The Odds of Winning a Lottery

October 26, 2023 by No Comments


Lotteries, or games of chance, are an ancient tradition. Whether in the form of a simple party game—like the Roman Saturnalia’s apophoreta, where tickets were given away to guests during dinner for a chance at prizes such as slaves or property—or as an official government-sponsored event for raising funds or selecting jurors or even for giving out land and other resources, drawing lots has been used since antiquity.

The fact is that lottery games are a gamble, and it’s usually not a good one for most players. As the economist Michael J. Sandel points out, “the value of a ticket is determined by the expected utility it provides: how much entertainment it delivers, plus the disutility of losing the money.” But for many people, especially the poor, the entertainment value is low or nonexistent, and the risk is high.

That’s why wealthy people tend to buy fewer tickets than the poor—except for when jackpots approach ten figures. Rich people spend, on average, only one percent of their income on tickets, while those making less than fifty thousand dollars spend thirteen percent.

But while most people know that the odds are long, most also have a tiny sliver of hope that they’ll win. They may have all sorts of quote-unquote systems that aren’t based on statistical reasoning, about buying tickets in particular stores or at certain times of day or about avoiding certain numbers or purchasing multiple tickets or about choosing the right number and checking the results after the drawing—but whatever they do, they understand that they’re unlikely to make a killing on the lottery.