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.

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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 draw result.

UK # 452. Sat 22nd Apr. 26.31.35.43.48.49.

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 6.7.8.9 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 to incorporate.

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. #452. X #451. X #450. X #449. X #448 X #447. X #446. X

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 group.

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 slot list.

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 to play.

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.

BUsing 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.

BI'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.

Steve Highfield.