Forty-three states run lotteries, and most of those lotteries are similar: You must select 6 out of 44 numbers correctly in order to win the jackpot. If you come close, there are some significantly lesser prizes, which we ignore for now. For each million dollars in the lottery jackpot, you receive $50,000 per year for 20 years, and your chance of winning is 1 in 7.1 million. A recent advertisement for a particular state lottery went as follows: “Okay, you got two kinds of people. You’ve got the kind who play Lotto all the time, and the kind who play Lotto some of the time. You know, like only on a Saturday when they stop in at the store on the corner for some peanut butter cups and diet soda and the jackpot happens to be really big. I mean, my friend Ned? He’s like

‘Hey, it’s only $2 million this week.’ Well, hellloooo, anybody home? I mean, I don’t know about you, but I wouldn’t mind having a measly 2 mill coming my way.…”

What is the present value of these payments?