The lottery is a popular form of gambling in which participants pay to have numbers or symbols randomly drawn by machines. Some lotteries offer cash prizes, while others award goods or services such as housing units in a subsidized apartment complex or kindergarten placements at a public school. A lottery can also be used to distribute statewide benefits, such as health care benefits or public works projects.

In the early days of the modern lottery, a common strategy for winning big was to purchase as many tickets as possible. The more combinations a player had, the higher their success-to-failure ratio would be. This approach is counterintuitive, because the likelihood of winning a prize decreases as the number of combinations increases. Nevertheless, Alexander Hamilton’s advice, from his 1824 book The Federalist Papers, “that the purchase of a ticket is a just and proper compensation for the chance of losing one,” was widely accepted.

Then, starting in the 1970s, lottery administrators began to raise prize caps and add more numbers, lowering the chances of winning even more. But this had the unintended consequence of encouraging more players. As Cohen points out, when lottery odds are low enough, the monetary loss can be outweighed by the entertainment value, or other non-monetary benefit, of playing, and the ticket purchase therefore becomes a rational decision for individual consumers.