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You roll a fair die and get X, I roll a fair die and get Y, and you are paid max(X - Y, 0). How much would you pay to play?

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You roll a fair die and get X; the interviewer rolls a fair die and gets Y; you are paid max(X - Y, 0). First give an 80% confidence interval for what you would pay to play, then compute the expected payoff. You may swap your fair die for one with three faces showing 1 and three showing 6: do you? Alternatively you may swap the interviewer's die for such a die: do you?

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