Lottery Odds

In a lottery, players pay for tickets and have a chance to win a prize by matching numbers in a random drawing. Prizes can be anything from cash to units in a subsidized housing block to kindergarten placements. Many states have lotteries, and the profits from them are often used for public goods. The lottery is not without its critics, and the evidence suggests that it tends to be addictive. But what do we know about the underlying math of lottery odds?

The first recorded lotteries were held in the Low Countries in the 15th century to raise money for town fortifications. Since then, lottery games have been popular with the general public. Today, almost all states and the District of Columbia have a state lottery or similar game. In a state lottery, participants purchase tickets and hope that their numbers match those randomly drawn by the computer for a prize.

This graph shows how lottery outcomes tend to be distributed around a distribution of winners – with the higher probability of winning going toward those with higher number combinations in the ticket. That distribution is not entirely random, though: it is biased toward higher numbers because the computer’s algorithm assigns each number to an application row and column a different number of times. That bias is why most people think the results are not totally random.

In most cases, a state legislature or government agency establishes the lottery by legislating a monopoly for itself; selects a public corporation to run the lottery and licenses private promoters in return for a cut of ticket sales; starts operations with a modest number of relatively simple games; and, under pressure from revenue needs, gradually expands the size and complexity of its offerings. These developments have given rise to a set of problems.