*For other articles concerned with Lotteries see Lottery (disambiguation)*

A **lottery** is a popular form of gambling which involves the drawing of lots for a prize. Some states forbid it, while others endorse it to the extent of organizing a *national lottery*.

## Countries with a national lottery

etc.

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.

Lotteries are most often run by governments 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 epithet of a "tax on stupidity". The phrase is largely rhetorical (playing the lottery is voluntary; taxes are not), but it is intended to suggest that lotteries 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 a 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. Playing the lottery certainly does not prove stupidity, but neither is it an act of economic rationality.

## Lottery in the United States

In the United States, the existence of lotteries is subject to the laws of each state; there is no national lottery. The first state lottery in the U.S. was established in the state of New Hampshire in 1964; today, lotteries are established in forty states and the District of Columbia. On October 8, 1970, New York held the first million dollar lottery drawing.

The first modern interstate lottery in the U.S. was Tri-State Lotto. Tri-State Lotto was formed in 1985 and linked the states of Maine, New Hampshire and Vermont. In 1988, the Multi-State Lottery Association was formed with Oregon, Iowa, Kansas, Rhode Island, West Virginia and the District of Columbia as its charter members; it is best known for its "Powerball" drawing, which is designed to build up very large jackpots. Another interstate lottery, The Big Game (now called Mega Millions), was formed in 1996 by the states of Georgia, Illinois, Massachusetts, Maryland, Michigan and Virginia as its charter members.

Other interstate lotteries include: Hot Lotto, Lotto South, and Wild Card 2. *For more detailed information on U.S. lotteries, see* Lottery (U.S.)

With the advent of the internet it became possible for people to play on-line, many times for free (the cost of the ticket being supplemented by merely seeing, say, a pop-up ad). Slight wanings in the overall number of people playing by "traditional" ways (paper ticket, $1 per chance) caused several states to combine into multi-state pools of much larger winning amounts. Some of the many websites which offer free games (after registration) include www.iwinweekly.com and the larger iwon.com, which is backed by the CBS broadcasting corporation.

See also: Keno

## Lottery in Canada

The first lottery in Canada was Quebec's Inter-Loto in 1970. Other provinces and regions introduced their own lotteries through the 1970s, and the federal government ran Loto Canada in the late 1970s before getting out of the lottery business.

Today, Canada has two national lotteries: Lotto 6/49 (which started in 1982), and Lotto Super 7 (which started in 1994). These games are administered by the Interprovincial Lottery Corporation , which is a consortium of the five regional lottery commissions, all of which are owned by their respective provincial and territorial governments:

All five regional corporations offer additional regional lotteries that are played only in their respective regions.

## Lottery in France

The first known lottery in France was created by King Francis I in or around 1505. After that first attempt, lotteries were forbidden for two centuries.

They reappeared at the end of 17th century, as a "public lottery" for the Paris municipality (called *Loterie de L'Hotel de Ville*) and as "private" ones for religious orders (mostly for nuns in convents).

Lotteries became quickly one of the most important ressources for religious congregations in the 18th century.

Lotteries helped to build or rebuild many churches (about 15 including the biggest ones) in Paris during the 18th century, including St Sulpice and Le Panthéon.

At the beginning of the century, the King avoided having to fund religious orders by giving them the right to run lotteries, but the amounts generated became so large that the second part of the century turned into a struggle between the monarchy and the Church for control of the lotteries. In 1774, the *Loterie de L'École Militaire* was founded by the monarchy (by Mme de Pompadour to be precise, to buy what is called today the *Champ de Mars* in Paris, and build a Military Academy that Napoleon Bonaparte would later attend) and all other lotteries, with 3 or 4 minor exceptions, were forbidden.

This lottery became known a few years later as the *Loterie Royale de France*. Just before the French Revolution (1789) the revenues from La Lotterie Royale de France were equivalent to between 5 and 7% of total French revenues.

Throughout the 18th century, philosophers like Voltaire as well as some bishops complained that lotteries exploit the poor. This subject has generated much oral and written debate over the morality of the lottery.

All lotteries (including state lotteries) were frowned upon by idealists of the French Revolution, who viewed them as a method used by the rich for cheating the poor out of their wages.

The Lottery reappeared in France in 1936, called *loto*, when socialists needed to increase state revenue. Since that time, *La Française des Jeux* (government owned) has had a monopoly on most of the games in France, including the lotteries.

