A lottery is a popular form of gambling which involves the drawing of lots for a prize. Some governments outlaw it, while others endorse it to the extent of organizing a national lottery. It is common to find some degree of regulation of lottery by governments.

At the beginning of the 20th century, most forms of gambling, including lotteries and sweepstakes, were illegal in many countries, including the U.S.A. and most of Europe. This remained so until after World War II. In the 1960s casinos and lotteries began to appear throughout the world as a means to raise revenue in addition to taxes.

Lotteries are most often run by governments or local states and are sometimes described as a regressive tax, since those most likely to buy tickets will typically be the less affluent members of a society. The astronomically high odds against winning have also led to the epithets of a "tax on stupidity", "math tax" or "voluntary tax". They are intended to suggest that lotteries, being an addictive form of gambling, are governmental revenue-raising mechanisms that will attract only those consumers who fail to see that the game is a very bad deal. Indeed, the desire of lottery operators to guarantee themselves a profit requires that an average lottery ticket be worth substantially less than what it costs to buy. After taking into account the present value of the lottery prize as a single lump sum cash payment, the impact of any taxes that might apply, and the likelihood of having to share the prize with other winners, it is not uncommon to find that a ticket for a typical major lottery is worth less than one third of its purchase price. The large multi million dollar prize lotteries in the USA are paid by annuity over 20 years. Therefore, if you take a one-time lump sum cash payment, plus pay the federal taxes, you will end up with about one third of the total prize money offered.

Lotteries come in many formats. The prize can be fixed cash or goods. In this format there is risk to the organizer if insufficient tickets are sold. The prize can be a fixed percentage of the receipts. A popular form of this is the "50-50" draw where the organizers promise that the prize will be 50% of the revenue. The prize may be guaranteed to be unique where each ticket sold has a unique number. Many recent lotteries allow purchasers to select the numbers on the lottery ticket resulting in the possibility of multiple winners.

The fact that lotteries are commonly played leads to some contradictions against standard models of economic rationality. However, the expectations of some players may not be to win the game, but to experience the thrill and indulge in a fantasy of possibly becoming wealthy. Even ignoring the thrill factor, there is the theoretical possibility that the purchase of a lottery ticket could represent a gain in expected utility, even though it represents a loss in expected monetary value, thus making the purchase a rational decision. Insurance, for instance, represents negative expected monetary value but is not considered to be a tax on stupidity because it is generally believed to deliver positive expected utility to the individual.

What motivates so many people to buy lottery tickets? Alexander Hamilton expressed the opinion that most people are willing to wager a little amount with a chance to win a large amount...and that they prefer a small chance of winning a great amount instead of a great chance to win a small amount. Simply put, it costs little to dream big, and you can't win if you don't play.

Lottery tickets are usually scanned in large numbers, using marksense-technology. With today's computer performance, it takes less than one second to check if a particular combination was picked up by anyone, even for lotteries like Euromillions or Mega Millions.

Early history

The first signs of a lottery trace back the Han Dynasty between 205 and 187 B.C., where ancient Keno slips were discovered. The lottery has helped finance major governmental projects like the Great Wall of China. From the Chinese "The Book of Songs" (second millennium B.C.) comes a reference to a game of chance as "the drawing of wood", which in context appears to describe the drawing of lots. From the Celtic era, the Cornish words "teulet pren" translates into "to throw wood" and means "to draw lots". The Iliad by Homer refers to lots being placed into Agamemon's helmet to determine who would fight Hector.

The first known European lottery occurred during the Roman Empire, and was mainly done as a form of amusement at dinner parties. Each guest would receive a ticket, and prizes would often consist of fancy items such as dinnerware. Every ticket holder would be assured of winning something. This type of lottery however, was no more than the distribution of gifts by wealthy noblemen during the Saturnalian revelries. The earliest records of a lottery offering tickets for sale is the lottery organized by Roman Emperor Augustus Caesar. The funds were for repairs to the City of Rome, and the winners were given prizes in the form of articles of unequal value.

The earliest public lottery on record is that which was held in the Dutch town of Sluis in 1434.

The first recorded lotteries to offer tickets for sale with prizes in the form of money were held in the Low Countries during the period 1443-1449. Various towns in Flanders (parts of Belgium, Holland, and France), held public lotteries to raise money for town fortifications, and raising money to help the poor. The town records of Ghent, Utrecht, and Bruges, indicate that the lotteries may well be of even greater antiquity. An early record dated May 9,1445 at L'Ecluse, refers to raising funds to build walls and town fortifications, with a lottery of 4,304 tickets and total prize money of 1737 florins.^[1] In the seventeenth century it was quite normal in The Netherlands to organize lotteries in order to collect money for the poor. Tickets cost about four guilders and the prizes were paintings (50 to 100 per lottery); some of these the paintings were produced by nowadays famous painters as Jan van Goyen.

The Dutch were the first to shift the lottery to solely money prizes and base prizes on odds (roughly about 1 in 4 tickets winning a prize). The lottery proved to be very popular, and was hailed as a painless form of taxation. In the Netherlands the lottery was used to raise money for e.g. supporting poor people, building dikes, construction of defense works for towns and to buy free sailors from slavery in the Arab countries. The English word lottery stems from the Dutch word loterij, which is derived from the Dutch noun lot meaning fate. The Dutch state owned staatsloterij is the oldest still existing lottery.