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Colin F
Lotto Systems Tester Creator & Analyst

To dream the impossible dream ...

Joined: September 30 2004
Location: Australia
Online Status: Offline
Posts: 678

Posted: August 27 2008 at 1:45am

Playing a Wheel with Guarantee, 3 if 4 in 19
or 30 Line Cover C(19,6,3,4)=30
in a Pick 6, Pool 49 Lotto Game
an Analysis of Win Groupings for 13,983,816 Possibilities
by Colin Fairbrother

Would you knowingly play a set of numbers in a Pick 6, Pool 49 Lotto game where for no good reason 3 of the combinations of 4 integers are repeated twice and repectively 57 of the combinations of 3 integers are repeated twice and 2 repeated 3 times. Well, that is the case with this Lotto Wheel or Cover which guarantees a Three win if 4 of the integers are correct in a pool of 19 you have chosen out of the possible 49. The decoy with these nonsense Covers, that have been touted since the 1980's by various con-artists and still are, is the guarantee, without consideration of how your chances of winning any prize or prizes are reduced!

This is Set 11 in an analysis comparing 15 differenty constructed sets of 28 (or near to that) numbers to play which includes other subset repeats, Covers or Wheels with Guarantees, Random Selections and the set which is proven to be the best, my Unique 3's ™ using all the integers for the game and maximizing the coverage of the potential winning numbers. You can generate these best numbers online and save them for later checking for wins at LottoToWin.

Regards
Colin

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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Colin F
Lotto Systems Tester Creator & Analyst

To dream the impossible dream ...

Joined: September 30 2004
Location: Australia
Online Status: Offline
Posts: 678

Posted: August 27 2008 at 8:33am

Playing a Wheel with Guarantee, 3 if 6 in 28
or 31 Line Cover C(28,6,3,6)=31
in a Pick 6, Pool 49 Lotto Game -
an Analysis of Win Groupings for 13,983,816 Draw Possibilities
by Colin Fairbrother

Using 28 integers from a Pool of 49 a noticeable improvement is shown over other Covers but with only 34% Covered after allowing an extra 3 combinations this is still well short of the 46% Coverage for my best set. Looking at the repeat table below we see that 46 Threes are repeated twice and 20 trice and 7 Fours are repeated twice wasting respectively 86 and 7 chances.

This is Set 12 in an analysis comparing 15 differenty constructed sets of 28 (or near to that) numbers to play which includes other subset repeats, Covers or Wheels with Guarantees, Random Selections and the set which is proven to be the best, my Unique 3's ™ using all the integers for the game and maximizing the coverage of the potential winning numbers. You can generate these best numbers online and save them for later checking for wins at LottoToWin.

Regards
Colin

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Colin F
Lotto Systems Tester Creator & Analyst

To dream the impossible dream ...

Joined: September 30 2004
Location: Australia
Online Status: Offline
Posts: 678

Posted: August 27 2008 at 10:37pm

Playing 28 Lines with Unique Threes
in a Pick 6, Pool 49 Lotto game without Maximizing Coverage -
an Analysis of Win Groupings for 13,983,816 possible draw results
by Colin Fairbrother

The reason I include this playset is to show that simply constructing your number set from a lexicograpic or numerical order enumeration and making sure you don't duplicate a CombThree and you do include all the Pool integers you end up with a set that makes a mockery of all the Covers with a reduced Pool at around 28 lines. The construction is simple - just enumerate lexicographically the combinations of six integers and you will find you have all 49 integers in 29 lines. Delete the 28th line and that's it - you have a set with 34% coverage. The old saying, "Couldn't see the wood for the trees" comes to mind.

This is ranked Set 13 in an analysis comparison of 15 differently constructed sets of numbers to play which includes other subset repeats, Covers or Wheels with Guarantees, Random Selections and the set which is proven to be the best, my Unique 3's ™ using all the integers for the game and maximizing the coverage of the potential winning numbers. You can generate these best numbers online and save them for later checking for wins at LottoToWin.

ID	LexID	Comb	Comment
1	1	01 02 03 04 05 06
2	54956	01 02 07 08 09 10
3	96115	01 02 11 12 13 14
4	126006	01 02 15 16 17 18
5	146901	01 02 19 20 21 22
6	160816	01 02 23 24 25 26
7	169511	01 02 27 28 29 30
8	174490	01 02 31 32 33 34
9	177001	01 02 35 36 37 38
10	178036	01 02 39 40 41 42
11	178331	01 02 43 44 45 46
12	220593	01 03 07 11 15 19	Already used {1,3,4} {1,3,5} {1,3,6} {8,9,10} {11,12,13)
13	231953	01 03 08 12 16 20	Already used {8,9,10} {11,12,13} {12,13,14}
14	242496	01 03 09 13 17 21
15	252262	01 03 10 14 18 22
16	324893	01 03 23 27 31 35
17	327421	01 03 24 28 32 36
18	329652	01 03 25 29 33 37
19	331610	01 03 26 30 34 38
20	341318	01 03 39 43 47 48
21	370322	01 04 07 12 17 22
22	380346	01 04 08 11 18 21
23	392020	01 04 09 14 15 20
24	400596	01 04 10 13 16 19
25	474134	01 04 23 28 33 38
26	476238	01 04 24 27 34 37
27	478784	01 04 25 30 31 36
28	480400	01 04 26 29 32 35	Not used
29	490408	01 04 40 44 47 49

There are 28 Prize Groupings for this set; the table below reduces this to 13 by giving the main prize grouping and a range for the lesser prizes. eg Of the 362,172 combinations with a single Four win 154,999 have no other prizes.

