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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.

Lottery’s luckiest choices revealed

Most Popular Today

January 24, 2010 | 5:00am

Lottery lovers, we’ve got your numbers.

If you have a dollar and dream — and believe you can beat the odds — start with 14, 36 and 48.

Those three numbers have hit more than any others among the 414 winning Mega Millions tickets sold between 2005 and Jan. 12.

And since June 24, 2005, when the latest version of the game launched, they’ve appeared on the winning six-number combinations the most often.

That’s according to an analysis of Mega Millions payouts compiled by Matthew Vea, a consultant in Ernst & Young’s financial services department in Midtown, who looked at the results of every drawing over the last 4½ years.

The game encourages players from 12 states, including New York and New Jersey, to plunk down a dollar in the hope of becoming fabulously wealthy.

A player’s six picks must match the numbers that come up when officials randomly draw a half-dozen balls numbered 1 to 56.

With odds of more than 175 million to 1, jackpots routinely reach hundreds of millions. The record payout was $390 million in 2007. Tuesday’s jackpot is an estimated $121 million.

The number 14 is a big winner.

Not only has it appeared on 48 of the 414 winning tickets since 2005 (a rate of more than 11 percent), it’s been the second-hottest number during the last three months, averaging just 30.2 days between appearances on somebody’s lucky ducat, Vea’s analysis shows.

The number 36 also popped up 48 times since 2005, while 48 appeared 47 times. Three others — 53, 5 and 46 — hit 46 times.

Experts caution that every drawing is random, so playing “hot” or “cold” numbers is, statistically speaking, still a losing proposition.

“It’s perfectly natural that in a small sample size, 414 drawings, that you would have a [hot] number,” said NYU math professor Gerard Ben Arus. “But of course if you get a huge sample size, tens of thousands, it would equal out.”

The most popular numbers chosen by players for New York’s Numbers and Win 4 games are 111 and 0000, lottery organizers say.

After 111, the next most popular Numbers choice is 222, followed by 333, 777 and 999.

Among Win 4, they are 1111, 2222 and 3333.

Officials said that news events sometimes spur a run on numbers, such as 911, which sells out every year on Sept. 11, and 1549, the number of the US Airways flight that hero pilot Chesley “Sully” Sullenberger safely landed in the Hudson River a year ago.

Omen numerals

A consultant at Ernst & Young studied the numbers picked for the Mega Millions lottery since 2005. The results:

Most frequent winning numbers

14 On 48 winning tickets — 11.6%

36 On 48 winning tickets — 11.6%

48 On 47 winning tickets — 11.4%

Least frequent winning numbers

47 On 23 winning tickets — 5.6%

6 On 25 winning tickets — 6%

49 On 26 winning tickets — 6.2%

OTHER US LOTTERIES

The hottest numbers in 107 state lottery drawings nationwide between Jan. 7 and Jan. 13 this year:

20, 23, 30, 42, 7, 32, 16

Most popular numbers picked by players:

111, 222, 333, 777, 999

Most popular numbers picked by players:

1111, 2222, 3333

OTHER POPULAR NUMBERS

911 Sells out every Sept. 11 and won in 2002

1549 The number of the US Airways flight that splash-landed in the Hudson

Lottery lovers, we’ve got your numbers. If you have a dollar and dream — and believe you can beat the odds — start with 14, 36 and 48. … ]]>