Understand your chances of winning the lottery in
5 minutes flat

Most lottery players fail to make the best of their chances of winning the lottery. Normally, understanding your lottery winning chances involves more maths than most of us ever did at school - and more thinking than we do in an average day at work!

But don't worry - no college degrees needed for our explanation!

We won't bore you to death with statistics and formulas - you hate that right? - so lets 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?!

You bend, pick your toast up, blow most of the hair and grime of 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!

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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 1 of them, what would your chances of winning the lottery be?

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

Right. So what happens if we add another ball. Easy right, chances of winning the lottery are now 1 in 3.

OK. So what if we now 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 1 01 01 02 02 03 03 Ball 2 02 03 03 01 01 02

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 drawn, you can see that 01, then 02 is the same as 02 then 01! If your numbers were 01 and 02 you'd hit the jackpot for both of those. So there are actually 2 ways of drawing every result, 01 then 03 - or 03 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, to get your actual 1 in 3 chance of winning the lottery.

You may now call yourself a student of lottery statistics.

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 1 01 01 01 01 01 01 02 02 02 02 02 02 Ball 2 02 02 03 03 04 04 01 01 03 03 04 04 Ball 3 03 04 02 04 02 03 03 04 01 04 01 03

Ball 1 03 03 03 03 03 03 04 04 04 04 04 04 Ball 2 01 01 02 02 04 04 01 01 02 02 03 03 Ball 3 02 04 01 04 01 02 02 03 01 03 01 02

Now look closely, like before. How many times is each set of number 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.

Looks what happens though if 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.

So what, then, are my chances of winning the lottery?

Well, you've pretty worked it out. It's 10,068,347,520 divided by 720, which comes out at roughly 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 of winning the lottery

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's not quite as much fun as entering every draw though.

The other (obvious) way to increase your chances of winning the lottery... - 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 though!

So accepting that the best way to really boost your chances is to buy more tickets, it's time to decide if you want to do that with your own money - or if you like the idea of sharing the cost, but can also accept the idea of sharing the winnings. If this sounds good - it's time to head for our lottery syndicate reviews!

Either way, Congratulations on becoming an Expert in Lottery Statistics.