Understand Your Chances Of Winning The Lottery In 5 Minutes Flat

confused about your chances of winning?

Most lottery players fail to make the best of their chances of winning the lottery. Because normally, understanding it all takes more maths than most of us ever did at school. And more thinking than we do in an average day at work!

So no college degrees needed for our explanation!

Starting With Toast

We won't bore you to death with statistics and formulas - you hate that right? - so let's keep it fun ok?

You're making breakfast. And as a result of your half open eyes and carpet slipper shuffle, you trip, catapulting your toast across the room..!

So, what is the chance it will land butter side down?

OK, so assuming 'sods law' is not at play in this particular universe, there are 2 sides the toast can land on. So, I think we can safely agree that it's actually a 1 in 2 chance of butter side staining your carpet...

This time, though you were 'lucky', it was dry side down.

That's lesson 1 done. Relieved..?

Picking Your Toast Up...

You bend, pick your toast up, blow most of the hair and grime off it and return it to your plate. Just as the dog barrels into your legs on route to a serious barking at the postman. Your bleary eyed dismay watches your toast take off for a second time...

So what chance it will stain your carpet this time?

If you said 1 in 2, well done, you've already got lesson 2 down. (And this is way more important than you think. It could save you a lot of wasted money.)

There are still 2 sides to your toast, and one of them still has some butter on it. That means there is still a 1 in 2 chance of a grease mark on your carpet!

The fact your toast fell dry side down the first time will not make it any more or less likely that it will be butter side this time.

Clearly it's your lucky day, it was dry side again. Just be thankful you didn't choose cornflakes today.

So, previous results do not affect the future. That's lesson 2. Easy stuff this probability theory!

What's this Got to do With My Chances of Winning the Lottery?

OK, let's start talking balls ("you already were...").

If there was a really dumb lottery that had only 2 balls. And they drew out just 1 of them to pick the winner. What would your chances of winning be?

Yes, it's the toast example in glorious lottery 3D. Which means, your chances of winning are 1 in 2.

And of course, it means if ball 1 was picked last week, there is no better chance of ball 2 being picked this week, is there?

[Side Note: There is a whole 'industry' built around the theory of hot and cold numbers - balls which people believe are less or more likely to be drawn. Hence they look at past results to help predict future results. But as we've just learnt, previous results have no impact on future results! A very silly 'industry' indeed then.]

More Balls Please!

Right. So what happens if we add another ball. Easy right, it's now 1 in 3. Because we are still picking out 1 ball, and there are now 3 of them in total.

OK. So what if we draw 2 balls out of 3...

Ouch. That got harder. It sounds like it might be 2 out of 3 - but it isn't.

Just to prove it to you. If you think about it a bit more (a cup of coffee is well deserved by now!), here are all the combinations that can be drawn:

Ball 1Ball 2

But wait a second. Did you spot it? When we're talking about your normal lottery draw, it doesn't matter what order the balls are drawn in, so long as they match the ones on your ticket - right?!

So, if you look a little closer at those numbers in the table, you can see that 01, then 02 is exactly the same result as 02 then 01! If your numbers were 01 and 02 you'd hit the jackpot for either of those. So there are actually 2 ways of drawing every result, 01 first then 03 - or 03 first then 01 etc.

Confused yet? Waddya mean 'no'!   ;-)

You have found the secret formula for working out your chances of winning the lottery!

No, really! You have.

You worked out there were 6 possible ways the balls could be drawn. And you worked out that there were 2 ways each set of results could be drawn - because it didn't matter what order the balls were in for you to win. The only thing you didn't do was to divide the 6 possible results by the 2 ways of drawing them. Whcih gives the actual 1 in 3 chance of winning.

You may now call yourself a student of lottery statistics and probability.

Even More Balls!

Let's get dangerous. We're going to jump up to a 4 number lottery with 3 balls drawn. Ooooooh. (Patience eager student, 49 balls shall come to those who wait!).

OK. So if you write down all the possible combinations that can be drawn, how many are there?

Oh, alright, I'll do them for you...

Ball 1Ball 2Ball 3

OK. So there's 24 combinations. Now look closely, like before. How many times is each set of numbers repeated? How many times, for example, can you see balls 01, 02 and 03 but in any order?

I make it six times. So with your magic formula, that means 24 possible combinations divided by 6 ways to draw each set of numbers - gives 4 - or a 1 in 4 chance of this jackpot.

Look What Happens When We Add One More Ball

So we still draw 3 balls, but now out of a total of 5 balls. Even I'm not going to write all those combinations down. But I will let you in on a nifty way to find out how many there are, for any number of balls.

All you have to do is this: 5 x 4 x 3 = 60 ways.

Eh, how did that work!?

Easy. You start with the highest numbered ball, in this case 5, and keep multiplying by the next smaller numbered ball, for as many balls as you are drawing.

So, if you were drawing 2 balls out of 3, like our example above, it's just 3 x 2 = 6 - which is what we worked out above.

Or, for 3 balls out of 4, it's 4 x 3 x 2 = 24, which is also the same as we worked out above.

Nifty isn't it!

But How Many Combinations Are There In A Real Big Lottery

Most of us play a lottery with 49 different balls, and 6 balls get drawn.

So that means, it's 49 x 48 x 47 x 46 x 45 x 44 = 10,068,347,520.

That's a big number and an awful lot of combinations! But don't fret too much. Don't forget that it doesn't matter what order the balls are drawn!

Here's another time saver - as it would take forever to work out how many times combinations are repeated by writing them all down...

It's simply 6 x 5 x 4 x 3 x 2 x 1 = 720.

You can probably spot where that little shortcut came from. 6 balls to be drawn, multiplied by 5 left to draw, then 4 left etc. Double check our answers above - when we drew 3 balls we worked out the combinations were repeated 6 times didn't we, which is 3 x 2 x 1. Easy when you know how.

That lottery statistics diploma is nearly in the bag!

So What, Then, Are My Chances Of Winning The Lottery?

Well, you've pretty much worked it out. It's 10,068,347,520 divided by 720, which comes out to 1 in 13,983,816.

And that's why you don't win the jackpot every week!

Well done for staying awake this far. If you've had less than 3 cups of coffee, I'm impressed!

How To Increase Your Chances

So now you know how tough the odds are, I suppose you now want to know how to make it easier to win?

One way is to play less often but play the same number of tickets overall.

5 lines played monthly in one draw have a better chance than 1 line played weekly for 5 weeks. (That probably made your head hurt for a second, but work it through). It is only slightly better, and not quite as much fun as entering every draw though.

The other (obvious) way to increase your chances is... buy more tickets.

It's easy to see that if you buy two tickets, you double your chances. So that 1 in nearly 14 million, becomes a much better 2 in 14 million, which is the same as 1 in 7 million!

Wahay, now you're gonna win big. ;-)

Don't forget though, that there are prizes for matching 5 numbers out of 6, or 4 numbers or just 3. So your chances of winning the lottery aren't quite as bad as they look. Still pretty grim for the jackpot though!

So knowing that the best way to really boost your chances is to buy more tickets, you have a question to answer.

Do you want to buy more tickets with your own money - or somebody elses?!

If you like the idea of sharing the cost, and don't mind sharing the winnings, then you need a lottery syndicate.

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Congratulations on becoming an Expert in Lottery Statistics and Probability.