The Powerball jackpot is now in excess of $1 billion, which means that there is a flurry of popular press articles discussing the lottery, statistics, odds, and expected value. All of the articles use slightly different numbers and logic but basically come to the same conclusion: the lottery is a poor investment because the expected payout is less than the cost of a ticket.
I take issue with this claim. Sure expected value can be an important consideration, but another important consideration that is often neglected is the variation in outcome. Variation is what gamblers pay for. Nobody would use a slot machine if it returned exactly $0.95 after each $1.00 pull. But slot machines don’t work that way. They return $0 most of the time, and large amounts much more rarely. So if I pull the lever once, I will likely walk away a loser, but I may walk away a big winner. People who gamble enjoy this variation, because any given person on any given day may be able to start playing with very little money and leave with very much. The lottery takes this idea to the extreme. For $2 you can become a pre-tax billionaire. It is by definition a high risk investment, and whether the expected return is positive or negative is essentially irrelevant in deciding whether the investment is good or bad.
Consider a thought experiment. What if the fraction of each ticket sale that went towards the jackpot were increased such that the expected return of the lottery were positive? You are still you, and so you still only have enough money to buy a small number of tickets. The odds of any ticket winning are still unchanged, and so you would almost certainly still end up with nothing. Even if the long term expected return were positive, it would likely take hundreds of lifetimes before you realized that positive return. That doesn’t sound like a very good investment to me. In other words, the expected return is not the key factor in determining whether a lottery ticket is a good investment — the perceived value of variation in outcome is. People who feel like they have enough see this variation as a cost. People who feel like they do not have enough see this variation as a benefit.
Some people say the lottery is a tax on people who don’t know math. I disagree. The lottery is a tax on dreaming of wealth.