The Mathematics of the Lottery


The lottery has a certain allure, perhaps because of its association with unimaginable riches. Its popularity has also been driven by its ability to fend off state budget crises without raising taxes or cutting services, or, in the case of public lotteries, enraging voters.

Whether the lottery is a rigged game or a mere form of entertainment, it relies on math. Almost every aspect of the system, from the way the tickets look to the mathematics behind them, is designed to keep you playing. In some ways, it’s not all that different from the tactics of tobacco companies or video-game manufacturers, though these strategies aren’t normally done under the auspices of a government agency.

A portion of the ticket price goes toward running the lottery system—the people who design the scratch-off tickets, record live drawing events, and work at the headquarters to help winners. This overhead is necessary for the system to function, but it also means that winnings aren’t as large as they could be.

The numbers you choose in a lottery draw aren’t randomly chosen—they’re predetermined by a mathematical formula, which has an inherent flaw that allows for the possibility of a pattern to emerge. Fortunately, mathematicians have discovered this flaw and are able to calculate how likely it is that you’ll win a particular number combination in a given drawing. To demonstrate this, the authors of a recent study created an interactive graphic that plots the results of a large set of drawings. The graph shows that, in a truly random outcome, each row and column should appear the same number of times.