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Running a lottery, for beginners

To appreciate why Lottery formats are what they are, consider how you would design an ongoing Lottery from scratch. Your aim is to maximise the total profit, within the legal constraints that all tickets are treated equally.

Lottery Formats

It is reasonable to assume that the more attractive your game, the higher the gross income. Experience indicates that the single feature that attracts players is the possibility of winning an enormous sum of money. The actual chance of winning seems to be relatively unimportant. If you sell enough tickets, even though each one has a remote chance of winning a life-changing sum, it is likely that someone will win. And that is enough to establish the possibility as real. Another observation is that many players like to win something from time to time (even just a free entry to the next lottery), to keep their interest up.

If N tickets are sold, each costing one unit of currency (a pound or a dollar, say), and a fraction f of this sum is returned as prize money, then the profits will be (1-f)N (less costs and any taxes imposed). The choice of f must be large enough to generate the potential of a very large prize, but also small enough to leave a worthwhile profit. As well as fixing f, how the prize money should be divided among larger and smaller prizes must be decided. The value of N will depend on the size of the target population, and the attractiveness of the game (in which the value of f will play a role).

Modern lotteries that have proved successful include three main formats: the Genoese type (with variations); Keno games; and Numbers games. Within any of these formats, there is a another choice: shall all winners at a given level get a fixed sum, or shall they have equal shares in a total amount allocated to that level? (In horse-race betting, both alternatives, bookmakers offering fixed odds, and the Tote using a pari mutuel system, operate in parallel.) The very highest prizes arise in lotteries that offer pari mutuel payouts.

The Genoese format

In the principal game offered in the UK, players select six numbers from a list of 49 numbers; then six (winning) numbers are selected at random from this list, and players win prizes according to how many of the winning numbers they have chosen (see The UK National Lottery – a guide for beginners in issue 29 of Plus). This is the Genoese format, named in honour of lotteries used in Genoa in the Middle Ages. A game in this family will be written m/M; the UK game is 6/49.

The choice of m=6 and M=49 is also found in Canada, Germany, South Africa and a number of states in the USA. The m/M format offers great flexibility. The chance that a player chooses all the winning numbers, usually also the chance of winning a share of the maximum prize – a jackpot – is p=1/ M Cm. Fine-tuning of the choices of M and m enables p to be close to any desired quantity. For example, 32 C6=906,192, 33 C6=1,107,568, suggest lotteries whose winning chances are either side of one in a million. Taking m=6 and M=49 gives p close to one in 14 million, and the Michigan Rolldown is 5/33, with p just over one in 250,000.

Choosing your format

If you expect to sell only about half a million tickets at £1 each, the jackpot prize cannot be enormous; and a 6/49 format here would mean that the top prize would be won rarely – once every 28 games. With such a remote prospect, interest might well evaporate quickly. The games offered reflect the sizes of the target populations.

But suppose the overall chance that nobody wins the jackpot is round about one in four, and the jackpot amount is shared equally among all who qualify – the pari-mutuel version. Then the trick of carrying unwon prize money forward to the next Lottery (a rollover) can boost the jackpot size, thereby enhancing the attractiveness of the next draw. Greater sales there increase the chance that this larger prize is actually won, reinforcing future sales. The UK Lottery has another method of tempting punters – the Superdraw, where extra money is added to the jackpot prize. (Although f=50% of ticket sales will eventually be returned as prize money, the amount allocated to immediate prizes is just 45% of that draw’s sales; the other 5% is accumulated for these special occasions.)

Variations on this Genoese lottery give convenient ways of tweaking the chances of winning. For example, in addition to selecting m numbers from M, players may be asked also to select one or more numbers from a separate list of K numbers. Jackpot winners are those who match all winning numbers in both categories. Powerball, played across 24 states in the USA, currently asks players to select five numbers from 53, and one other (the Powerball) from a separate list of 42, giving 53 C5=120,526,770 different choices available.

