The Math Behind the Lottery

Across the country, Americans spend billions of dollars on lottery tickets each week. Some people play for the sheer thrill of it; others believe that winning the lottery is their only, last, or best chance at a better life. However, the odds of winning are extremely low. It’s important for anyone thinking about playing to understand the math behind it.

A lottery is a method of selecting a subset of a larger group by random selection (drawing). Prizes may be cash or goods. The earliest recorded lotteries took place during the Roman Empire, where prizes were often luxury items like dinnerware. During the 1500s, towns in the Low Countries began to use lotteries to raise money for town fortifications and poor relief.

Modern state lotteries are regulated by law and operate on the basis of probability theory. They are designed to distribute prizes among a large population by using a combination of probabilities and combinatorial mathematics. They also employ mathematical models of human decision making.

The first state lottery was established in New Hampshire in 1964. Inspired by this success, other states quickly followed suit. Typically, a state legislates a monopoly for itself; establishes a state agency or public corporation to run the lottery (as opposed to licensing a private firm in return for a share of profits); begins operations with a modest number of relatively simple games; and, motivated by steady pressure for additional revenues, progressively expands the lottery’s scope of offerings.