Lottery is a form of gambling in which winnings are determined by chance. The term is derived from the Latin lotere (“to draw lots”), but the concept dates back centuries. In fact, Moses’s instructions to count the people in Israel were a kind of lottery, and Roman emperors gave away property and slaves by chance. Lotteries have also been a popular way to fund state projects. In the United States, they are legal and contribute billions to the economy each year. But are they fair? This article looks at the mathematics behind the lottery and why it may not be as unbiased as we think.
Lotteries are not a perfect solution for public policy, but they can be useful in certain situations, such as when there is something of high demand but limited supply (e.g., kindergarten admission at a reputable school or units in a subsidized housing block). In these cases, the disutility of monetary loss can be outweighed by the utility of non-monetary gains, and the purchase of a ticket would be an optimal decision for an individual.
A second feature of a lottery is the drawing, which is a procedure for selecting winners from a pool of tickets or counterfoils. Usually, the selection is made by some mechanical means such as shaking or tossing, and then the tickets are sorted by the number of matching numbers or symbols. Computers are becoming more common for this purpose, as they can store information about many tickets and produce a random selection with great precision.
The result of the drawing is a set of winners who will receive the prizes that are offered in a particular lottery, and the remainder of the prizes will remain in the prize pool for future drawings. This process is known as a closed lottery. A closed lottery is more likely to be unbiased than a random drawing, because it ensures that each application will be awarded a similar number of positions. This is demonstrated in the figure below, which shows a plot of the results for every lottery run since 1844, with each color representing the number of applications that were awarded that position. The plot shows approximately the same colors for each lottery, indicating that the results are very close to being unbiased.
The popularity of the lottery has soared in recent decades, partly because of the large jackpots that attract attention on news websites and television. But even as the size of these jackpots increases, the odds of winning are still very low. In addition, the regressive nature of the lottery makes it harder for poorer people to afford to play. This dynamic has created a powerful incentive for state governments to promote the lottery, but they must do so carefully. Their message should convey that playing the lottery is fun and not a serious gamble, while reminding players that their chances of winning are very small. Achieving this balance requires a thoughtful mix of advertising and education.