The way the odds of winning the UK Lotto Draw, also known as the UK National Lottery Draw, are calculated are extremely complex. The odds are based on you matching any six numbers between 1 and 49 if you want to win the jackpot, if you were lucky enough to however match 3 out from the 49 numbers you would be in line for a whopping £10, how many times over the last year have you matched 3 numbers? From the calculations below you will see how the chances of even winning a tenner are stacked very heavily against you.

• The Jackpot - 6 Numbers (Typical prize: £2 million)
  6 numbers are drawn at random from the set of integers between 1 and 49, which means there are 49!/(6!*(49-6)!) combinations of numbers - this means that the jackpot chance is 1 in 13,983,816 or approximately 1 in 14 million.
  
• 5 Numbers + Bonus Number (Typical prize: £100,000)
  You are still matching 6 numbers from the 1 to 49 set as above, but you can now do it in 6 different ways (by dropping each of the main numbers in turn), therefore the chance is 1 in 13,983,816/6, which works out as 1 in 2,330,636.
  
• 5 Numbers (Typical prize: £1,500)
  This is 42 times more likely than getting 5 numbers + the bonus number - the chance is 1 in 2,330,636/42, which evaluates to 1 in 55,491.33333.
  
• 4 Numbers (Typical prize: £65)
  Firstly, let’s take the case of the first 4 of your numbers matching and the last 2 not matching.
  In this single case (where each set of chances relies on the previous event occurring):

Chance that your 1st number matches a winning lottery number is 1 in 49/6.
Chance that your 2nd number matches a winning lottery number is 1 in 48/5.
Chance that your 3rd number matches a winning lottery number is 1 in 47/4.
Chance that your 4th number matches a winning lottery number is 1 in 46/3.
Chance that your 5th number doesn’t match a winning number is 1 in 45/(45-2) [because there are still 2 unmatched winning numbers].
Chance that your 6th number doesn’t match a winning number is 1 in 44/(44-2) [yes, still 2 unmatched winning numbers].

Now you need to accumulate all those chances by multiplying them together:
1 in (49/6)*(48/5)*(47/4)*(46/3)*(45/43)*(44/42) which is 1 in 15486.953.
Now this is the chance for that single case occurring, but there are 15 combinations of matching 4 from 6, so you divide the answer by 15 to get 1 in 15486.953/15 or 1 in 1032.4.

• 3 Numbers (Constant prize: £10)
  Follow exactly the same scheme as the 4 match above to get these figures:
  1 in (49/6)*(48/5)*(47/4)*(46/43)*(45/42)*(44/41) (which is 1 in 1133.119) for a single case.
  There are 20 combinations of 3 from 6, so the chance of a 3 match is 1 in 1133.119/20 or 1 in 56.7.

The chance of you winning any of the above prizes is approximately 54 to 1 - it is said that an average of one million people per draw will win a prize. As you can see from the details above, the odds are very heavily stacked against you and you would statistically, probably have more chance of getting run over by a car crossing the road to buy your lottery ticket than actually winning the Jackpot.

So how do you improve your chances of winning?

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