value + Losing Probability * Bet Value

= 0.60 * 80 + 0.40 * (-100) = $8

Total profit when Bet on Team B = Winning probability * Bet value + Losing Probability * Bet Value

= 0.60 * (-100) + 0.40 * (120) = $-12

I will bet on Team A without better information.

Expected Payoff is $8.

b. THe expert will provide the perfect information so it will always be a win- win situation.

so Maximum Earning = 0.60 * 80 + 0.40 * 120 = $96

so Value of this information is = $96 - $ 8 = $ 88

c. Expert's tip is 75% accurate.

so Maximum earning = Pr( Expert is right) * Pr (Earning) + Pr(Expert is wrong) * Pr (Losing)

= 0.75 * ( 0.60 * 80 + 0.40 * 120) + 0.25 * (0.40 * (-100) + 0.60 * (-100)

= $47

value of the information = $ 47 - $8 = $39

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