The lottery is a fixture in our society, with people spending billions buying tickets every year. States promote lotteries as ways to raise money for children or other worthy causes, and most of us have heard the message that even if you lose, you’re doing your civic duty by buying a ticket. But what we don’t hear is how much these lotteries cost people.

The first European lotteries in the modern sense of the word appear in 15th-century Burgundy and Flanders, with towns trying to raise funds for town fortifications or to help the poor. They were similar to venturas, an ancient form of public lottery that awarded prizes like goods or property rather than cash. Francis I of France approved venturas in many cities in 1520 and 1539, allowing the development of private and public lotteries with a variety of prize categories.

People don’t know how rare it is to win, and when lotteries change their odds, they don’t notice. That’s because human intuition is very good at developing an intuitive sense of how likely risks and rewards are within our own experience, but not very well adapted to very large scales such as the odds of winning a big jackpot.

When the chances of winning are too low, people won’t play, and lottery revenues decline. To increase revenue, lotteries may increase or decrease the number of balls or alter the odds in other ways. But increasing the odds also increases the risk that someone will win a huge sum of money almost every week, or that the jackpot will never grow large enough to attract players.