• 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%. 

   

Regards
Colin Fairbrother

1. Over 50% of players play Random Selections or Quick Picks as produced by the Lotto operator which have a typically, low incidence of repetition in the subset three combinations and should give close to probability expectations for the lower prizes over an extended number of draws for the plays made. The drawback for players like myself is that we like a bit more control over what we play and like to know the actual makeup or structure of the set and the extent of repetition of the subsets so that the number of draws with no wins is minimized. Even if you play as low as 10 lines more often than not you will have repeat subset Threes which is definitely not maximizing your chances of success. So, when I got 5 right in a 6/44 Lotto game I could take some credit for the result by my method of play plus Lady Luck, of course.
   .
2. The next level of participation is by Systems or Full Wheels or all the combinations (5, 6 or 7 depending on the game) for a pool of integers as offered by the Lottery operators which can be conveniently specified on an entry form by filling in one block and then the system number or simply asking the terminal operator for say, a Quick Pick System 8. System entries have an extremely high repetition of the subset three combinations in Lotto. I do not recommend System or Full Wheels play and am 100% certain that there would be a lot more winners with 5 integers correct in a line were it not as popular as it is. If you are a System player with the same numbers each draw then you have justifiable fears for missing a draw. Based on my tests the excessive concentration of the subset 3's, 4's and 5's combinations relies upon that continuity to give for about 50% of the trial runs a significant percentage return above that for what probability indicates to expect; for the other 50% it can be significantly below. The relevant question is how many players these days play that way, rather than as I do, when prompted by some advertisement for a significant multi-million dollar 1st prize? System plays with other than the same integers each draw on average and over the long term under perform Random Selections or Quick Picks.  
   .
3. The third level of participation is by players randomly filling in the squares or using integers which are family birthdays etc which is close to (1) but with some personal input.
   .
4. The previous three levels probably account for 99% or more of the overall participation. The remaining 1% or so can be divided up as follows:
   .
   • The various road to riches schemes peddled by con artists. which invariably are either Covers or Wheels with Guarantees. Anyone who claims their bunch of sixes without repeats is better than another at getting First Prize in a Pick 6 Lotto game is a con-artist. Each combination of 6 integers has an equal chance of being picked at every draw and there is no improvement possible. With the subset 3's, 4's and 5's, yes, by avoiding duplications. I will put my money where my mouth is and donate $10,000 to charity if I can't prove that those who say different including the check (cheque) fraudsters are spouting absolute rubbish (You want to take me on Mr Terry Fisher?). 
     .
      
     These schemes have in common: -
     .
     (a) a predilection towards those that guarantee just one occurrence of a winning subset if the winning integers in the pool are satisfied.
     .
     (b) no distinction between the few with no or a low incidence of repetition of the subset threes and the predominant with extremely high repetition and therefore subject to the continuity of participation with the same integers each draw comments as outlined in (2) for System plays which makes a mockery of (c). Why the section of the mathematical community, including a Professor of Combinatorics, deemed it appropriate to foist all Covers on the Lotto playing public as being worthwhile continues to baffle me.
     .
     (c) a restriction on the pool of integers used which is most often fed by analysis of absence or recency and occurrence of the integers in the recent history of the particular Lotto's draws. (Any accurate advice or proof that the history has no relevance to the future draws is rejected or ignored by these recalcitrants.) I know of no academic that postulates there is anything to be gained by doing some calculation on the history of draws to come up with a set of numbers to play for the next as yet non-existent draw.
     .
     
   • The weirdo astrology or numerology or pseudo science or occult based twisted cogitations of bunkum based befuddlery that only the borderline insane can see the sense in for what is obviously nonsense.
     .
5. This brings me to the quiet, isolated voice of yours truly extolling the wisdom of playing sets of numbers with a low or no incidence of repetition of the subset threes to maximize one's chances of success. Verily and merrily, I say unto thee that it shall come to pass that a great bulk of the transgressors to event independence and double count will cover up their involvement by pretending to search in the rabbit warrens.

...

 

The Moving Finger writes; and, having writ,

Moves on: nor all thy Piety nor Wit

    Shall lure it back to cancel half a Line,

Nor all thy Tears wash out a Word of it.

 

...

 

THE RUBÁIYÁT OF OMAR KHAYYÁM OF NAISHÁPÚR

Persian poet and astronomer of the eleventh century.

• 1 win or 1 integer correct in 8 lines played would see you down by $5.82.
  .
• 2 Wins or 2 integers correct in 8 lines played - still down by $3.64.
  .
• 3 Wins or 3 integers correct in 8 lines played which is close to that expected from our probability calculation - still down $1.46.
  .
• If you get 4 correct then you would be ahead by 72¢.
  .
• If you get 8 correct you would be ahead by $9.44.
  .
• It's possible though for you to get 6 integers correct in all your 8 lines by simply playing the same line giving you $104.64 a 1308% return or $96.64 in front. The odds are 1 in 13,983,816 and even if you play 2 million lines of the same number your odds still remain the same!

Entering Lotto Number Sets in a Google search brought up an interesting Lotto article by VnutZ in OmniNerd titled Pattern Analysis of MegaMillions. VnutZ at first glance appears to be one of the main contributors on OmniNerd a repository of articles with at least some nerdy content. Unlike this site they do get a few intelligent comments. Interestingly, if you thought I was the only person to use the word "obfuscate" regularly - well, you're in for a surprise. 

• Idiots that know nothing about something and feel it is their duty to inform you of that.
  .
• Regulars that take their presence so seriously that on just about anything it is imperative that you know whether they agree or not hence the "I agree".
  .
• Prevaricators that really have nothing to contribute on a topic but insist on treating you to their waffle qualified by the proviso that they could be wrong without any reason for their compulsion to waste your valuable time.
  .
• Sneaky shysters that take every opportunity to promote their line of nonsense which has become so much a part of their life that they are in denial about anything that may put a shadow on it - to them it would be like being put on public display with their hands tied cross-like and naked.
  .
• Snake oil salesmen and women steeped in the lunacy of numerology, astrology and other wierdo occult nonsense.