This means the winning chance is so small that, despite the large number of players, rollovers are frequent: the potential jackpot can then exceed two hundred million dollars. The UK game, Thunderball, is a humbler affair, with fixed prizes: players choose five numbers from 34, and one from 14, so the chance of winning the top prize of is , just better than one in four million. A Kansas game asks players to choose two numbers from 26 White numbers, and also two from 26 Red numbers, which leads to one chance in 105,625 of winning the top prize in this state with a small population. Noting that , a game in which players chose four White numbers from 14, and also four Red numbers from 14 would give a winning chance trivially different from one in a million.

In all these formats, lesser prizes can be won by matching just some of the winning numbers. Statistically, the hypergeometric distribution is used to compute the chances of winning at any level. If there are winning numbers, losing numbers, and players select of these numbers, the chance they have exactly winning numbers is

provided only that the winning numbers are chosen at random.

Interestingly non-random

There is one other important factor to consider in designing a game: left to their own devices, players do not select all possible combinations with equal probabilities. Some types of choice – see The UK National Lottery – a guide for beginners in issue 29 of Plus – are far more popular than average, others less so. Because the draw itself is random, this skewness in player choice leads to MORE rollovers than a genuine random choice by players would give. As rollovers tend to increase sales, hence profits, it is in the Lottery designers’ interest that players tend to select some combinations far more often than others.

This point is illustrated by the experience of the New Zealand Lottery, where a large proportion of players use an official random choice facility. This tends to even out the choice frequencies, leading to very few rollovers, and a relatively predictable (and disappointing) jackpot.

Keno is often played for 16+ hours per day, with draws every few minutes. In its most common format, winning numbers will be selected at random from numbers, while players try to match some fixed number , say , of them. A prize might require at least of the player’s numbers to be among the winning numbers; the hypergeometric formula above will give the various winning chances.

Because of Keno’s frequency of play, the fixed prize format is the norm. Prizes associated with very low winning chances can be set at an eye-catching level, but with one proviso: if players are permitted to select their own numbers, their non-random choices could mean an occasional disaster for the Lottery, when too many of them all qualify for a large sum. As a form of risk control, it is prudent to specify a maximum amount that can be paid out on any one game.

The integrity of any lottery is vital. Genoese lotteries tend to use a physical device, such as numbered balls swirling round a transparent plastic tub; if this can be shown live on TV, so much the better. But Keno, like rapid-play internet gambling games, usually invokes the pseudo-random number generator of a computer. This is inherently dangerous: not only have some such generators been found to have severe flaws, but the possibility of corruption is plain.

To illustrate Keno, the Table shows the winning chances (rounded), and prize levels for unit stake, when players select 10 numbers in the Massachusetts (M, in red) and Washington (W, in blue) versions. Note the nod towards players who consider themselves unlucky — a prize is given for matching no numbers.

Number matched 0 5 6 7 8 9 10
Chances: 1 in 22 19.5 87 620 7,400 160,000 9,000,000
Payout(M) 2 2 20 80 500 10,000 100,000
Payout(W) 3 2 5 50 500 5,000 100,000

It may not be immediately clear which represents better value to the player: but on average, over 69% of stake money is returned in Massachusetts, under 49% in Washington. In a different gamble, cautious players may place bets on just one number, giving themselves one chance in four of winning: even here, Washington pays out only $2, while Massachusetts pays $2.50 to a winning one dollar stake. Some Lottery designers are far more generous than others!

In a standard Numbers Game, four (or sometimes three) digits are drawn independently, and in a definite order, from the list <0,1. 9>. There are thus 10,000 (or 1000) different possibilities. Players attempt to match all, or some, of the digits. This game is usually played with fixed payouts, with a mean return of about 50%, but the Massachusetts version is pari mutuel, and returns 60%. Working out the winning odds here is plainly straightforward. Players may “box” their bets, i.e. select the digits, without specifying their order. Thus boxing four different digits divides the stake among 24 outcomes, while boxing (say) 5,5,5,6 splits the stake among four outcomes.

