In a small, unnamed village on June 27th each year, people gather at the town square to participate in an annual lottery. They buy tickets for a chance to win prizes ranging from a sack of grain to a new car. Old Man Warner quotes an old proverb: “Lottery in June, corn be heavy soon.”

The casting of lots to make decisions and determine fates has a long history in human culture; the first recorded public lottery to distribute prize money occurred in the 15th century, when a variety of towns held lotteries for such purposes as town repairs and aiding the poor. In the modern world, governments at all levels have embraced lotteries as a source of tax revenues.

Typically, a state government establishes a monopoly for itself and organizes a public corporation to run the lottery; it usually begins with a modest number of relatively simple games, and is subject to constant pressure to increase game offerings in order to maintain or grow revenues. State government officials also have to grapple with the question of how to allocate the prize pool between few large prizes and many small ones.

The drawing of winners must be conducted in a manner that ensures that chance and only chance determines the selection of winners. The typical method involves thoroughly mixing a pool of tickets and their counterfoils (as shown in the figure below); this is done by shaking or tossing, although computer-based techniques are becoming more common. A random-number computer then generates the winning numbers or symbols.