## What are my chances of winning a Lottery jackpot ?

The simple answer is: vanishingly small!

The chances of winning a lottery jackpot are principally determined by several factors: the count of possible numbers, the count of winning numbers drawn, whether or not order is significant and whether drawn numbers are returned to the 'bag' or not.

In a typical 6/49 lotto, 6 (k) numbers are drawn from a range of 49 (n) and if the 6 numbers on your ticket match the numbers drawn, you are a jackpot winner - this is true no matter the order in which the numbers appear. The odds of this happening by the way are 1 in 14 million (13,983,816 to be exact). So, why are the chances of winning so slim ?

Let's work through an example. If you start with a bag of 49 differently-numbered lottery balls, clearly you have a 1 in 49 chance of predicting the number of the 1st ball out of the bag. Looking at it in a different light, there are 49 different ways of choosing that first number. When you come to draw the 2nd number, there are now only 48 balls left in the bag (in case of no return of the drawn balls to the bag), so you have a 1 in 48 chance of predicting this number (i.e. there are 48 different ways of choosing that second number).

Thus, each of the 49 ways of choosing the first number has 48 different ways of choosing the second. This means that the odds of correctly predicting 2 numbers drawn from 49 is calculated as: 49 x 48. On drawing the third number you only have 47 ways of choosing the number; but of course you could have gotten to this point in any of 49 x 48 ways, so the chances of correctly predicting 3 numbers drawn from 49 is calculated as: 49 x 48 x 47. And so it goes on until the sixth number has been drawn, giving the final calculation: 49 x 48 x 47 x 46 x 45 x 44 (also written as 49! / (49-6)!). This works out at a really scary number (10,068,347,520) but clearly a whole lot bigger than the 14 million we were talking about above. So how do we get to that final figure of 1 in 13,983,816 ?

The last step we need to take is to understand that the order of our 6 numbers is not significant. That is, if your ticket says 01 02 03 04 05 06, then you'll be popping the champagne so long as all the numbers 1 through 6 are drawn, no matter what order they come out. To put it another way, given any set of 6 numbers, there are 6 x 5 x 4 x 3 x 2 x 1 = 6! = 720 ways they could be drawn. Dividing 10,068,347,520 by 720 gives **13,983,816**, also written as 49! / (6!·(49-6)!), or more generally as

- .

To put this number in context, let's say that you're immortal and are going to play 1 ticket with the same numbers every week forever. Since 13,983,816 weeks is roughly 269,000 years you probably would win the jackpot only **once** in your first quarter-million years! To add insult to injury, your heroic patience and faithful play over the millennia will be cruelly rewarded, for you probably will have spent two to three times more money buying tickets than you will receive at long last with your one jackpot win.

Alternatively, imagine a computer randomly drawing 6 lottery numbers every second of every day. Starting it off at 1 second past midnight on January 1st, you would have to wait until 8:23pm on June 11th before it had executed 13,983,816 times. That is, picking the 6 winning numbers is as hard as picking a single second out of more than 5 months!

**Note 1: your lottery mileage may vary.** The odds of winning your favorite lottery just might be better than in this example, but given the trends in lottery design your odds may well be worse. Possibly **much** worse. For instance, "Powerball" (see above) is a very popular multistate lottery in the United States which is known for jackpots that grow obscenely large from time to time. This attractive feature is made possible simply by designing the game to be diabolically difficult to win: 1 chance in 120,526,770. That's almost nine times **worse** than the already depressing example above, the result of a design that is somewhat more complex. Powerball players also pick six numbers, but two different "bags" are used. The first five numbers come from one bag that contains numbers from 1 to 53 (the order doesn't matter). The sixth number -- the "Powerball number" -- comes from the second bag, which contains numbers from 1 to 42. When the drawing is held, your first five numbers must match the first five drawn **and** your Powerball number must match the Powerball number drawn, or else you fail to win the jackpot. 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 you had all the right numbers, the Powerball number at the end of your ticket doesn't match the one drawn, so you would be credited with matching only four numbers (10, 25, 33, 42).

**Note 2: the jackpot is usually not the only prize.** Most lotteries give lesser prizes for matching just some of the winning numbers. The Powerball game described above is an extreme case, giving a very small payout (US$3) even if you match only the Powerball number at the end of your ticket. The odds of doing this are refreshing: 1 in 70. Match more numbers and 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 they add a little to the value of the ticket.

## See also

Last updated: 05-13-2005 07:56:04