After much research I am going to share some very interesting findings with regards to my "Ball Placement Probability theory ©".

 

I am listening to snow patrols new album while writing this, its excellent, Called Out In the Dark is a really good track, anyway to the research.

Its long been my belief that I could get a computer to analyse any set of combinations from any pool / pick lottery providing real odds on the entire draw. LSA is an excellent example of single number ball placement probability theory however the goal was to produce an algorithm that could be applied to any combination of numbers be it sets of 2,3,4,5 or even 6 balls , the problem is that there are billions of combinations and no software can handle such massive amounts of data in a fast enough time to make a viable consumer app.

Well I am excited to announce after running my quad core PC 24 hours a day for a little over 2 years with custom software I wrote I have completed this mammoth task.

I will use the world's most favourite draw to show this example 6/49

I can now put proof to my theory that 

A: The way you place the numbers on a single line (ticket) effects your chances of a win in the whole pool.

B: The way you place the numbers on multiple tickets can amplify your chances of a win from the entire pool.

Example using the 4 numbers 01 10 20 30

In the 6/49 you have to pick 6 numbers on 1 line, now with my new research I am able to find where to put numbers on a ticket to maximize win coverage, and what numbers work best.

Ball 1	Ball 2	Ball 3	Ball 4	Ball 5	Ball 6	6 Ball Combos Covered
1	10	20	30	?	?	171
1	10	20	?	?	30	36
1	10	20	?	30	?	171
1	?	10	20	30	?	152
1	?	10	?	20	30	72

Above shows that

01 10 20 30 ? ?

is better than

01 10 20 ? ? 30

In fact by just moving the positions of the numbers on the same line the odds have been reduced giving 135 less possible chances of a win using 01 10 20 _ _ 30

Now let's look at possible 3 ball combinations in the 6/49

 

Ball 1	Ball 2	Ball 3	Ball 4	Ball 5	Ball 6	6 Ball Combos Covered
01	10	20				3,654
01	10		20			3,654
01	10			20		1,044
01	10				20	84
01		10	20			3,248
01		10		20		2,088
01		10			20	288
01			10	20		812
01			10		20	252
01				10	20	52

 

It can be seen from the above chart that placing the numbers 01 10 and 20 in position

01 10 20 _ _ _ or

01 10 _ 20 _ _ you will win if any one of 3,654 combinations appear where as putting them on a ticket in the following order 01 _ 10 _ _ 20 you can only win from 288 combinations from the 13,983,816 possible.

My task is now to analyse all possible variations and find the best numbers to play.

05 15 25 _ _ _ = You win if any one of 2,024 combinations appear from 13,983,816

04 12 23 _ _ _= You win if any one of 2,600 combinations appear from 13,983,816

02 08 26 _ _ _= You win if any one of 1,771 combinations appear from 13,983,816

02 08 _ 26 _ _ = You win if any one of 4,301 combinations appear from 13,983,816

02 08 _ 30 _ _ = You win if any one of 3,591 combinations appear from 13,983,816

02 _ 08 _ 30 _ = You win if any one of 855 combinations appear from 13,983,816

The above are just random numbers typed in to see what ball placement probability they have.

Now what's really exciting is you have 3 spaces left so you can double up on the above coverage.

 

05 15 25 _ _ _ = You win if any one of 2,024 combinations appear from 13,983,816

_ _ _ 29 38 45 = You win if any one of 3,276 combinations appear from 13,983,816

 

So 05 15 25 29 38 45 = 2,024 + 3,276 = 5,300 lines that can appear that will give you a win with this ticket, it gets better. There are 20 ways to arrange 3 balls in 6 balls 15 ways to arrange 4 and 6 ways to arrang 5 from 6.

So doing the math for them all I can put a ranking system in place.

Then from this ranking system I can make wheels.

Using this system to balance all 3,4,5 combinations I can realise my goal of finding the mathematically perfect wheel for this draw.

I will be putting numbers on the lotto this week using this new system.

If your a user of LSA then you can see the power of knowing single number placement proberbility so you can appriciate the power of any set of combnations being able to do the same.

Thank you for reading, any feedback or comments are most welcome.

Jamie