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Covers or Wheels with Guarantees and Unique 3's
 LottoPoster Forums : NUMBER SETS TO PLAY FROM DIFFERENT METHODS : Covers or Wheels with Guarantees and Unique 3's
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Colin F
Lotto Systems Tester Creator & Analyst
Lotto Systems Tester Creator & Analyst
To dream the impossible dream ...

Joined: September 30 2004
Location: Australia
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Posts: 678
Quote Colin F Replybullet Topic: Covers or Guarantee Wheels - Primer or Refresher
    Posted: June 12 2005 at 1:47am
Covers or Guarantee Wheels - Primer or Refresher
by Colin Fairbrother

My approach to Covers or Wheels with a prize guarantee and in fact most of what I do in relation to Lotto is that of a programmer with relational database skills - we have our own bag of tricks and ways of approaching tasks which can't easily be simulated with arrays without much tedious work and advanced coding. This goes way beyond Microsoft Excel which is most commonly used in this field of Lotto number analysis with its "flat file" constraints.

Regularly, I see on other Forums enthusiasts struggling to get Excel to do something which is relatively easy to accomplish once the GRID is dropped - grids are great for spreadsheets and jails, but not good for creative programming. Like most things there is an initial steep learning curve - but once you get over that, well it doesn't necessarily get easier because so many new vistas open up that you're on a never ending learning curve.

Over thirty years of troubleshooting has taught me never to forget the BIG PICTURE - don't get bogged down in detail, know enough to know where to look for the detail, look for the simplest solution first and never be timid about using wizards or tools to get the job done quicker and easier ie more efficiently. 

Covers come from set theory in Mathematics and they have their own jargon but there is some overlap of terminology with other fields of interest such as blocks which is used by programmers or database people. It is not my intention to wade through every Cover  - I will go through a few of the simple ones to give an idea of what they're all about.

Covers for a small pool of numbers can be done manually - as you head into the bigger pools you need a computer tool such as CoverMaster or as in my case and other specialists in this field with programming knowledge we make our own and this requires advanced coding skills. 

You will find an expression used with Coverings which is worth becoming familiar with and can easily be remembered by using the mnemonic PoPiMaHi ie Pool, Pick, Match and Hits. C(7,6,3,3)=4 simply means we are restricting our combinations to those formed from a pool of 7 integers in a Pick 6 Lotto game and we want a minimum of one Comb3 prize guaranteed if we get 3 correct from our pool in the winning Comb6. C is the minimum Lines or Combinations of 6 integers (whole numbers) to assure this. Kudos are given if you can do it in a lesser number of Combinations than has been achieved before although in some cases it is mathematically impossible. C(7,6,6,6) means we want a 6 prize if  from our pool of 7 integers we get 6 of the winning Comb6 integers correct - this is a System 7 or Full Wheel 7 and there is no way it can be done for less than all the combinations of 6 from a pool of 7 integers which is 7 combinations.

You should bear in mind that where the pool is less than that used in the Lotto game then it is all hypothetical, some like me would say pure baloney as all the possible combinations of 6 from a pool of 7 is only 7 or for Pool 22 only 74,613 whereas a pool of 45 gives 8,145,060 and 49 gives 13,983,816 - in other words it is like a drop in the ocean or basing something on the assumption that the cow has already jumped over the moon. You will hear this garbage trotted out ad nauseam by those whose very ignorance is given away usually before they have completed one garbled sentence - but in their own peanut brains they live in a delusionary world where they think they are "gurus'.

For a hypothetical but still valid in concept Lotto game with a Pick of 6 and a Pool of 7 you are guaranteed to get first prize by playing the following 7 lines.

01 02 03 04 05 06
01 02 03 04 05 07
01 02 03 05 06 07
01 02 04 05 06 07
01 03 04 05 06 07
02 03 04 05 06 07

However, this guarantee is meaningless when the same 7 lines are applied to a real Jackpot type Lotto game where the smallest Pool is 25 as in the West Virginia game. The token prize for getting 3 correct in the winning Comb6 is better achieved by randomizing the following template:

01 02 03 04 05 06
07 08 09 10 11 12
13 14 15 16 17 18
19 20 21 22 23 24
01 02 07 13 19 25
03 04 08 14 20 25
05 06 09 15 21 25

The difference is phenominal with the 7 line guarantee only covering 34,300 of the possible 177,100 combinations of 6 integers for the Pool 25 game or 19.37% for a match 3 integers whereas the latter tailor made 7 lines covers 122,671 or 69.27%. You may notice the following repetition in the guarantee lines: -

7 Comb1's repeated 6x
21 Comb2's repeated 5x
35 Comb3's repeated 4x
35 Comb4's repeated 3x
21 Comb5's repeated 2x

Contrast this with the 7 maximized coverage lines for Pool 25 where the paying Comb3's, Comb4's and Comb5's are not repeated at all.

The attributing of a guarantee for a small Pool as having some merit when applied to a much larger Pool is one of the three biggest con-artist tricks in Lotto analysis and ranks alongside that of thinking the history of draws is relevant and numerology based filters can improve your chances and they are  all debunked on this site.

We will look at the merits of partial or % Covers or Wheels, because you will see an obsession with meeting the full requirements of a Cover means you may be including a Comb 6 which has 20 threes in it just because 1 three is not covered. Contrast this with in a 6/49 Lotto at the outset of building up your cover any six will cover 260,624 sixes from the 13,983,816 - a significant difference.

The question is raised as to whether your percentage progress towards achieving the goal of a cover gives any merit to a partial set given that a high premium is paid for guaranteeing a partial entitlement in each game ie in a 6/49 Lotto the odds say you should get an average of 3 three prize wins every 170 plays whereas your guarantee is only 1 fom a 163 line C(49,6,3,6) cover. It will be shown that a random selection of 163 combinations on average gives a better percentage return than the distorted prize distribution cover that guarantees a paltry comb3 prize when compared to the amount outlaid and as per the odds an average 3 comb3 prizes are obtained anyway.

Colin Fairbrother

Lotto Draws have no relationship to one another; the integers serve just as identifiers. Any prediction calculation on one history of draws for a same type game is just as irrelevant as another.
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