How to work out all the chances of winning on the
 
 
How to calculate the different chancesThe main thing to know is that the total number of ways of choosing your six numbers is:
the jackpot chance = 1 in 45,057,474 or about 1 in 45 million  
MATCHING THREE NUMBERS: we have to work out how many ways you can select your six numbers so that three of them match up and three of them don't.
You get 20 x 23426 = 468,520. That's how many different ways you can match three winning numbers, so your chances of matching 3 numbers are 468,520 out of the 45,057,474 possible ways the numbers could come up. Obviously this looks a bit mind boggling, so to make it simpler you divide 45,057,474 by 468,520 to work out that the chance of matching 3 numbers = 1 in 96.167 which is about 1 in 96.  
MATCHING FOUR NUMBERS: this time we need to see how many ways there are of picking four numbers from the winning six, and then multiply this by how many ways there are of picking two numbers from the 53 losers. The sums look like this: As there are 20,670 ways of matching four winning numbers, your chances are 20,670 in 45,057,474. It works out that the chance of matching 4 numbers = 1 in 2,180  
MATCHING FIVE NUMBERS: this time we need to see how many ways there are of picking five numbers from the winning six, and then multiply this by how many ways there are of picking one number from the 53 losers. (This last bit's easy: if you have a choice of 53 things and you can choose one, how many choices have you got? 53 of course!) Here comes the sums: This means there are 318 ways of matching five winning numbers, but before we look at the chances, remember that with some of these ways your sixth number will also match the bonus number.  
MATCHING FIVE NUMBERS AND THE BONUS: The sums here are slightly different. Have a think about this:
You've just seen the main six numbers drawn on the lottery. You've matched five of them, and are leaping about the room and kissing the telly. The trouble is that ONE of your chosen numbers did not match up. So for just five numbers, the chances are 312 in 45,057,474 which means the chance of matching 5 numbers without the bonus = 1 in 144,415 And for five numbers and the bonus, the chances are 6 in 45,057,474 which gives us the chance of matching 5 numbers plus the bonus = 1 in 7,509,579
 
What's more likely than winning the UK National Lottery Jackpot?
The odds of winning the UK National Lottery are 1/45,057,474. If you just buy one lottery ticket in your life, these things are more likely to happen to you...
One FINAL thought about the lottery:Assuming your life expectancy is 75 years, on average you should hope to be alive for a total of about 40,000,000 minutes. This means that your chances of dying in any particular minute are 1/40,000,000. Therefore, if you want a lottery ticket, be sure to buy it in the last minute before the draw is made. If you leave a gap of longer than a minute, then you are more likely to die while you are waiting for the draw than you are to win the jackpot.Good luck!  
 
The chances of other National Lottery JackpotsWhen comparing the chances of winning on different lotteries, you should also factor in the returns. As a simple example, if you have a 1 in 10 chance of winning $100 this isn't as good as a 1 in 100 chance of winning $5,000. Also, different lotteries cost different amounts to play, jackpot sizes and rollover rules can vary and the smaller prizes also affect the potential return.Here we're only looking at some of the jackpot chances, and not the potential returns.
 
 
There are more stats and facts about games here: Craps  How to play, Chances and Payouts Blackjack  Hit, Stand, Double Down or Split? The Betting Guide  and how to work out the Bookie's profit! The Roulette Wheel ... and how to worry the casino! The OneArmed Bandit Slot Machine  
Where does 45,057,474 come from?The way the UK lottery works is that you have a card with the numbers 159 marked on it and you have to choose any six of them. What we need to work out is how many different ways you can choose 6 numbers out of the 59 available.
To use the formula you need to know that the "!" sign is called a "factorial" which means you need to multiply the number by every smaller number down to 1. So for example 5! = 5x4x3x2x1 = 120. (Some calculators have a ! button on them.) If we wrote the top line of this formula out in full we'd get 59x58x57x56.... right down to ...4x3x2x1. The bottom line is 6x5x4x3x2x1 x 53x52x51x50...etc down to ...4x3x2x1. It all seems awful but DON'T PANIC! The fun part is that monstrous sums like these cancel themselves to bits and you can actually rip though them really quickly. This one produces the answer that there are 45,057,474 combinations in total, and only ONE of them will win you the jackpot. So your chances of winning the jackpot are 1 in 45,057,474. Now you've understood all this, let's get back to the top
