The casting of lots to determine decisions and fates has a long history in human societies, both as an ancient form of divination and for material gain. Lotteries are the modern form of this practice, involving people paying to enter competitions where their names are drawn for prizes such as money or goods. Some states even use lottery revenues to fund a variety of public services, such as providing low-income residents with units in subsidized housing developments or kindergarten placements at reputable public schools.

In each of these contexts, the lottery serves as a painless source of revenue to support the operations of state government. While lottery advocates promote the benefits of this source of money, critics focus on its social costs, arguing that it promotes gambling addiction and regresses against lower-income communities. In addition, the nature of lottery as a business requires that it be constantly promoted to generate income for its operators and state agencies. This can raise issues about whether it is appropriate for the state to be promoting gambling at all.

To understand the controversies surrounding lottery, it is helpful to examine its history. The first public lotteries were held in the 15th century, with records from cities such as Bruges, Ghent and Utrecht showing that towns used them to raise funds for municipal repairs and the poor. The first state-sponsored lotteries began in the 17th century, with the Dutch Staatsloterij (the oldest still running lottery) starting operation in 1726.

These early lotteries were akin to traditional raffles, with the public buying tickets and winning prizes by attending a drawing for which they would need to be present. In the 1970s, however, innovations were made that dramatically transformed the industry. New games such as scratch-off tickets and keno were introduced, and the industry as a whole adopted a more commercial orientation. The shift to commercialization prompted a second set of questions and concerns.

While the popularity of lottery increased, the number of winners declined. The fact that a large proportion of those who played lost, rather than won, led to criticisms about the social costs of the game, particularly its regressive effect on poorer communities.

The truth is that the chances of winning any lottery are based solely on chance. Those who play regularly are more likely to win than those who do not. This is because the law of large numbers concludes that the more tickets a person buys, the higher his or her likelihood of winning. But the probability of winning any given draw remains unchanged. Those who have studied the odds of winning a lottery know that it is necessary to choose the numbers carefully. But they also know that a gut feeling is not sufficient. This is why they turn to mathematics. Using mathematics to select their numbers increases their expected utility and decreases their risk of losing.