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Analysis by Grouping Win Results per Possible Winning Number
 LottoPoster Forums : ANALYSIS OF VARIOUS LOTTO NUMBER SETS : Analysis by Grouping Win Results per Possible Winning Number
Message Icon Topic: Unique 3's 158 lines beats 163 line Lotto Cover. Post Reply Post New Topic
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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: Unique 3's 158 lines beats 163 line Lotto Cover.
    Posted: May 29 2008 at 3:26am


Why playing 158 Lotto numbers with Unique 3's™
is better than the minimum Three prize
163 line Cover or Wheel with Guarantee.
by Colin Fairbrother
Much has been made of the Cover or Wheel with Guarantee which guarantees a minimum Three prize win if the 163 numbers, blocks or lines are played each draw. This certainty for what is a token prize of some $2.00 after expending some $81.50 has a penalty in that to achieve this dubious goal in Lotto, inefficiency has to be built into the number set by duplication through merging two Covers C(22,6,3,6,1)=77 with C(27,6,3,4,1)=86. 
An analysis of both the 163 line Cover set and a 158 Line set I constructed where no combination of 3 of the 49 integers used in the Lotto game is repeated follows.
From the data for the Cover we see that 3,595,746 or 25.71362% of the possible 13,983,816 winning numbers would produce only a Three win or some $2.00. As the Fairbrother Unique 3's set is only 158 lines there is a saving each draw of some $2.50 which more than compensates for the 115,048 combinations that pay nothing. For the remaining 99.17728% the return is generally significantly greater for the Fairbrother set in the up to 4 Three prizes -
  • for 1,018,273 a minimum saving of $2.50 plus 1 Three win of $2.00 better than the Cover's 1 Three win.
  • for 2,577,473 a minimum saving of $2.50 plus 2 Three wins or $4.00 better than the Cover's 1 Three win.
  • for 444,482 a minimum saving of $2.50 plus 2 Three wins of $4.00 better than the Cover's 2 Three wins.
  • for 2,817,161 a minimum saving of $2.50 plus 3 Three wins of $6.00 better than the Cover's 2 Three wins.
  • for 1,114,905 a minimum saving of $2.50 plus 3 Three wins of $6.00 better than the Cover's 3 Three wins.
  • for 57,847 a minimum saving of $0.50 over the Cover.
  • for 2,623,490 a minimum saving of $2.50 over the Cover.

With the Cover's emphasis on minimum prize delivery it is clearly seen that for 10,768,679 combinations or 77% of the lower prizes the Fairbrother Unique 3's™ set is decidedly in front of the Cover. Bearing in mind the chances of getting a Three prize in a 6/49 Lotto game are 1 in 56.65 one should expect at 57 lines for the 1 Win group to be dominant, at 113 lines the 2 Win group to be dominant and at close to 170 lines the 3 Win group dominant. This is obvious for the Fairbrother Unique 3's™ with the 3 Win Group dominant at 28.53% but the 163 line Cover is obviously distorted with the dominant group still the 1 win group at 25.71%. 

To ram the point home of the 13,983,816 possibilities for a draw for the Cover C(49,6,3,6,1)=163, 85.56% or 11,966,891 combinations of 6 integers deliver total Three prizes of 32,579,551 whereas the Fairbrother Unique 3's for a lesser percentage of 84.75% delivers 2,676,787 more at 35,256,338 - and with only 158 lines. If this does not convince the "Coverists" then one simply has to dismiss them as brain dead!
Cover C(49,6,3,6,1)=163
Fairbrother 158 Line Unique 3's™ Set
The distortion built into the C(49,6,3,6,1)=163 Cover becomes apparent when the Dependency Charts as produced by CoverMaster are compared below. The Fairbrother Unique 3's™ set has a smooth linear shape after the first 8 Combs that one should expect with the coverage proportionally decreasing as the number of combinations increases. Restricting the combinations used to those where no combination of 3 integers is repeated the line when extrapolated indicates a Cover can be obtained of around C(49,6,3,6)=300 but the curve considerably flattens out before that mark making the blocks required a bit more.
The 163 line Cover clearly shows its origins from a C(22,6,3,3)=77 optimally packed Cover merged with a ragged performance in the context used C(27,6,3,4)=86. (If you don't play more than 77 combs this begs the question why not use a 3if3 in the first place?). What is most evident is that removing 1 combination from any of the C(22,6,3,3) has an impact in each case of leaving 34,588 Combs uncovered for the Cover compared to the Fairbrother Unique 3's™ with only some 13,000 maximum. It should be obvious from this that the context of using Covers with the minimum number of blocks alone as the criteria is not applicable to Lotto where the highest percentage return is the real goal. 
Cover C(49,6,3,6,1)=163 Dependency Chart
Fairbrother 158 Line Unique 3's™ Set Dependency Chart
Looking at the yield from the first 8 Combinations where all the integers are unique begs the question why not play those only? An analysis from CoverMaster is shown below. Well, I won't argue against playing a lesser number of tickets than 163 saving $78.50 per draw. As you can see for 14% of the possible winning combinations you will get a Three prize. The point is that the magic 163 lines is not a valid objective in Lotto unless you have some overwhelming need to get at least 1 Three win every draw.
The only scenario I can think of where getting a certain Three win would be applicable is if you managed to make an even money bet with someone for more than your cost of some $82.00 (based on a ticket price of 50¢) and winner take all. You win if you get a prize in the next draw which you know is a certainty! (Ah, if only there were enough punters who scoffed at Lotto knowing of Lotto player acquaintances that had not had a win for years to take you up on that. Just make sure a trusted 3rd party holds the bets as I don't think you'll get a second go. Come to think of it the history buffs may decide it's a certainty to fail on the 2nd or 3rd draw!)
Failing that then be aware there is a penalty as the structure of the set is skewed to producing 1 Three win only for nearly 26% of the possible 13,983,816 numbers. My advice is to play an amount that you're happy to lose and structure your set of numbers if you're so inclined to give you the maximum chances of winning 1 of the prizes in each category as is achieved in my Unique 3's™.
Coverage has merit when used in a straight forward way using the full set of integers applicable to the Lotto game, the total possible combinations for the main integers as your test base, eliminating duplicate combinations of 3 integers and not treating the mimimum combinations for a guaranteed win as being an objective but rather the number of combinations you play as being a function of what you are comfortable to lose. Unfortunately, gimmickry has become the norm combined with an intention to deceive by obfuscating the true picture. Merges and multi-prize Covers do not deliver as well when the value of the wins is considered as a set of numbers with no combination of three integers repeated, from the full pool of integers and with the structure maximized for wins from the top down ie Fives, Fours and then the puny Threes ie 3if3. Contriving a set of numbers to maximize wins for the lowest prize is just another name for idiocy.
I am glad that I have made a worthwhile contribution in unraveling the spurious nonsense associated with Covers as applied to Lotto that has prevailed since the 1980's. The incontrovertible fact is that despite it being only 158 tickets or lines from my Unique 3's™ in a Pick 6 from 49 integers Lotto game it has 3,160 distinct Combinations of 3 of the integers compared to the Cover's 3,007 plus 253 duplicates; in anybody's language that amounts to more chances of winning and raises the question of why not play the 3,007 distinct Threes from the Cover in 151 lines with a bonus 13 distinct Threes and no Three subset duplications ie 3,020 distinct Threes. The day they do the Cover in 154 lines with just 10 Three repeats, well, then I will be really impressed as to the extent nonsense can be pursued. 
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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