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Topic: Correlation between Lotto Cover/Wheel Guarantees  
Author  Message 
Colin F
Lotto Systems Tester Creator & Analyst To dream the impossible dream ... Joined: September 30 2004 Location: Australia Online Status: Offline Posts: 678 
Topic: Correlation between Lotto Cover/Wheel Guarantees Posted: September 16 2012 at 10:10pm 
CORRELATION BETWEEN LOTTO COVER OR WHEEL GUARANTEES
FOR VARIOUS POOL SIZES by Colin Fairbrother Real Lotto players that give some thought to the numbers they play in a rational way realize that a first prize win is highly unlikely but for what should be a modest sum wagered not impossible and for that sum they would like to maximize their wins. If you played around 3 times 57 lines ie 171 random selection lines per draw you would reasonably expect to get an average of 3 wins per draw. If for 163 lines played per draw an average of close to 3 wins per draw was guaranteed then this would be relatively attractive (still negative return), if you were bent on wagering as in the UK £163 for £30 or 18% return. However, if the guarantee is only £10 or 6% return and on analysis you find that the structure of the set played is skewed or distorted towards obtaining a single CombThree prize instead of a multiple prize of 3 CombThree wins then the attraction is practically nonexistent for most rational players. There are a few irrational, obdurate players who when confronted with these facts still express a preference for a guaranteed prize no matter what the cost and how little the return. For 1,000 plays or around 6 draws playing 163 random selections the calculated chances of not getting a prize are an insignificant ¼ of 1 percent and only a 16% chance of a single CombThree prize with a 83% chance of getting multiple CombThree prizes and a CombFour for an overall percentage return using UK ticket costs and payouts of 21.6%. By comparison the 163 line cover guarantees only 1 CombThree prize and a 33.3% chance that it will be a single CombThree prize of £10. There is only a 66.7% chance of getting multiple CombThree prizes and a CombFour for an overall, lower percentage return of 16.6%. See chart here for various Covers and Pools per line quantity. Any student of Lotto number set or structure analysis needs to be familiar with Covers or Wheels with Guarantees, without as in my case necessarily endorsing them as a method to play. The minimum number of lines to achieve the guarantee and the structure of the set can be used for reference purposes. In Lotto Cover or Wheel parlance the Pick is the quantity of numbers filled in for 1 line played and the Pool is the quantity you can choose from. For a 6/49 Lotto game a 3if3 guarantee Cover or Wheel is the minimum number of lines that will ensure when played that of the 49c3 or 18,424 possible CombThrees at least 1 will match with the current record minimum of 1084 lines. The following chart shows there is a correlation between the various guarantees in this case 3if3, 3if4, 3if5 and 3if6 for various Pool sizes and the number of lines required. Silly assertions as by Professor Iliya Bluskov (click for article) that a 3if6 Cover is possible in about 87 lines ie about half the current record of 163, are shown to be absurd. Quite simply as shown in the chart as the Pool is increased for the 3if6 curve there is an increase in the number of lines to make a cover and a dip from around 163 lines to 87 for Pool 49 is just impossible as the entire correlation between the guarantees and for each guarantee curve would defy reconciliation. Here is what Professor Iliya Bluskov wrote on page 9 in his thesis of 1997 called New Designs and Coverings "If the syndicate chooses to play with tickets that correspond to the blocks of a (14,6,4) covering then they will get
at least one 4win whenever any 4 of their 14 numbers are drawn. Thus the syndicate will secure a certain garantee. Since any
(14,6,4) covering gives the same guarantee, they should choose the most "economical" covering; that is, the covering with the
smallest known number of blocks, which is currently 80, and hence they purchase the fewest number of tickets."
This is pure speil  coming from the likes of snake oil sales people like Gail Howard or Ken Silver it is expected  from a University Professor in Mathematics and Science in a mathematics thesis it begs belief. Whatever the complexity of any equation Bluskov came up with I for one would not accept it at face value. Where is the relevance to reality in those two paragraphs? To secure a certain prize in a hypothetical Pick 6, Pool 14 Lotto game only 4 lines need to be played ie C(14.6,3,6)=4 and for a 4win only 14 lines ie C(14.6,4,6)=14. Based on the number of lines (a lot less than 80) surely these are the most "economical" coverings according to the Professor despite their irrelevance to a 6/49 Lotto game? The odds for getting a 4win in a 6/49 Lotto game are 1 in 49c6/((6c4) x (43c2)) = 13983816/(15 x 903) = 1032.39. A 4win is expected on average roughly every 1000 plays and for a random seletion 80 line set using the Pool of 49 once every 13 draws. In fact you don't have to wait that long for a prize as getting any prize is 1 in 54 so a prize would be obtained on average every draw playing just 54 random selection lines. The odds for getting a 4win in a Pick 6, Pool 14 hypothetical Lotto game are 1 in 7 so playing 80 lines at least 34 3wins and 4 4wins are expected every draw with a 5win or greater with other prizes 73% of the draws and bearing no relation to the results in a 6/49 Lotto game. The chances of getting a 4win in a hypothetical Pick 6, Pool 14 Lotto game playing the 80 line Cover are certain but not when applied to a Pick 6, Pool 49 Lotto game. In fact due to the highly distorted structure of the 80 line Cover or Wheel your chances of getting a 3Win let alone a 4Win compared to a random selection using the full Pool of 49 are severely diminished. The possible number of distinct CombThrees for 80 Pick 6 lines are 80 x 20 = 1600 and distinct CombFours 80 x 15 = 1200 and in a Random selection of 80 lines close to this is achieved as there are 18,424 distinct CombThrees and 211,876 CombFours available. However the C(14,6,4,4)= 80 Cover or Wheel has 220 CombThrees repeated 4 times and 144 repeated 5 times with 95 CombFours repeated 2 times, 20 repeated 3 times and 16 repeated 5 times. For a CombThree match instead of 1600 working towards this aim there are only 364 and for the CombFours instead of a possible 1200 distinct CombFours there are only 870. The absurdity of qualifying the statement with "... 80 random tickets (on the same 14 numbers) guarantee nothing!" is blatently obvious. BEFORE THE DRAW THERE IS NO GUARANTEE; IN THE UNLIKELY EVENT THAT ANY FOUR OF THE RESTRICTED POOL NUMBERS CHOSEN ARE ALSO IN THE WINNING SIX NUMBERS DRAWN THEN THE CONSTRUCTION OF THE SET PLAYED GUARANTEES A COMBFOUR PRIZE. THE RUB IS THAT BECAUSE OF THE DISTORTED STRUCTURE WITH SO MANY REPEAT PAYING SUBSETS THIS IS DEFINITELY AND QUANTITAVELY LESS LIKELY TO HAPPEN. Mostly, major Lottery countries do not offer random selections on anything other than the Pick and Pool applicable to the game which in this case is 6 and 49 and where they do, like Australia it is restricted, in this case to System Entries or Full Wheels up to 18 integers or 18,564 lines. Even if someone went to the trouble of generating 80 Pick 6 random selection lines with a Pool restricted to 14 then this set would yield over 1,000 plays an 11% return with wins more often compared to 9% for the C(14,6,4,4)=80 Cover. 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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