- You play a game where you earn the face value of the die ($1 if you roll a one, $2 if you roll a two, so on and so forth). If you can roll the die one time, how much would you pay to play this game?
- You play the same game but only this time, you have an option to roll one more time. How much would you pay to play this game?
- Because you have an equal probability of rolling 1, 2, 3, 4, 5, or 6, you need to find the expected payoff/value. Expected value is 3.5 or you would be willing to pay up to $3.50 to play this game.
- (1)*(1/6) + (2)*(1/6) + (3)*(1/6) + (4)*(1/6) + (5)*(1/6) + (6)*(1/6) = 3.5
- If you roll a 4, 5, or 6 on your first roll, you would not roll again since your expected value on one roll is 3.5 (answer above). But if you roll a 1, 2, or 3, you would roll again. Therefore, you have 1/2 probability of not rolling and 1/2 probability of rolling again. Your “reroll” also has an expected value of 3.5. As rolling a 4, 5, or 6 is equally likely, the expected return is 5. Expected value on 2 rolls is the following: (5)*(1/2) + (3.5)*(1/2) = 4.25 or you would be willing to pay up to $4.25 to play this game.
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