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Calculating the odds
Picking all 6 numbers is the name of
the game in the lottery. Calculating the odds of correctly
doing this is pretty easy, since all the numbers are
drawn from the same pool. Each time you get one right,
the number in the pool falls by one, and the probability
of guessing the next one correctly falls.
So, to correctly guess one number, the odds are:
49 X 48 X 47 X 46 X 45 X 44
1 X 2 X 3 X 4 X 5 X 6
which equates to
10,068,347,52
720
Or in other words, odds of 1 in 13,983,816
The odds for picking one ball are the easiest to work
out. It’s simply a case of having 6 chances in
49, which equates to a little over a 1 in 8 chance.
Yes that’s right, you have less than a 1 in 8
chance of picking a single number!
Calculating the odds for other prizes requires a different
formula. Let's calculate the odds of getting '5 of 6'
in a 6/49 game:
The 6-number winning combination can be broken down
into 6 groups of 5 numbers each (1,2,3,4,5 / 1,2,3,4,6
/ 1,2,3,5,6 / 1,2,4,5,6 / 1,3,4,5,6 and 2,3,4,5,6).
Each 5-number group can be combined with 1 number from
the rest of the field. There are a total of 258 different
ways of getting a set of 5 numbers. Therefore one winning
6-number combination offers 258 chances of '5 of 6'.
Therefore, the probability of hitting '5 of 6' is calculated
by dividing total possible combinations by total chances
of 5 of 6: 13,983,816 / 258 = 54,200.8.
Therefore you have a 1 in 54,200.8 chance of getting
5 numbers.
The same approach as for 5 straight numbers can be
used to calculate the odds of getting '4 of 6' in a
6/49 game. The 6-number winning combination can be broken
down into 15 groups of 4 numbers each (1,2,3,4 / 1,2,3,5
/ 1,2,3,6 etc). Each 4-number group can be combined
with 2 numbers from the rest of the field, making a
total of 13,545 different winning combinations. Therefore,
the probability of hitting '4 of 6' is calculated by
dividing total possible combinations by total chances
of '4 of 6': 13,983,816 / 13,545 = 1,032.4 to 1.
Therefore you have a 1 in 1,032.4 chance of getting
4 numbers.
Again, the same approach can be used to calculate the
odds of getting '3 of 6' in a 6/49 game. The 6-number
winning combination can be broken down into 20 groups
of 4 numbers each. Each 3-number group can be combined
with 3 numbers from the rest of the field, making a
total of 246,820 different winning combinations. Therefore,
the probability of hitting '3 of 6' is calculated by
dividing total possible combinations by total chances
of '3 of 6': 13,983,816 / 246,820 = 56.66 to 1.
Therefore you have a 1 in 56.7 chance of getting 3
numbers. Yes that’s right – you pay out
£1 and have only a 1 in 57 chance of winning £10.
That means, if you ignore the possibility of winning
a larger prize, you are likely to lose £47 for
every £57 you spend. Not exactly great odds…
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