The Odds of Winning the Lottery Jackpot


The lottery is a gambling game that involves paying a small amount of money for the chance to win something much bigger. Almost all states run lottery games. Some award prizes that are limited in quantity or demand, such as kindergarten admissions or units in a subsidized housing block; others, like the financial lottery, dish out cash awards to paying participants. There are even lotteries for jobs, sports draft picks, and prestigious medical fellowships. The most popular lottery, of course, is the one that dishes out big cash prizes to paying participants.

Cohen’s book starts in 1964, when growing awareness of the profits to be made in the lottery business met a crisis in state funding. With the baby boom bringing ever more people into the workforce, inflation climbing and the Vietnam War consuming a significant portion of federal spending, many states were running deficits that threatened to deplete state coffers and jeopardize essential services. At the same time, a tax revolt was gathering steam, making raising taxes or cutting services highly unpopular with voters. State legislators, desperate for revenue, hit upon the idea of creating a lottery to generate revenue without the unpleasant side effects of raising taxes.

In the late nineteen-sixties, the first state-run lottery was launched in New Hampshire, and the idea spread rapidly. At that point, winning the jackpot was still a very unlikely event. But as the lottery’s popularity grew, prize sizes exploded and the odds of winning dropped. This was a classic paradox: the lower the odds became, the more people wanted to play.

When the prize pool gets huge, lottery officials often make sure the public knows how rare it is to win. They may tout the jackpot’s sum as a “one-in-three-million” figure or as one that would be invested in an annuity for three decades and pay out only thirty annual payments, each 5% larger than the previous year’s. Such a prize structure can be misleading, however. In fact, the vast majority of lottery winners don’t keep the entire sum they win.

The reason is that most lottery winners have to share the prize with other ticket holders. For example, if you win Powerball or Mega Millions, your share of the prize will be divided by anyone else who picked the same numbers as you, including those who picked their children’s birthdays. It is possible to improve your chances by playing more tickets, but if you choose numbers that are close together or sequences that other people frequently play (for example, 1-2-3-4-5-6), the number of times they appear will increase and thus reduce your probability of success. Knowing how combinatorial math and probability theory work can help you avoid these traps.