Working with Lottery Number Gaps, what it's all about
For a 6/49 game, here's a simple way of attempting to reduce
the field of 49 numbers down to 30.
Then maybe once in a while you 'might' be able to place yourself
in the right picking 'areas' or 'groups' of numbers where the
next 6 winners lie.
The following is based on the UK National Lottery 6/49
but will apply to any 6/49 game. The bonus number is
excluded. Numbers are dealt with in ascending order
not drawn order.
The method is based on the principle that usually
3 or 4 of the 6 numbers drawn will have a gap size
between them of no more than1 to 5 numbers.
Here's an example of what I mean using an actual
UK # 452. Sat 22nd Apr. 220.127.116.11.48.49.
26 to 31 = gap of 5 numbers
31 to 35 = gap of 4 numbers
43 to 48 = gap of 5 numbers
48 to 49 = gap of 1 number
In the last 53 draws from #400 to #452 inc,
20 draws had 4 numbers with a gap size between 1 and 5.
21 draws had 3 numbers of the 1-5 gap size.
3 of the draws had 5 numbers with a 1-5 gap size.
Only 1 draw contained a 1-5 gap size, the remaining
draws had 2 numbers with a 1-5 gap size.
The next most common gap size encountered is 6-10,
that's a count of between 18.104.22.168 or 10 numbers *to* or
*from* an adjacent number in the 6 drawn numbers.
This size of gap appears approx 50% less than
the 1-5 group.
The next sizes of gap are 11-15. 16-20. 21-25. 26-30. 31-35.
sizes above these are rare.
Depending on the placement amongst the 6 available slots
and over useage, these groups can also become impossible
If you want to see what and where these gap sizes appear, plot
out on graph paper as below for each of the 6 slots.
Get your record of the last 50 draws and go down the column
of all the 1st numbers drawn. On your chart mark an X under
the approriate group that your 1st numbers corresponds as in
this example below.
These are the first numbers drawn for draws #452 to #446
#452 = 26.
#451 = 1.
#450 = 2.
#449 = 9.
#448 = 18.
#447 = 2.
#446 = 3.
And plotted thus -
1st number drawn (1st slot)
1-5. 6-10. 11-15. 16-20. 21-25. 26-30. 31-35.
The 2nd, 3rd, 4th, 5th and 6th slots are set out as above.
But in these slots you note the count from the preceding
number then enter an X under the corresponding gap size
You go down the column of the 2nd numbers drawn and
plot those to their corresponding groups for the 2nd slot.
Same with the 3rd 4th 5th and 6th slots.
You'll now have a picture of the gap size groups being used
for each of the 6 slots for each draw.
When you play the groups it must be remembered that
you are selecting a group of 5 numbers from where you
hope the first number will be drawn from within the 1st
Once you have chosen a group it's up to you how you
pick your number(s) from that group.
Moving on to the 2nd slot. Here one bears in mind that
you are now picking a size of gap that you hope the
second number will be away from the first, *Not* the
actual 2nd number drawn but a group of 5 possible numbers
from which a correct selection has to be made that
once picked is added to your first number choice.
Going back to the #452 result above, the 1st number
drawn - 26 belonged to the 26-30 group. The 2nd
number - 31 belongs to the 1-5 group because the
gap between 26 and 31 = 5.
Thus, the first two correct gap size choices for extracting
numbers are - 1st slot 26-30, 2nd slot 1-5.
The correct choice of numbers from those groups
are 26 - the first number, and 5 from the 2nd group
so 26 + 5 = 31 the real 2nd game number.
The third number in our example result is 35.
35 is 4 gaps from the 2nd number 31, so again
the correct gap size is 1-5. The correct pick from
this group of 5 numbers is number 4.
Add the 4 to the previous 2nd number which is 31
thus 31+4= 35, your 3rd game number.
The full result for draw #452 according to gap sizes is -
Slot No. Gap size Pick No. Lotto No.