Getting the numbers wrong

Lottery designers are generally careful in their approach, but some blunders have been made, even in modern times. In the Scramble Game in Canada in 1981, players would select six digits, (as in a Numbers game) and win a fixed sum if their selection matched the winning six-digit selection in any order. Thus, 123456 had 720 winning chances, whereas 222222 had just one chance! In another Canadian game in 1978-9, in which the digits 0 to 9 should have had equal chances of selection, an oversight meant that for each eight times a digit from 6 to 9 appeared, a digit from 3 to 5 would arise ten times, while digits 0 to 2 would arise eleven times. And the early rules of the Massachusetts Numbers game meant that players who restricted their bets to just three of the four numbers would obtain a higher mean return than players who bet on all four.

About the author

John Haigh is Reader in Mathematics and Statistics at the University of Sussex. His book, Taking Chances, (now translated into Spanish and Chinese, and in a second edition) aimed at helping the layperson understand ideas of probability, is an all-time Plus favourite. You can read our review in Issue 13.

Comments

Maths

Great article, but while discussing Powerball in the ‘choose your format’s section you said 53c5 is 120 million, which it’s not, I believe it should be 53c5 x 42.

May 2004 To appreciate why Lottery formats are what they are, consider how you would design an ongoing Lottery from scratch. Your aim is to maximise the total profit, within the legal constraints that all tickets are treated equally. Lottery Formats It is reasonable to assume that the more attractive your game, the higher the gross income. Experience indicates that the single

Running a raffle or lottery

Why is this important?

If you intend to run a lottery, prize competition or free draw for charitable purposes you need to follow any gambling regulations that may apply, including laws relating to the process of allocating prizes fairly. The regulation tends to refer to all these activities as lotteries.

A typical small-scale lottery is a raffle where players buy a ticket with a number on it. The tickets are randomly drawn and those holding the same numbered ticket win a prize.

Another version is a sweepstake, for example, where the participants pay to randomly draw the names of a horse in a race. The person who draws the winning horse wins a stated proportion of the entry money with the remainder (usually 50%) going to the good cause.

There are other versions too, including:

  • a tombola – often found at a funday or summer fete
  • a 100 club which is often a weekly event organised, for members only, perhaps by a local Versus Arthritis branch.

There is no maximum price for a ticket, in each lottery all tickets must cost the same. That way everyone has the same chance of winning for the same outlay. Incidental lotteries are the exception to this rule and do not have specific ticket requirements.

What exactly is a lottery?

A lottery is a kind of gambling which has four essential elements:

  1. You have to pay to enter the game.
  2. There is always at least one prize.
  3. Prizes are awarded purely on chance.
  4. All tickets must cost the same (with the exception of incidental lotteries).

What type of lottery am I running?

Incidental lotteries

Tombolas, lotteries and raffles held at events which are held as part of a fundraising event are referred to as ‘incidental lotteries’ and don’t need a licence or permission from any authority (although you should get permission from the event organiser or site owner).

All tickets must be sold at the location/time of the event but the draw can be at the event or after it has finished. Promoters of the lottery may deduct from the proceeds of the lottery no more than £100 for expenses and no more than £500 spent on prizes (other prizes may be donated). There are no rollovers.

There are also two other types of lottery for which you do not need permission, outlined below.

Private society lotteries

These must raise money for the purposes for which the society is conducted or to raise funds to support a charity or good cause. They can only be promoted by authorised members of a society and each person to whom a ticket is sold must either be a member of the society or on premises wholly or mainly used for the administration of the society. There are no rollovers.

Work lotteries/residents’ lotteries

This category is only for colleagues who work at, or people who live on, the same single set of premises*. No rollovers are allowed. These must either:

  • make no profit (i.e. all the proceeds are used for reasonable expense and prizes)
  • raise funds for a charity or good cause (e.g. Versus Arthritis).

*Single set of premises

This term does not include multiple sites. For example a company with premises in more than one location would not be able to sell tickets for a single work lottery across all of their premises.

If you’re not running an incidental, work or private lottery then you’re going to be running a society lottery

Society lotteries are categorised as either small or large.

Small society lotteries

As a rule of thumb if you’re printing and selling tickets to the general public outside of a specific workplace or residence then you’re running a small society lottery.
The official requirements are that:

  • proceeds do not exceed £20,000 for a single draw
  • proceeds do not exceed £250,000 in a calendar year.

