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The Odds / Chances Of Winning The Lottery

The chances of winning a lottery jackpot are determined by several factors, including: the count of possible numbers, the count of winning numbers drawn, whether or not order is significant and whether drawn numbers are returned for the possibility of further drawing. In the UK lottery there are 49 numbers, 6 main numbers and a bonus number drawn, the order does not matter and drawn numbers are not redrawn.

You win the jackpot, or a share of it at least, if you match all six numbers. The bonus ball is only of interest if you have matched five of the six main numbers. This can offer large prizes if you match five numbers and the bonus ball. Smaller prizes are offered for five numbers (without the bonus ball), four numbers and three numbers (£10).

Therefore, the odds on winning the UK lottery are,

6 Numbers (Jackpot)
1 in 13,983,816
5 Numbers and the Bonus Ball
1 in 2,330,636
5 Numbers
1 in 55,492
4 Numbers
1 in 1,033
3 Numbers (10)
1 in 57

These odds are calculated as follows,

Jackpot (6 numbers)

Match 1st number: There are 49 numbers and you have 6 chances of matching this number so the chances are 1 in 49/6 = 8.17

Match 2nd number: There are 48 numbers and you have 5 chances of matching this number so the chances are 1 in 48/5 = 9.6

Match 3rd number: There are 47 numbers and you have 4 chances of matching this number so the chances are 1 in 47/4 = 11.75

Match 4th number: There are 46 numbers and you have 3 chances of matching this number so the chances are 1 in 46/3 = 15.33

Match 5th number: There are 45 numbers and you have 2 chances of matching this number so the chances are 1 in 45/2 = 22.5

Match 6th number: There are 44 numbers and you have 1 chance of matching this number so the chances are 1 in 44/1 = 44

To calculate the chance of matching all six numbers you need to multiply all these chances together,

(49/6) X (48/5) X (47/4) X (46/3) X (45/2) X 44 = 13,983,816

The formula for this is 49! / (6! * (49 -6)!)

Your chance therefore of matching all six numbers is 1 in 13,983,816

Match 5 Numbers (And The Bonus Ball)

To calculate this you need to know how many combinations of 5 numbers from the 6 winning numbers there are and then multiply this by the number of possible losing numbers.

There are 6 different combinations of 5 numbers and there are 43 possible losing numbers, therefore, the number of ways of matching 5 numbers are 5 X 43 = 258.

However, of these 258 matches, some of them will match the bonus ball. There are 43 losing numbers before the bonus ball is drawn so the chance of matching with the bonus ball is 1 in 43. So the number of combinations matching 5 numbers and the bonus is (1/43) X 258 = 6. Therefore, the number of combinations matching 5 numbers but not the bonus ball is 258 - 6 = 252.

Your chance of matching 5 numbers and the bonus ball is

1 in (13,983,816 / 6) = 1 in 2,330,636

Your chance of matching 5 numbers but not the bonus ball is

1 in (13,983,816 / 252) = 1 in 55,492

Match 4 Numbers

To calculate for 4 numbers we again need to know how many combinations of 4 numbers from the winning 6 numbers there are and then multiply this by the number of ways there are of picking 2 numbers from the losing 43 numbers.

There are 15 combinations of 4 numbers and 903 combinations of 2 losing numbers, so the number of combinations of 4 winning numbers and 2 losing numbers is 4 X 903 = 13,545.

Your chance of matching 4 numbers is

1 in (13,983,816 / 13,545) = 1 in 1,033

Match 3 Numbers

It is similar again to calculate for 3 numbers. You need to know how many combinations of 3 numbers from the winning 6 numbers there are and then multiply this by the number of ways there are of picking 3 numbers from the losing 43 numbers.

There are 20 combinations of 3 winning numbers and 12,341 combinations of 3 losing numbers, so the number of combinations of 3 winning numbers and 3 losing numbers is 20 X 12,341 = 246,820.

Your chance of matching 3 numbers is

1 in (13,983,816 / 246,820) = 1 in 57

 

You can increase your chances of winning by joining a syndicate and therefore buying yourself more chances of winning.

 

 

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