In decision theory, one sometimes computes the expected value of perfect information (EVPI), which tells you how much, on average, perfect information would be worth in the particular decision tree. Perfect information is knowing the outcome of every chance event in the problem before making any decisions.

Consider the following problem: A shoebox is equally likely to contain a $1 or a $10 bill. Someone gives you the choice of either taking the contents of the box or taking $5 from him or her.

a) How much do you make, on average, if you take the box?

b) Suppose that you knew what was in the box before choosing. This would be perfect information (EVPI). Show that you would make $7.50 on average.

c) EVPI is how much better with the perfect information than you could do on your own. Show that in this problem, the ROI for EVPI is $2.