A lottery is a form of gambling which involves the drawing of lots for a prize.
Lottery is outlawed by some governments, while others endorse it to the extent of organizing a national or state 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 come in many formats. For example, the prize can be a fixed amount of cash or goods. In this format there is risk to the organizer if insufficient tickets are sold. More commonly the prize fund will 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. Many recent lotteries allow purchasers to select the numbers on the lottery ticket, resulting in the possibility of multiple winners.
The purchase of lottery tickets cannot be accounted for by decision models based on expected value maximization. The reason is that lottery tickets cost more than the expected gain, so one maximizing expected value should not buy lottery tickets. Yet, lottery purchases can be explained by decision models based on expected utility maximization, as the curvature of the utility function can be adjusted to capture risk-seeking behavior. More general models based on utility functions defined on things other than the lottery outcomes can also account for lottery purchase. In addition to the lottery prizes, the ticket may enable some purchasers to experience a thrill and to indulge in a fantasy of becoming wealthy. If the entertainment value (or other non-monetary value) obtained by playing is high enough for a given individual, then the purchase of a lottery ticket could represent a gain in overall utility. In such a case, the disutility of a monetary loss could be outweighed by the combined expected utility of monetary and non-monetary gain, thus making the purchase a rational decision for that individual.
The first recorded signs of a lottery are Keno slips from the Chinese Han Dynasty between 205 and 187 B.C. These lotteries are believed to have helped to finance major government 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 "teulel pren" translates into "to throw wood" and means "to draw lots". The Iliad of Homer refers to lots being placed into Agamemnon's helmet to determine who would fight Hector.
The first known European lotteries were held during the Roman Empire, mainly as an 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 in the City of Rome, and the winners were given prizes in the form of articles of unequal value.
The first recorded lotteries to offer tickets for sale with prizes in the form of money were held in the Low Countries in the 15th century. Various towns held public lotteries to raise money for town fortifications, and to help the poor. The town records of Ghent, Utrecht, and Bruges indicate that lotteries may be even older. A 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. In the 17th century it was quite usual in the Netherlands to organize lotteries to collect money for the poor or in order to raise funds for all kinds of public usages. The lotteries proved very popular and were hailed as a painless form of taxation. The Dutch state-owned Staatsloterij is the oldest running lottery.
Early modern history
Although the English probably first experimented with raffles and similar games of chance, the first recorded official lottery was chartered by Queen Elizabeth I, in the year 1566, and was drawn in 1569. This lottery was designed to raise money for the "reparation of the havens and strength of the Realme, and towardes such other publique good workes." Each ticket holder won a prize, and the total value of the prizes equalled the money raised. Prizes were in the form of silver plate and other valuable commodities. The lottery was promoted by scrolls posted throughout the country showing sketches of the prizes.
Thus, the lottery money received was an interest free loan to the government during the three years that the tickets ('without any Blankes') were sold. In later years, the government sold the lottery ticket rights to brokers, who in turn hired agents and runners to sell them. These brokers eventually became the modern day stockbrokers for various commercial ventures. Most people could not afford the entire cost of a lottery ticket, so the brokers would sell shares in a ticket; this resulted in tickets being issued with a notation such as "Sixteenth" or "Third Class."
Many private lotteries were held, including raising money for The Virginia Company of London to support its settlement in America at Jamestown. The English State Lottery ran from 1694 until 1826. Thus, the English lotteries ran for over 250 years, until the government, under constant pressure from the opposition in parliament, declared a final lottery in 1826. This lottery was held up to ridicule by contemporary commentators as "the last struggle of the speculators on public credulity for popularity to their last dying lottery."
Early America, 1612–1900
An English lottery, authorized by King James I in 1612, granted the Virginia Company of London the right to raise money to help establish settlers in the first permanent English colony at Jamestown, Virginia.
Lotteries in colonial America played a significant part in the financing of both private and public ventures. It has been recorded that more than 200 lotteries were sanctioned between 1744 and 1776, and played a major role in financing roads, libraries, churches, colleges, canals, bridges, etc. In the 1740s, the foundation of Princeton and Columbia Universities was financed by lotteries, as was the University of Pennsylvania by the Academy Lottery in 1755.
During the French and Indian Wars, several colonies used lotteries to help finance fortifications and their local militia. In May 1758, the State of Massachusetts raised money with a lottery for the "Expedition against Canada."