Small society lotteries do not require a licence but must be registered with the local authority in the area where you’re operating.

Details of registration requirements and procedures should be available from the licensing department of the relevant local authority.

Large societies lotteries

If you think your raffle or lottery is likely to exceed £20,000 in a single draw or over £250,000 in a single year please contact the local fundraising team for further guidance.

Ticket requirements

There are specific guidelines for what your tickets need to show based on the type of lottery that you’re running.

Incidental lottery

A ticket must be provided but there are no specific requirements for tickets (e.g. you could use cloakroom tickets).

Private/ residential or work lottery

A ticket must be provided but there are no specific requirements for tickets. The price payable for each ticket must be the same and the rights created by the ticket are non-transferable.

Small society lottery

Tickets must show:

  • the name of the society or local authority
  • the ticket price
  • the name and address of the organiser
  • the date of the draw.

Age restrictions

At an incidental lottery you can sell tickets to anyone attending the event, however, if the prizes include alcohol you must not give alcohol as a prize to anyone under 18.

If you’re running a private/work/residential or small society lottery you must not sell tickets to anyone under 16.

The draw

The draw must be witnessed and you should make a record of the result. With an incidental lottery this can be done by making the draw during the event.

For other lotteries you should record the results and make them available if people request to see them.
You must include all paid-for, valid ticket entries in the draw.

For non incidental lotteries, if you’re going to transfer late entries to the next draw, you must be clear about this when you sell the ticket.

Again for non incidental lotteries if, for any reason, the draw date needs to be delayed from that shown on the ticket, you must take all reasonable steps to make sure that everyone who has bought a ticket knows about the change and you must discuss it with the issuer of the licence.

After the draw (this applies to small society lotteries and residential/work/private lotteries)

You must return all filled-in ticket stubs and payments to the named promoter for audit purposes.

If the owner of a winning ticket donates their prize back to a society, this must be shown in your lottery’s accounting records as a donation.

You must not make details of winners public without their permission.

You must not make public the details of winners in a way that will identify them i.e reveal their name and address or name and telephone number.

You must contact all winners within seven days of the draw.
You must make all reasonable efforts to award prizes to the holders of winning tickets.

Handling the cash you have raised through your raffle or lottery

Keep safe when handling money by following these guidelines:

  • Do not leave unsecured cash unattended.
  • Count your money raised in a secure place not in the open.
  • Wherever possible, ensure all cash collected in counted and recorded by two unrelated people.
  • Ensure cash donations are collected in sealed containers/ collecting tins.
  • Open collecting tins yourself with another person unrelated to you.
  • Bank the money from collections as soon as possible by sending it to Versus Arthritis in the full amount without taking fees/expenses. You can bank money into your personal account and send a bank transfer or cheque to Versus Arthritis.

Risk assessing your activity

The fundraising regulations state that you should carry out and record a risk assessment of any fundraising activity and this includes raffles and lotteries.

Risk assessments are a way of recording the potential for things to go wrong at an event and what you can do to stop that happening. They’re a useful part of your event planning, often working as an event checklist. Some venues or insurers may ask to see a risk assessment.

You can call the Events team on 0300 790 0402 for support.

Handling personal data

In the process of running a raffle or lottery you may find yourself processing personal data, such as contact details.

As a charity we take the protection and processing of people’s data very seriously. Check out our privacy policy to see how we handle data.

As a fundraiser you’re likely dealing with personal data. Only collect data you need, do not share this data and only keep the data for as long as you need it.

Things to keep in mind:

  • Only collect data you need.
  • Store data safely by keeping hardcopies in a cupboard and password protecting electronic copies.
  • Destroy data you don’t need.
    Remove data upon request or in case of data of deceased individuals.

Protecting personal data ensures people can trust fundraisers to use their data legally, fairly and responsibly.

Certain special category data such as information about religion, race or health might have stronger protections. We see no valid reason for fundraisers to hold any special category data and we would ask you not to do this.

If you're running a raffle or lottery you must make sure it's legal. Read the guidelines for ticket requirements, age restrictions and types of lottery. ]]>