Lottery Revenues and Expected Value Maximization

A lottery is a form of gambling in which multiple people buy tickets for a small price in order to have a chance to win a large sum of money, often running into millions of dollars. They are a common way of raising money for governments, charities and other organizations.

The first recorded lotteries that offer tickets for sale with prizes in the form of money date back to the 15th century, with several towns holding public lotteries to raise funds for town fortification and to help the poor. Although these lotteries may be as old as the Roman lottery, it was not until the 17th century that lotteries were widely used in Europe and the United States to raise money for political causes.

Many critics argue that state lotteries are a major regressive tax on lower-income groups, promoting addictive gambling behavior and increasing the likelihood of problem gamblers. They also question whether the revenues generated by lotteries are well-targeted for their intended use or are at cross-purposes with other public interests.

In general, lottery purchases cannot be accounted for by decision models based on expected value maximization; these types of decisions usually require an individual to pay a consideration (e.g., property, work, money) in exchange for a chance of receiving a prize. However, decision models based on expected utility maximization or other general utility functions can be adjusted to account for lottery purchases.

Players of lotteries are not likely to be maximizing their expected utility, but they may still gain from the experience of playing and might be willing to pay a small amount of money for the hope of winning a prize. This non-monetary gain is usually more than offset by the disutility of a monetary loss, making the purchase a rational decision for those who have enough expected utility to make it worthwhile.

Lottery Revenues and Boredom

The number of games offered by a lottery usually expands significantly after a lottery is introduced, but revenues typically level off as players become bored with the game. As a result, governments are forced to introduce new games or change the game format in order to keep interest high and revenues high.

These changes include the introduction of instant-win scratch-off games, daily numbers and other games with a lower prize structure that provide a greater opportunity for winning. A popular example of this is the Powerball lottery, which offers a $2 multi-jurisdictional game with the potential for huge jackpots.

The government regulates lotteries, which includes selecting and licensing retailers who sell tickets and redeeming winning tickets; training employees of retail companies to sell the lottery and help players understand how to play; and enforcing rules and laws for the lottery. The government can exempt certain types of lotteries from these regulations, for example, those run by charitable, religious and other non-profit organizations. In addition, the government can impose penalties for violations of the lottery rules and laws. The laws governing lottery are often complex and can be difficult to understand, but they usually make sense and are in the public interest.