Benjamin Franklin organized a lottery to raise money to purchase cannon for the defense of Philadelphia. Several of these lotteries offered prizes in the form of "Pieces of Eight." George Washington's Mountain Road Lottery in 1768 was unsuccessful. However, these rare lottery tickets bearing George Washington's signature have become collectors' items which sold for about $15,000 in 2007. Later, in 1769, Washington was a manager for Col. Bernard Moore's "Slave Lottery", which advertised land and slaves as prizes in the Virginia Gazette.
At the outset of the Revolutionary War, the Continental Congress used lotteries to raise money to support the Colonial Army. Alexander Hamilton wrote that lotteries should be kept simple, and that "Everybody ... will be willing to hazard a trifling sum for the chance of considerable gain ... and would prefer a small chance of winning a great deal to a great chance of winning little." Taxes had never been accepted as a way to raise public funding for projects, and this led to the popular belief that lotteries were a form of hidden tax.
At the end of the Revolutionary War the various states had to resort to lotteries to raise funds for numerous public projects. For many years these lotteries were highly successful and contributed to the nation's rapid growth. The lotteries were used for such diverse projects as the Pennsylvania Schuylkill – Susquehanna Canal (lottery in May 1795), and Harvard College (lottery in March 1806). Many American churches raised building funds through state authorized private lotteries.
However, lotteries eventually became a cause of financial mismanagement and scandal. Most notorious was the Louisiana State Lottery (1868–1892) which was aptly called the "Golden Octopus" because its tentacles reached into every home in America.
Toward the end of the 19th century a large majority of state constitutions banned lotteries. Finally, on July 29, 1890, U.S. President Benjamin Harrison sent a message to Congress demanding "severe and effective legislation" against lotteries. Congress acted swiftly, and banned the U.S. mails from carrying lottery tickets. The Supreme Court upheld the law in 1892, and that brought a complete halt to all lotteries in the United States by 1900.
The numbers game operated out of "Policy shops", where bettors choose numbers, were in the U.S. prior to 1860. In 1875, a report of a select committee of the New York State Assembly stated that "the lowest, meanest, worst form ... [that] gambling takes in the city of New York, is what is known as policy playing." The game was also popular in Italian neighborhoods known as the Italian lottery, and it was known in Cuban communities as bolita ("little ball").
By the early 20th century, the game was associated with poor communities, and could be played for as little as $0.01. One of the game's attractions to low income and working class bettors was the ability to bet small amounts of money. Also, unlike state lotteries, bookies could extend credit to the bettor. In addition, policy winners could avoid paying income tax. Different policy banks would offer different rates, though a payoff of 600 to 1 was typical. Since the odds of winning were 1000:1, the expected profit for racketeers was enormous.
When lotteries raised their head again in 1964, it would take many years of constitutional amendements by the various states before the lotteries were allowed to flourish again. On March 12, 1964, New Hampshire became the first state to sell lottery tickets in the modern era.
Probability of winning
The chances of winning a lottery jackpot can vary widely depending on the lottery design, and are determined by several factors, including the count of possible numbers, the count of winning numbers drawn, whether or not order is significant, and whether drawn numbers are returned for the possibility of further drawing.
In a 6-from-49 lotto, a player chooses six numbers from 1 to 49 (no duplicates are allowed). If all six numbers on the player's ticket match those produced in the official drawing, then the player is a jackpot winner. This is true regardless of the order in which the numbers are drawn. For such a lottery, the chance of being a jackpot winner is 1 in 13,983,816 (note that most lotteries have much worse odds).'' The derivation of this result (and other winning odds) is shown in the Lottery mathematics article. To put these odds in perspective, suppose a person buys one lottery ticket per week. In a quarter-million years of play, the person would be expected to win the jackpot only once (13,983,816 weeks is roughly 269,000 years). Or a ticket every other second for one year, he would probably win the jackpot just once. Mega Millions is a very popular multi-state lottery in the United States which is known for jackpots that grow very large from time to time. This attractive feature is made possible simply by designing the game to be extremely difficult to win: 1 chance in 175,711,536. That's over twelve times higher than the example above. Mega Millions players also pick six numbers, but two different groups of numbers are used. The first five numbers come from one group that contains numbers from 1 to 56. The sixth number – the "Mega Ball number" – comes from the second group, which contains numbers from 1 to 46. To win a Mega Millions jackpot, a player's first five numbers must match the first five numbers drawn and the Mega Ball number chosen must match the Mega Ball number drawn. In other words, it is not good enough to pick 10, 18, 25, 33, 42 / 7 when the drawing is 7, 10, 25, 33, 42 / 18. Even though the player picked all the right numbers, the Mega Ball number at the end of the ticket doesn't match the one drawn, so the ticket would be credited with matching only four numbers (10, 25, 33, 42).
