Did you ever wonder what the odds of winning any one of the prizes in the UK National Lottery are? Or what your chances are of winning a jackpot? Well now you can find out and work out for yourself if buying lottery tickets is worthwhile.
What Are The Odds Of Winning The Lotto Jackpot?
To win a jackpot prize in the National Lottery (Lotto) you must correctly predict all six winning numbers. Here we can calculate the chance of this happening.
The numbers you have to select from for the National Lottery Lotto game are 1 to 49. So, for the first winning number there are 49 balls that have an equal chance of being selected. On your Lotto ticket you have picked 6 numbers - the first ball drawn by the National Lottery machine, just has to match one of your chosen numbers as the order in which they are selected doesn’t matter. The chances of the first ball being drawn matching any of the 6 numbers on your ticket is therefore 49 divided by 6.
For the second drawn number, there are now only a maximum of 48 balls to select from and you have 5 numbers remaining unmatched numbers on your Lotto ticket. The chances of the second drawn ball matching your Lotto ticket is therefore 48 divided by 5.
For the third winning number you are left with just 47 balls and 4 selections to match it with. This gives you chances of 47 divided by 4. , and so on up to the sixth and final winning number when there are a only 44 balls remaining and only one unmatched number left on your ticket.
If you multiply all of these numbers together, you get:
49/6 x 48/5 x 47/4 x 46/3 x 45/2 x 44/1 = 13,983,816 (just under 14 million)
So the chances of you winning the UK National Lottery (Lotto) Jackpot if you only buy oneLotto ticket for a particular draw is approximately 1 in 14,000,000.
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What Are The Odds Of Winning Any Of The Other Prizes?
With five tiers of prizes in the Lotto game, you do not have to win the jackpot to receive a cash prize - matching 3 numbers, 4 numbers, 5 numbers or 5 numbers plus the bonus ball, would result in you winning a prize. The following are the odds of winning one of the lower tier prizes in the UK National Lottery Lotto game:
Matching Three Numbers:
Here is the calculation for working out the chance of matching any 3 numbers from the 6 drawn. To calculate these odds we first work out the following:
- The chances of matching the first drawn number: 49 divided by 6 (49 possible balls, divided by 6 chances)
- The chances of matching the second drawn number: 48 divided by 5 (48 possible balls, divided by 5 chances)
- The chances of matching the third drawn number: 47 divided by 4 (47 possible balls, divided by 4 chances)
- The chance of not matching the fourth drawn number: 46 divided by 43 (45 possible balls, divided by the remaining 42 balls that do not match the selection on your ticket)
- The chance of not matching the fifth drawn number: 45 divided by 42 (45 possible balls, divided by the remaining 42 balls that do not match the selection on your ticket)
- The chance of not matching the sixth number drawn: 44/41 (44 possible balls, divided by the remaining 41 balls that do not match the selection on your ticket)
If we multiply all these together, this is what we get:
49/6 x 48/5 x 47/4 x 46/43 x 45/42 x 44/41 = 1133.119
Depending on the order in which you matched the balls, you have 20 different ways of matching exactly 3 balls. You could match the first second and third balls as in the example shown above, or you could match the third fifth and sixth balls, or any other combination across all 6.
So this is the calculation for working out the odds of matching exactly three numbers:
1133.119/20 (chance of matching 3 balls divided 20 by the number of possible combinations) = 56.65593
This then gives you odds of winning a Lotto prize for matching just three numbers as approximately 1 in 57.
Matching Four Numbers:
Calculating the chances of matching 4 numbers is not dissimilar to the way we worked out the odds of matching 3 numbers, the only difference being that this time we first take the odds of matching 4 numbers and the odds of not matching two numbers. This is how it looks:
49/6 x 48/5 x 47/4 x 46/3 x 45/43 x 44/42 = 15,485.95
As the total number of combinations possible for matching 4 numbers is 15, We now have to divide this by 15 to get the exact odds:
15,485.95/15 = 1032.397
Therefore your odds of winning a Lotto prize for matching four numbers is approximately 1 in 1032
Matching Five Numbers:
To calculate the chances of matching exactly five numbers is marginally different, because at this point you need to take into account the bonus ball - if you were to also match the bonus ball you would win an even bigger cash prize. To do this we have to multiply the chances of matching five drawn numbers by the chances of not matching the final number or indeed the bonus ball (43/42 - 43 remaining undrawn balls divided by the remaining 42 balls that do not match those on your ticket):
49/6 x 48/5 x 47/4 x 46/3 x 45/2 x 44/43 x 43/42 = 332948
You then have to divided by the number of possible combinations which is six:
332948/6 = 55491.33
Giving you odds of winning a prize for matching 5 Lotto numbers of approximately 1 in 55,491.
Matching Five Numbers plus the Bonus Ball:
To work out the chances of matching five numbers and the bonus ball, we can use the calculation we used for matching five numbers but we change the bonus ball part. Now we are looking at the chances of matching five of the drawn numbers multiplied by the chances of not matching the sixth and final number multiplied by the chances of matching the bonus ball (43/1 - 43 remaining balls and only one last remaining chance):
49/6 x 48/5 x 47/4 x 46/3 x 45/2 x 44/43 x 43/1 = 13,983,816
Divided that by the number of possible combinations which is six, the same as matching only 5 balls:
13,983,816/6 = 2,330,636
This gives your odds of winning a Lotto prize for matching 5 numbers + the bonus ball as 1 in 2,330,636.
Matching All Six Numbers For The Jackpot:
As shown at the start, these are 1 in 13,983,816
So What Are The Odds Of Winning One Of The Prizes?
Using these calculations we can also work out the chances of winning any prize in the National Lottery lotto game - approximately 1 in 53.7. In other words, if you were to buy 1 ticket for 57 consecutive Lotto draws, the likely hood is that you will win a prize once out of those 57 attempts. That doesn’t sound too bad until you realise that when you do win, it will probably only be £10 for matching 3 balls.
Don’t let this put you off through. Read our article on lottery syndicates and find out how you can slash those odds without spending any more money.
Alternatively, join the 1,000’s signing up to Free National Lottery Tickets to get Free Lotto and EuroMillions tickets for all the draws!
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