The casting of lots to determine decisions and fates has a long record, but lotteries are relatively modern in human history. The first recorded public lotteries to offer tickets for sale with prizes in the form of money were in the Low Countries in the 15th century, when towns used them to raise funds for town fortifications and to help poor citizens. In the immediate post-World War II period, states adopted lotteries to subsidize their social safety nets without especially onerous taxes on middle- and working classes.
State lotteries are run like businesses and thus have a strong incentive to maximize revenues. As a result, they tend to grow dramatically in the first few years of operation and then level off or even decline. To keep revenues up, they introduce new games. Some critics fear that these innovations exacerbate lottery alleged negative impacts: targeting poorer individuals, luring problem gamblers, and so on.
A key question is whether a lottery game’s entertainment value (or other non-monetary benefit) exceeds the disutility of its monetary cost for each individual who purchases a ticket. If it does, the ticket purchase will be a rational decision for that individual.
The data in the graph below show that for most categories, the odds of winning are close to 50-50. The graph also shows that the average jackpot amount is much less than the total of all the prizes offered in each category. In addition, we can see that the probability of winning a specific prize is proportional to its value, with the biggest prizes attracting the most entries.