The SuperEnalotto of Italy is possibly the most difficult, as players try to match 6 numbers out of 90. The odds in making the jackpot are 1 in 622,614,630, while the odds of matching 5 numbers are 1 in 1,235,346
Most lotteries give lesser prizes for matching just some of the winning numbers. The Mega Millions game is an extreme case, giving a very small payout (US$2) even if a player matches only the final Mega Ball number on the ticket. The weekly 6/49 lottery operated by the ILLF offers a two-ball cash prize to make the odds of winning some prize only 1 in 6.63. Matching more numbers, the payout goes up. Although none of these additional prizes affect the chances of winning the jackpot, they do improve the odds of winning something and therefore add a little to the value of the ticket. On the other hand, multiple smaller prizes usually mean smaller jackpots. It is very common for the jackpot to be split evenly if multiple players have tickets with all the winning numbers.
In the UK National Lottery the smallest prize is £10 for matching three balls.
It is a hard, in most cases open, mathematical problem to calculate the minimum number of tickets one needs to buy to guarantee that at least one of these tickets has (at least) 2 matches or 3 matches, etc. In the 5-from-90 lotto this minimum number that can guarantee a ticket with at least 2 matches is exactly 100. The odds of a guaranteed 3 matches is 57.
The expected value of lottery bets is often notably low. In the United States, an expected value of 50% of the purchase price is available only in the small-payout, non-jackpot games. For example, when a player buys a "pick-4" lottery ticket for $1.00, he might be getting a ticket with an expected value of only $0.50. Hence, buying a lottery ticket reduces the buyer's expected net worth. This is in sharp contrast with financial securities like stocks and bonds whose prices are theoretically based on their economic value, as judged by the markets at any given point in time.
Lotteries are sometimes described as a regressive tax, albeit a voluntary one, since those most likely to buy tickets, and to spend a larger proportion of their money on them, are typically less affluent people. The astronomically high odds against winning the larger prizes have also led to the epithets of a "tax on stupidity" and a "math tax". Although the use of the word "tax" is not strictly correct, these descriptions are intended to suggest that lotteries are government-sanctioned operations which will attract only those people who fail to understand that buying a lottery ticket is a poor economic decision. Indeed, after taking into account the present value of a given 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 major lottery is worth less than one third of its purchase price. In other words, if a lottery ticket costs US$1 to purchase, its true economic worth may be only US$0.33 or so at the time of purchase. Of course, this is just a hypothetical example, and the actual value will depend on the details of each lottery. Some lotteries may offer tickets that are worth less than 20% of their price, while others may be worth over 50%. To raise money, lottery operators must offer tickets worth much less than what one pays for them, so the lottery is a bad choice for customers trying to come out ahead.
In a famous occurrence, a Polish-Irish businessman named Stefan Klincewicz bought up almost all of the 1,947,792 combinations available on the Irish lottery. He and his associates paid less than one million Irish pounds while the jackpot stood at £1.7 million. There were three winning tickets, but with the "Match 4" and "Match 5" prizes, Klincewicz made a small profit overall.
There can be some problems associated with winning a lottery jackpot. There are security and safety risks associated with publicly announcing the lottery winners such as holding family members for ransom. In addition, Winners sometimes feel anomie from the dramatic change of lifestyles.
Scams and frauds
Lottery, like any form of gambling, is susceptible to fraud, despite the high degree of scrutiny claimed by the organizers.
Rigging the machine
One method involved is to tamper with the machine used for the number selection. By rigging a machine, it is theoretically easy to win a lottery. This act is often done in connivance with an employee of the lottery firm. Methods used vary; loaded balls where select balls are made to pop-up making it either lighter or heavier than the rest.
In some US states, such as Kansas and Minnesota, losing lottery tickets can be mailed in for a raffle of special prizes. The trouble with that is that employees of stores that sell lottery tickets sometimes collect the lottery tickets that are thrown away and send them in. As a lottery official put it, "the retailers have an unlimited supply of free tickets. You do not need to be an FBI agent to realize that is a tremendously unfair advantage."
Advance fee fraud
Some advance fee fraud scams on the Internet are based on lotteries. The fraud starts with spam congratulating the recipient on their recent lottery win. The email explains that in order to release funds the email recipient must part with a certain amount (as tax/fees) as per the rules or risk forfeiture.
