Lottery 101: Winning The Biggest Prize of All



Challenging Assumptions


Sometimes it’s worth challenging our basic assumptions.  Take the lottery for example. Let’s say you buy $7 worth of lottery tickets every week.  Clearly, the decision to buy a ticket falls under Webster’s definition of gambling. (i.e. you are putting your money down on an uncertain outcome).  Of course, when you gamble your intention is to come out ahead, but the real hope is to win the big prize.  You might even picture holding one of those huge checks as you collect your winnings, before driving away in a brand new BMW.


Somebody’s Gotta Win.  It Might As Well Be Me!


Have you ever read the back of your lottery ticket?  It talks about odds.  Maybe your chances of winning the big prize are 1 in 7 million.  “Okay,” you say, “the chances are pretty slim to win and that’s why I buy seven tickets instead of one.  Doesn’t that improve my odds to 1 in 1 million?  Isn’t that a lot better?”  Odds are a bit tricky.  If you delve into the math you start talking fractions and percentages and end up talking averages and probability.  Pretty soon your eyes glaze over.


You may think your odds go way up if you buy additional lottery tickets.  In truth, odds do get better as you buy more and more tickets, but not by much.


In our example above, when you buy a single ticket your odds to win are 1 in 7 million.  Buy two and it becomes 2 in 7 million. Those are puny chances.  If you divide 1, 2 or even 100 by 7 million, you end up with a number with a lot of zeros in it after the decimal point.  A fraction, say 1/2, is another way to express odds, but odds can also be expressed numerically or as a percentage.  The chart below shows the result of doing the math.


The odds don’t lie. Your chance of winning the big prize is practically zero.


Mucking With The Numbers


The first column lists the number of tickets we plan to purchase for a single lottery drawing.  The second column represents all possible ticket combinations for the same drawing.  Players need to correctly pick six or more numbers to win the grand prize. In this case, let’s assume there are seven million unique combinations of six numbers.  Statisticians have a formula for calculating this number depending on the total “balls” or numbers drawn, but all you really need to know is the bigger the number, the harder it is to win.



Let’s look at a specific example on this chart.  If you buy ten tickets and there are 7 million ways to win, this gives you ten chances in 7 million to win.   Another way to say the same thing is your odds of winning are 10 divided by 7 million.  This is a fraction which can also be expressed numerically—in this case .00000143 (i.e. 10 divided by 7,000,000). You can find this numerical representation in the third column.


Sometimes the odds are given as a percentage. For instance, when you flip a coin, you can say that the odds are 50% that you’ll get heads or tails—that’s one chance out of two possible outcomes. If you have a 100% chance of winning, it’s the same as saying you can’t lose.  Of course, you’ll never find a lottery with those odds.  Your odds as a percentage are listed in the fourth column.


Hey, There’s Something Goofy Here.


“Wait just a second!” you say.  “How come the last column in the chart is all zeros?”  Let’s take a closer look.  As you can see in the fourth column, all of the percentages of winning are extremely small for this game.  That remains true even if we buy as many as a hundred tickets at a time.


Our example demonstrates that with 7 million possible combinations to choose from, the odds to win are minuscule.  In fact, even to buy 100 tickets the odds remain WAY less than one percent.  In this instance, we are talking about a number just over one one-thousandth of one percent.  That’s still a teeny tiny percentage.


There is another even bigger problem with the numbers.  Buying a ticket to the lottery gives you a chance to win, but it doesn’t guarantee a win.  You could buy 3000 or 5000 tickets every week for the rest of your life and still lose every game you play.  In fact, the only fail-safe system to “win” the lottery would be to buy all the various number combinations possible.  If it costs a dollar to play each and every combination, it would cost you 7 million dollars to guarantee a win.  In a game like that, the grand prize would need to exceed 7 million dollars by several additional millions for you to come out ahead.  Don’t forget taxes take a big bite out your winnings.  Remember:  The odds can only tell you of a likely outcome, never guarantee a win.


A Big Fat Zero


Clearly, buying more tickets improves your odds, but the numbers are stacked against you.  When the odds are as high a 1 in 7 million your chance to win is practically zero.


It’s hard to put big numbers in perspective.  When talking about a number like 7 million we often have no clue how to make sense of it.  One thing we can do to is to convert our number into a smaller number more easy to visualize.  For example, the world’s tallest building is located in the Kingdom of Dubai.  At 2,716.5 feet tall the “Burj Khalifa” as they call it is a monster.  When it’s cloudy you wouldn’t see the top if you stood at the base.  Let’s pretend we were going to build a new structure 7 million feet tall out of additional Burj Khalifa towers.  It would take 2,577 of them standing atop one another to go that high.   Or look at miles.  If you started traveling around the circumference of the earth you would have to go around 281 times before reaching the 7 million mile mark.  Wouldn’t you like the frequent flyer miles on that trip?


If you’re still unclear what it means to say the odds are stacked against you, here’s a question to drive it home:  How many tickets would you need to buy to increase the chance of winning the jackpot to just one-percent?  The answer may shock you.


If we write out 7 million we get 7 followed by six zeros, or 7,000,000.  Now, multiply that by 1% or .01 and the answer you get is 70,000 tickets!  Here’s the problem: If you bought 5 tickets per week it would take you over 269 years to buy that many tickets.


Unfortunately, there is an even bigger issue to consider: Spreading out ticket purchases over weeks, months or years won’t improve your odds.  Many people make the mistake thinking that if they play every week, over time the odds to win improve.  That’s not true at all.  If you want better odds, all your tickets must be purchased for the same drawing.  Perhaps now you can see why it’s so difficult to improve odds.  In the case above, you would need to spend a small fortune on tickets just to improve your chances a measly one percent.  Take another look at the chart.  It shows that when you buy just five tickets for a given drawing, your odds are only 0.000071% to win that drawing.  That’s practically zero and it wouldn’t change tomorrow, next week or in the next lifetime.


Turn The Odds Around


Sometimes it’s worth turning numbers around to see what they really mean.  Say your odds of winning the lottery are 1 in 5.  Turn that around and it means you have a 4 in 5 chance of losing.  Another way to say that is if you have five friends and you each buy a ticket, on average one of your four friends will win instead of you 80% of the time.


It gets uglier when the odds go way up.  One chance to win in 7 million is six million, nine hundred and ninety-nine thousand, nine-hundred and ninety-nine chances to lose!  That’s 99.999986% or so close to 100% that you might as well call it a sure bet for losing.


What’s Under The Mattress


If you have enough money to burn, shred or cut up into tiny paper dolls, you may decide playing the lottery is more fun.  Alternatively, if money is precious, but you just can’t let go of the possibility you’re going to be the next winner, do yourself a big favor:  Buy one ticket each week instead of five.


Now, take the extra $4 you saved and stuff it under your mattress.  In six months you should have a lump worth $104 (6 months is 26 weeks times $4 per week is $104).  In five years, your lump would grow to a tidy, though perhaps uncomfortable sum to sleep on, of $1040.  By the time your bed is worn out, say twenty years down the line, you would be sleeping on $4160.


Skip the lotto and save it instead.

I’m liking these odds.

Still not convinced?  How would you like to increase those “guaranteed winnings” by over a thousand dollars?  That’s easy!  Skip the lottery altogether and you’ll end up with $5200 and one very lumpy mattress.


Now, that’s an idea worth sleeping on.




For dozens of ways to save money, check out our Great Savings Tip series.

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