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# rules of the lottery

## Lotteries

A lottery is a type of gambling where people buy tickets, and then win if their numbers get chosen.

A “lot” is something that happens by chance. You may have heard people say “let us decide by drawing lots” or “so that is my lot”.

### Rules

Different Lotteries have different rules.

Here we will use a typical lottery where the player chooses 6 different numbers out of 49.

#### Example:

You enter the lottery by buying a ticket and selecting your six numbers.

You choose: 1, 2, 12, 14, 20 and 21

On Saturday they draw the lottery, and the winning numbers are:

3, 12, 18, 20, 32 and 43

You matched two of the numbers (12 and 20):

• Is that enough to win you anything? No.
• Usually you must match at least three numbers to get a small prize.
• Matching four numbers gets a bigger prize,
• Matching five is even bigger.
• But if you match ALL SIX of the numbers you might win millions.

The chances of winning all 6 numbers is 1 in 13,983,816 (calculated below).

### Choosing Numbers

These might win.

The numbers don’t know what they are!

A Lottery is just as likely to come up “1,2,3,4,5,6” as “9,11,16,23,27,36”

Instead of numbers they could be symbols, or colors, the lottery would still work.

In fact the result below really happened (Florida Fantasy 5 on 21 March 2011):

So it doesn’t matter what numbers you choose, the chances are all the same.

### More Likely Numbers?

So you have read that some numbers come up more often than others? Well of course they do, that is random chance.

The people who run lotteries have strict rules to stop the “rigging” of results. But random chance can sometimes produce strange results.

For example, using The Spinner I did 1000 spins for 10 numbers and came up with this:

Wow! 7 came up 115 times,
and 8 only 81 times.

Does this mean 7 will now come up more often, or less often? In fact it doesn’t mean anything, 7 is just as likely as any number to get chosen.

Try it yourself and see what results you get.

### Popular Numbers

But there is a trick! People have favorite numbers, so when popular numbers come up you are sharing the winnings with lots of people.

Birthdays are popular choices, so people choose 1-12 and 1-31 more often. Also lucky numbers.

So maybe you should choose unpopular numbers so when you DO win you get more money.

(This assumes your lottery is one where prizes are shared among winners.)

### Regret

Don’t choose the same numbers every week. It’s a trap! If you forget a week you then worry that your numbers will come up, and this forces you to buy a ticket every week (even when you have other more important things to do).

Make a list of many unpopular numbers.
Choose randomly from this list every time.

### Syndicates

A “Syndicate” is a group of people who all put in a little money so the group can buy lots of tickets. The chance of winning goes up, but your payout each time is less (because you are sharing).

Syndicates can be fun because they are sociable . a way of making and keeping friendships. Plus some syndicates like to spend small winnings on everyone going out for a meal together.

Another good reason for joining a syndicate is that your chances of winning go up (but what you win goes down).

Think about it . winning Ten Million would really change your life, but One Million would also improve your life a lot. You might prefer ten times the chance of winning one million.

### Chance Of Winning the Big Prize

OK. What are the chances of you winning the big prize?

The chances of winning all 6 numbers is 1 in 13,983,816

You can use the Combinations and Permutations Calculator to work it out (use n=49, r=6, ‘No’ for Is Order Important? and ‘No’ for Is Repetition allowed?)

The actual calculation is this:

49 C6 = 49!/(43! x 6!) = 13983816

So how many times do you need to play to win?

#### 1 Week

Suppose you play every week

The probability of a win after 1 week is:

1 13983816 = 0.0000000715.

So the probability of no win after 1 week is:

1 в€’ 1 13983816 = 0.9999999285.

#### 50 Years

Let’s say you play for 50 years, that’s 2,600 weeks.

The probability of no win over 2,600 weeks is:

( 1 в€’ 1 13983816 ) 2600 = 0.999814.

That means the probability of winning (after 50 Years) is: 1 в€’ 0.999814. = 0.000186.

Still only about 0.02%

And you would have spent thousands for that small chance.

You may have had some good holidays for that money.

BUT it IS fun thinking “I just may win this week!”

Just keep it as a fun thing to do, OK?

### Your Turn

• Find out the rules for winning Lotto in your area.
• How many numbers do you have to choose and how many numbers do you choose from?
• Calculate the probability of winning in any one week.
• Calculate the probability of winning if you play every week for 50 years.
• How much money would you save by not playing? What can that money buy?

A look at lotteries from a mathematical viewpoint.

## Rules of the lottery

Graphic courtesy Nebraska Lottery
Lotteries/Lotto rules and how to play:

(For Powerball rules, payoffs, odds, power play option see Powerball.)

Each national/state lottery has its own rules and they are usually published on their websites. When visiting a lotto or lottery website, look for a link titled ‘Lottery rules’, ‘Lotto rules’, ‘Rules’ or ‘Regulations’.

Below are some basic lottery rules or regulations, and how to play the game, and game summary. For lottery tips, books, results and other links, see the ‘ Topic Menu ‘ on the right.

Choose six Numbers from 1 to 49. Six Numbers are drawn plus a bonus Number, out of 49 numbered balls. Match all 6 Numbers to win the jackpot. Match 5 Numbers and the bonus Number to win the second highest prize. Match five, four or three Numbers to win smaller prizes.

How to play the lottery

First, mark six numbers on any individual lottery board , lottery ticket , or lottery playslip, play slip . On some lottery tickets or playslips you can play with more than one set of numbers. You can also buy tickets without completing a playslip. You let the computer terminal choose your six-number combinations at random.

Where applicable, check ‘which draw’ you are playing and mark it as appropriate on your Lotto/Lottery ticket/playslip.

Some tickets/playslips let you play the same numbers for more than one week (for several draws). You need to mark the appropriate section accordingly. You will only receive one ticket, but your numbers will be entered for the draw-days and number of weeks selected.

Take your completed lottery ticket/playslip to your retailer or lottery terminal. They will enter your selections into the terminal and give you a Lotto/Lottery Game ticket. You are responsible for checking that the information it contains is correct – your numbers, the days you wish to play, the number of weeks and the draw date(s).

Where applicable, you must also check that the bar-coded serial number on your ticket is clearly readable and that the ” Void ” box has not been marked. Keep your ticket safe. You’ll need it to claim your prize, as it is the only proof that you are a winner. It is recommended that you put your name and address on the reverse of the ticket for security purposes.

If the six-number Lottery/Lotto Game selections on your ticket matches the main six numbers drawn in the relevant Lottery/Lotto Game draw – in any order – you are a jackpot winner . You may have to share the jackpot with other winners. You can also win by matching five, four or even three main numbers out of six. Look out for the seventh ‘bonus number’ drawn. If you have matched five numbers already, matching the bonus number will win you the second highest prize.

Basic lottery game rules or regulations for popular Lotteries

• You must be 16/18/21 years of age or older to buy Lottery tickets and claim prizes.
• Players are responsible for checking their tickets before leaving the Retailer location.
• A ticket is void if stolen, unissued, mutilated, illegible, tampered with or altered in any way, defective or incomplete.
• The Lottery is not responsible for lost or stolen tickets.
• A Lotto/Lottery ticket may be cancelled only if presented before the drawing to the Retailer where it was originally purchased. Powerball tickets cannot be cancelled.
• Multi-drawing bets on the same number(s) may be made in advance for all games. Ask Retailer for details.
• You must fill in your name, address and phone number on the back of your winning ticket before you file a prize claim.
• All winning tickets are subject to validation by the Lottery.
• All winning tickets are bearer instruments.
• All prizes must be claimed within 6 months/one year from date of drawing.

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