Another form of lottery scam involves the selling of "systems" which purport to improve a player's chances of selecting the winning numbers in a Lotto game. These scams are generally based on the buyer's (and perhaps the seller's) misunderstanding of probability and random numbers. Sale of these systems or software is legal, however, since they mention that the product cannot guarantee a win, let alone a jackpot. Several companies offer a service where they will buy tickets for online clients in any of dozens of countries otherwise inaccessible to them, for a massive mark up, of many hundred per cent. Some national and international lotteries have residency and minimum age requirements.
There have also been several cases of cashiers at gas & convenience stores who have attempted to scam customers out of their winnings. Some locations require the patron to hand the lottery ticket to the cashier to determine how much they have won, or if they have won at all, the cashier then scans the ticket to determine one or both. In cases where there is no visible or audible cue to the patron of the outcome of the scan some cashiers have taken the opportunity to claim that the ticket is a loser or that it is worth far less than it is and offer to "throw it away" or surreptitiously substitute it for another ticket. The cashier then pockets the ticket and eventually claims it as their own.
Lotteries in popular culture
In George Orwell’s novel 1984, in Oceania there are frequent large lotteries and the proles buy lottery tickets hoping for a big win. The relevant section of the book hypothesizes that the "large winners" are amongst the things manufactured with Party propaganda. Lotteries are also a popular theme in film and television fiction.
Notable prizes on different continents are:
Lottery Country Winner Date Notes $ 390 million Mega Millions United States Won by one ticket holder from New Jersey and one from Georgia. 6 March 2007 World's largest jackpot € 185 million or £161 million EuroMillions United Kingdom Colin and Chris Weir 12 July 2011 Europe's largest jackpot ₱ 741 million Grand Lotto 6/55 Philippines One ticket holder from Olongapo City 29 November 2010 Asia's largest prize (€13m) R$ 195 million Mega-Sena Brazil Four winners 31 December 2010 South America's largest prize AUS$ 106 million OZ lotto Australia Two winners 30 June 2009 Australia's highest
Payment of prizes
Winnings (in the U.S.) are not necessarily paid out in a lump sum, contrary to the expectation of many lottery participants. In certain countries, mainly the U.S., the winner gets to choose between an annuity payment and a one-time payment. The one-time payment (cash or lump sum) is a "smaller" amount than the advertised (annuity) jackpot, even before applying any withholdings to which the prize is subject to. While withholdings vary by jurisdiction and how winnings are invested, it is suggested that a winner who chooses lump sum expects to pocket 1/3 of the advertised jackpot at the end of the tax year. Therefore, a winner of a $100,000,000 jackpot who chooses cash can expect $33,000,000 net after filing income tax document(s) for the year in which the jackpot was won.
Lottery annuities often are for a period from 20 to 30 years. Some U.S. lottery games, especially those offering a "lifetime" prize, do not offer a lump-sum option.
In some online lotteries, the annual payments are only $25,000, with a balloon payment in the final year. This type of installment payment often is made through investment in government-backed securities. Online lotteries pay the winners through their insurance backup. However, many winners choose lump sum, since they believe they can get a better rate of return on their investment elsewhere.
In some countries, lottery winnings are not subject to personal income tax, so there are no tax consequences to consider in choosing a payment option. In Canada, Australia, Germany, Ireland, Italy, and the United Kingdom all prizes are immediately paid out as one lump sum, tax-free to the winner. In Liechtenstein, all winnings are tax-free and the winner may opt to receive a lump sum or an annuity with regard to the Jackpot prizes.
In the US, federal courts have consistently held that lump sum payments received from third parties in exchange for the rights to lottery annuities are not capital assets for tax purpose. Rather, the lump sum is subject to ordinary income tax treatment.
Rollovers and Roll Downs
When there is no winning ticket for a lottery then the prize is said to Rollover to the following week leading to notable increases in prize funds. If a lottery hits a certain threshold of Rollovers then the total prize fund becomes automatically payable and is paid to the lower tier of winners. In the case of the Euromillions lottery the draw of 22 September 2007 lead to a total of 20 winners sharing a Roll Down jackpot of € 180 million or $230 million
In 2011, it was reported that Joan R. Ginther, a statistics professor, had won four different multi-million dollar jackpots from purchasing scratch-off lottery tickets in Texas. It was speculated that there was actually a pattern to where and when the winning tickets were sold, and that Professor Ginther had figured out this pattern.
- Betting pool
- Combinatorial number system
- Gaming mathematics
- GTech Corporation
- Lotteries by country
- Lottery payouts
- Lottery Wheeling
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