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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: Myth & Fallacy for distorted Partial Lotto Covers
    Posted: April 16 2007 at 12:51am
Myth and Fallacy for distorted Partial Covers or Wheels
By Colin Fairbrother
A Cover is only a Cover when the final combination is added to whatever lines it took to give the guarantee. Once you have a Cover that guarantees, say, that you will get a single three prize if you have 6 of the integers in a 6/49 Lotto ie C(49,6,3,6)=163  - then your reward is far short of what you can expect to get on average in lower prize wins according to probability - in fact about a third. Even if you spend a high amount per draw as with a Cover that guarantees you pretty well 20 threes per draw (C(49,6,3,3)=1222 this is still only in accordance with or less than the odds for threes for around that number of tickets.
To achieve the Cover in the minimum number of lines distortions are introduced which effect the yield. For example to get the 163 lines for a guarantee of a Three prize in the 6/49 Lotto game a Steiner system is used C(22,6,3,3)=77 which certainly gets as many Threes as possible into 77 lines (1540) but does not give the best coverage for all the 13,983,816 combinations of six integers for that number of lines. ie only around 8% compared to 88% with still 1540 unique Threes.

The construction of such a minimun line cover using whatever distortions means it can't be used progressively on a partial basis. Randomize the 163 line 6/49 cover and the coverage fo 77 lines is only 56% a very poor result indeed. Just as a broken bike chain is useless and when usable is only as strong as the weakest link, so a set of numbers that is distortingly produced is inferior to random selections where the prescribed intent and purpose is to maximize the yield.
A construction method for your 3if6 Cover using the full pool of integers, avoiding duplicate threes while maximizing coverage and definitely not using merges would give you progressively valid numbers of combs until coverage is achieved as I have done in 365 combs. Even for a Lotto game with a low pool of integers as in the USA West Virginia 6/25 game this is not the way it is done to achieve the "optimum" Cover as 3if3 and 3if4 merges are used and you end up with 91 Threes repeated twice, 4 Threes repeated thrice, 8 Fours repeated twice and 1 Four repeated thrice and that definitely ain't nice.
Looking further at the now infamous (due to my debunking) C(49,6,3,6,1)=163 Cover built by merging a C(22,6,3,3,1)=77 with a C(27,6,3,4,1)=86 ie you will get at least one Three if you play the 163 lines and indeed, out of all proportion that is all you will get for some 26% of the 13,983,816 possibilities for the winning draw. (You're excused for thinking that for playing 163 combinations the dominant grouping would be that which returned 3 Threes ie in accordance with the odds of 1 in 57.) .
Taking the first 77 Combinations of the 163 line Cover we have an inferior 56.19136% progress score towards full coverage if we get 6 integers matching the winning number. Compare this with generating 77 Combs 3 if 3 using the full 49 integers (with no duplicate Threes) which gives 64.07404% Coverage for the 3 if 6. If you go the extra distance and maximize the coverage while still maintaining no duplicate Threes as in my Unique 3's ™ then for the 77 Combs you get a whopping 86.88079% Coverage. To twist the knife, further progression shows an increasing disparity due to the insane obsession of those who wish to achieve a stupid objective and who are prepared to distort and reduce the percentage return no matter what the cost - say no more Colin.   
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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