1st slot = 26-30. 26 26
2nd slot = 1-5 5 31
3rd slot = 1-5 4 35
4th slot = 6-10 8 43
5th slot = 1-5 5 48
6th slot = 1-5 1 49
As I said at the start, the method is to try and put you in the
right picking area. This will not be a means of picking the exact
wining number. Nobody can predictively do that. Simply a guide
to possible areas from which to choose numbers.
*IF* you manage to pick the right group for each of the 6 slots,
you have a 1in 5 chance *per slot* of picking the right number
from each group. You pick a number from your 2nd gap size
choice and add that to your first number, the same for the 3rd
gap size, add the number to the second number and so on
to the 6th number, thus creating a set of 6 numbers to play.
Obviously a jackpot hinges on your very first number in your
first slot being correct, however, even if that is wrong you
are not necessarily out of the running for 5 numbers +B.
That is of course if you only wish to pick 1 line of 6 numbers
The whole point of this ? Well, earlier I mentioned that
usually you can expect 3 or 4 numbers to have a gap
size of 1-5. A total of 44 draws out of 52 contain 3 or more
of the 1-5 gap size groups.
The problem in the first place is positioning the correct
gap size groups to the 6 slots. If you've set out your charts
you can be subjective as to which slots you wish to place
your 1-5 groups in and how many of that particular group
you want to use amongst the 6 slots.
Further and more difficult, we can see from draw # 452
that the first number was 26, hence the start was
using the 26-30 gap size group, an uncommon start group,
but that's random for you. So you need to include some
of the larger size groups amongst the 1-5's. Obviously
you can't use 2 of the 26-30 gap sizes because you
will be outside the parameters of 49 after your first number!
The use of combinations can help to a certain extent
if one should wish to use 3 or 4 of the 1-5's groups.
Using 3 of those 1-5's groups in any of the 6 slots
requires 20 combinations to ensure that on one occasion
you will have at least got those groups in the right slots.
Or, using 4 of the 1-5's groups in any of the 6 slots
requires only 15 combinations.
All you have to do in that case is pick correctly
the other 2 remaining group sizes. Then of course, the
really hard bit is picking out the one correct number from
the available 5 numbers in each group to make your
line of 6 numbers. Bits of numbered paper from a hat
is one way. You could of course pick 2 numbers from
each of your groups to give you a set of 12 numbers
for wheeling, 3 numbers from each group to give you
18 numbers to wheel etc.
The method can be adapted to varying sized pools
such as the UK Thunderball 5/34 or the
U.S. Powerball 5/49 for example. But do not expect
to see as many of the 1-5's groups, they will be there
but to a lesser quantity simply due to field size versus
amount drawn calculations.
For a 6/49 game the expected gap is 6 divided
by 49 = 8.166r round to 8.
A 5/34 game = 6.8 round up to 7
5/49 = 9.8 round to 10.
I'm sure someone will step in here and explain
what happens to the expectation of gap size to
the remaining balls when the field size depletes
after the 1st ball is drawn then the 2nd ball is drawn etc.
But initially, the more drawn from a set field size the
smaller the gaps between the numbers. The fewer
drawn the bigger the gap. In theory.
For the 6/49 game the gap sizing 1-5 was achieved
by trial and error, also bearing in mind that if one
would wish to randomly extract numbers from groups
then the groups have to be of reasonable balanced size
to give a reasonable chance - 1 in 5 of pulling out the right
number in each group. If you try gap sizing of 1-7 which
fits neatly into 49 that's ok but makes life harder when
you're only giving yourself a 1 in 7 chance of extraction.
Going the other way and dividing groups into smaller
gap sizes would be more accurate on a good day
but an absolute rascal to choose in the first place.
It all comes down to moderation and balance.
The method is exempt from the 'psychological'
dependence of those unreliable so called
'hot numbers' but of course can be manipulated
to perform in that way.
It is really intended to incorporate the elements of
randomness within the confines of a simple principle
and methodical approach.
Even if you manage to select all the correct groups
and get them in the right order it's still a very long
shot to extract the next 6 winning numbers from
them, but perhaps this is one way of chipping at
that mighty powerful 'thing' we call random and
might be of some value or addition to your methods.