Primer: Wheeling Lotto Numbers, Playing Wheels or Reduced Lotto Systems

By Ion Saliu, Founder of Lotto Wheeling Mathematics

Written on September 3, 2002.

• Wheeling lotto numbers or playing lotto wheels (abbreviated lotto systems) is the main tool of the so-called expert lotto players. The concept has been around for over two hundred years. In fact, it is a tiny part of a mathematical branch named theory of sets. Let's take the most basic set and wheel its elements: 12 numbers. We can divide the numbers in 4 groups of 3 numbers each: A, B, C, D. Group A=1,2,3; group B=4,5,6; group C=7,8,9; group D=10,11,12. We can combine the 4 groups 2 at a time in a total of C(4,2)=6 combinations of 6 numbers. AB, AC, AD, BC, BD, CD. Converting the groups to their initial compositions, we get:

1,2,3,4,5,6
1,2,3,7,8,9
1,2,3,10,11,12
4,5,6,7,8,9
4,5,6,10,11,12
7,8,9,10,11,12

This is a new sub-set, constructed from the inclusive set C(12,6)=924 combinations of 6 numbers each. In my theory of sets, if the inclusive set has a main completion rule, a sub-set can be constructed if and only if it has a specific completion rule derived from the main completion rule. Six winning numbers are drawn for the example above. The drawing is random, therefore the 6 winning numbers will have a random spread among the 4 3-number groups: 3,3,0,0; 3,2,1,0; 2,2,2,0; 2,2,1,1; etc. Since all the groups are paired with one another, our 6-combination sub-set cannot have fewer than 4 winning numbers. This is a most basic 'abbreviated lotto system' or 'lotto wheel'. It assures a so-called 'minimum guarantee': '4 of 6' in this example. If the 6 winning numbers are among the 12, the wheel guarantees that at least one combination will contain at least 4 of the winning numbers.

Knowledgeable players will not play combinations such as 1,2,3,4,5,6. I detailed in another message how wasteful such play really is. The players will usually select their own numbers, also known as 'picks'. For example: 7,13,24,8,33,35,42,28,19,37,40,49. The next important step is wheeling the picks. That is, the player needs to replace the theoretical numbers 1,2,3,4,…12 by the picks 7,13,24,8,…49. The process can be done manually, but it is tedious and error prone. The players use software to wheel their lotto numbers. Software wheeling cost money, up until I released freeware to wheel lotto numbers. Previous software wheelers were also limited in scope. They could only wheel their own abbreviated lotto systems. Generally, they were unable to wheel third-party wheels or powerball systems. My free wheeler is the most comprehensive to date. It can wheel any kind of wheel, for up to 100 numbers per combination. It can also wheel powerball abbreviated and keno wheels systems. Program name: FillWheel, available as a free download from my FTP download site.

The set theory and wheeling are not priorities for me now. But I have been able to find very efficient completion rules. Also, using my own software, I have been able to devise the most efficient possible lotto wheels. For example, my 10-number lotto wheel in 3 combinations offers the '4 of 6' minimal guarantee, following exactly the lotto odds. The previous best wheel in that category consisted of 5 combinations.

But be aware that the lotto wheels can do more harm than good. Read my post “The myth of lotto wheels or abbreviated lotto systems”. The player must use a good strategy of picking lotto numbers, before using lotto wheels. Please read the main lotto lottery strategy page at this site. My own software, LotWon, SuperPower\$ and 'MDIEditor and Lotto' comes with a number of lotto wheels or systems. Please keep in mind that those systems were not optimized according to my own set theory. The wheels contain more combinations than the respective lotto odds. Such systems aimed at hitting better prizes. They are meant to be used in conjunction with the strategies I have presented at this website.

* 10 numbers, 100% '4 of 6', 3 combinations (exactly the lotto odds)
1 2 3 4 5 6
1 3 4 8 9 10
2 5 6 7 9 10

* 11 numbers, 100% '4 of 6', 5 combinations (20% over the lotto odds)
1 2 3 4 5 6
1 2 8 9 10 11
1 3 5 8 10 11
2 3 5 7 9 10
4 6 7 8 9 11

Ion Saliu

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