Almost all states have lotteries, and Americans spend an estimated $100 billion a year on tickets. Lotteries have won broad public approval for their ability to raise money for specific public goods, such as education, without imposing onerous taxes on low- and middle-income residents. However, they also have been criticized for the dangers of compulsive gambling and their regressive impact on lower-income groups.
While many people play lotteries for fun, it’s not unreasonable to say that a disproportionate number of lottery players are among the poorest in society, which may be why critics argue that the games operate as a disguised tax on those least able to afford them. In addition, lottery retailers and suppliers earn significant profits from sales.
The lottery draws lots to allocate prizes, and the idea of using chance to distribute property has a long history in human societies. The Old Testament has a passage that instructs Moses to divide land by lot (Numbers 26:55-55) and Roman emperors used lotteries to give away slaves during Saturnalian feasts. The first recorded signs of the game date back to the Chinese Han dynasty between 205 and 187 BC, when they were called “keno slips.”
A modern lottery is run as a business, and its advertising is designed to maximize revenues. Its promotion aims to encourage people to buy tickets and to think of winning as an exciting goal. But the way this message is delivered obscures its regressive nature.
In the United States, for example, most lottery winners are required to choose a combination of numbers that has a high probability of being picked. If the winner selects numbers such as their children’s ages or birthdays, they have to split the prize with anyone else who picks those same numbers. Harvard statistics professor Mark Glickman recommends playing the Quick Pick option, which allows people to avoid selecting the same numbers as others and increases their chances of winning by reducing the number of other possible combinations.
When the winner’s name is announced, the press often refers to the prize as “a lump sum.” This implies that the winning amount will be paid out in one payment, but withholdings — which vary by state and how winnings are invested — reduce this amount significantly. In addition, the time value of money reduces the advertised jackpot by about a third, even before taking into account income taxes.
Despite the fact that many people are convinced of their chances of hitting the jackpot, the likelihood of winning is quite low. This is because lottery results depend on the behavior of a large population, and each application has an equal chance of being selected. This fact is reflected in the color of each cell in the graph below, which shows the number of times each application was awarded from the first row to the last column. The fact that the colors are close to each other is indicative of a random outcome.