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how many lottery tickets can you buy at one time

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.

One Thing You MUST Do to Win Big With Lottery Scratchers

A Legit Way to Boost Your Odds of Hitting a Scratch-Off Jackpot

Matthew Horwood / Getty Images

Are you planning on buying some lottery tickets for yourself or as a gift for a loved one? If you pick up lottery scratchers at your local convenience store or gas station, you know that you’re probably going to end up winning no more than a buck or two, maybe $20 if you’re lucky. But of course, you hope to win one of those big jackpots with an advertised value of $10,000, $50,000, or more.

But did you know that there’s a chance that you could buy a scratcher ticket that advertises a big grand prize — and have absolutely no chance of winning that prize? Would you still buy that scratch-off ticket if you knew the odds of winning more than a few bucks weren’t just low but zero? Especially if other games had better chances of a jackpot payout?

Before you buy a lottery scratcher, you must do one important thing: research which game you are going to play.

Why You Need to Do Research on Lottery Scratchers

Lottery scratchers are distributed to retailers in large rolls, and each roll is guaranteed to have a certain number of winners. Those winning scratch-off prizes will have values, some smaller, some bigger.

The lottery scratchers usually advertise grand prizes like a “$1 Million Merry Millions” jackpot. But unless the game has just been released, there’s a chance that someone else had already won that jackpot.

If the winning scratch-off ticket has already been redeemed, the lottery knows that the big prize is gone, but they still sell tickets to that game because smaller prizes are still available.

Nothing prevents the lottery from legally selling those tickets, even if it involves advertising a prize that’s no longer available.

Not fair? Well, even if the grand prizes are gone, there may still be attractive prizes available to you. But if you don’t want to settle for a smaller win, a little bit of research will ensure that you have the best chances of winning a grand prize.

How to Research Your Lottery Scratchers

To make buying lottery tickets more attractive, the state lottery websites publish information about which scratch-off prizes are still available. While there’s a small chance that someone has bought a winning ticket but hasn’t redeemed it yet, checking the lottery website before you buy gives you the best odds of a big win.  

Here’s how to find the information you need:

  • Visit the lottery website for the state where you’re buying the tickets
  • Look for the scratchers or scratch-off section
  • Look for a break-down of all the different games and the prizes they have remaining
  • Pay attention to when the records were last updated. If you can, try to buy shortly after the lottery releases an update so you’re using the most recent information.

Once you know which prizes are still available, you can decide which game you want to play based on factors like the ticket price, the size of the prizes being offered, and how many prizes are still available.

What If You Can’t Check the Website?

If you’re buying tickets spontaneously or you don’t have access to the internet, you might not be able to check the state lottery’s website. So what can you do to boost your odds of choosing a big winner?

First, you’ll want to look at the odds of winning versus the payout.

A rough rule of thumb is that scratchers that cost more money have better odds of winning and higher prize payouts.

If you have time to do a quick calculation, you can also use the risk to reward ratio to calculate where your best chances lie.

Another thing you can do is to look for games that offer a guaranteed winner per roll of tickets. This means that somewhere in the roll, there is a winning ticket (although it won’t tell you whether it’s been claimed or not).

Next, you can ask which number the next ticket on the roll has before you buy. Although this may vary by state, rolls are often numbered sequentially starting with 000, so if the ticket number is low, it’s less likely that one of the winning tickets from that roll is already gone.  

If you find a low-numbered roll with a guaranteed prize, you might want to buy a series of tickets from that roll. Each non-winning ticket you buy from the same roll gets you, theoretically, closer to a winning ticket. Switching games, however, means that the losing tickets won’t necessarily bring you any closer to a winning ticket.

Controversial – but successful – lottery player Richard Lustig recommends always buying at least 10 tickets from the same roll to improve your odds.

Finally, you can ask the store clerk whether they’ve had a recent win from that roll. The clerk might not know, or might not be willing to answer. But if they do say that they’ve had a winner recently, your odds might be better if you pick a different game.

By taking a bit of time to strategize before you buy, you can raise your odds of winning a jackpot through a lottery scratch-off.

If you buy lottery scratchers hoping to win big prizes, you're setting yourself up for disappointment if you don't do this one thing first.