Regards
Colin

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Colin F
Lotto Systems Tester Creator & Analyst

To dream the impossible dream ...

Joined: September 30 2004
Location: Australia
Online Status: Offline
Posts: 678

Posted: February 15 2009 at 7:25pm

Playing 28 Random Selections or Quick Pick Lines
in a Pick 6, Pool 49 Lotto game -
an Analysis of Win Groupings for 13,983,816 possible draw results
by Colin Fairbrother

Unlike the 14 other sets of numbers analysed in this series Random Selections vary a bit in their structure. To be seen to be fair in choosing a representative example I have included a table below showing the first 28 draws for the year in 4 USA 6/49 State games. As you can see the variation is small and even the lowest percentage covering of any prize at 40% comfortably beats the best of the Covers or Wheels with Guarantees by 7% and the worst by 35%. I have chosen Wisconsin 2007 as being the closest to the average to do the analysis on.

For the self styled "experts" who have disparaged Random Selections the egg is on your face. For all the courageous people who through no fault of their own have limited speech ability, some of whom I worked with many years ago and found to be highly intelligent, this is a win I dedicate to you.

This is ranked Set 14 (ie the second best) in an analysis comparison of 15 differently constructed sets of numbers to play which includes other subset repeats, Covers or Wheels with Guarantees, Random Selections and the set which is proven to be the best, my Unique 3's ™ using all the integers for the game and maximizing the coverage of the potential winning numbers. You can generate these best numbers online and save them for later checking for wins at LottoToWin.

The figures given here are from my own Lotto set analyzer. There are 37 Prize Groupings for this set; the table below reduces this to 14 by giving the main prize grouping and a range for the lesser prizes. eg Of the 368,211 combinations with a single Four win 228,246 have no other prizes.

Repeats Analysis Random Selections sample:

For the Ones we see that only 46 of the 49 are used and the idea of "balancing" or having them appear the same number of times is proven absurd. For the Threes which do pay unlike the ones 10 are repeated twice and 1 Four is repeated. So, to avoid the repetitions which reduce your chances for a prize use my Best Unique 3's ™.

Regards

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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Colin F
Lotto Systems Tester Creator & Analyst

To dream the impossible dream ...

Joined: September 30 2004
Location: Australia
Online Status: Offline
Posts: 678

Posted: February 15 2009 at 7:25pm

Best possible Set of Numbers to play in
Pick 6, Pool 49 Lotto analyzed by grouping of
Win results for all possible 13,983,816 winning numbers
by Colin Fairbrother

Playing just 28 numbers in a 6/49 Lotto game this Lotto Design gives you nearly a 46% chance of getting a prize each draw! The other designs shown with excessive repeat subsets don't even come close, even when a few extra plays are allowed for the Covers or Wheels with Guarantees. Those that are within 10% proximity are definitely not Covers or Wheels with Guarantees and effectively this proves wrong that Covers or Wheels with Guarantees are superior for this number of combinations as advocated by the likes of Professor Iliya Bluskov and Gail Howard. Moreover, due to the distortionary nature of maximized Covers, with excessive repetitions, as related to Lotto where the minimum pool is 25, my Unique 3's ™ using the full Pool and maximizing Coverage against the main numbers are always superior by a long margin.

How does the 54% no win per draw stack up against probability formula? One must be wary here because 13,983,816 possibilities is not the same as that many random draws. Considering 28 plays over 13,983,816 draws is unrealistic and it is unnecessary as over just say, 2,000 draws your chances of getting any prize per draw will be around 52% which also means your chances of getting nothing per draw are 48%. There is a correlation with the difference in the figures being explained through nearly 9% of the possible draws giving multiple wins which when averaged out increases the Win percentage. It's a good measurement of getting something or nothing or the grouping most likely for a draw to occur in and realistically nothing, a Three or a Four is what you are more likely to get.

I believe I have made an absolutely solid case for using -

Unique 3's™ (and therefore no duplicate Fours, Fives or Sixes)
.
With all integers used in the Lotto game
.
And Coverage of all possible winning sixes maximized

"You can lead a horse to water but you can't make it drink!"

Interestingly, those who have looked through the test results forum would have recognized a familiarity with a post I made back in December, 2004 on a 50% Cover for a 6/49 Lotto game using all integers twice and with the best coverage. At that stage I had not worked out the fatal flaw with optimized Covers or Wheels with Guarantees ie sacrificing your chances of multiple wins by stupidly guaranteeing one pitiful win. Looky here!

Regards
Colin

ps 1 Having established the principles for the best Lotto Play Sets my objective in starting this web site has been achieved. I hoped with the forum format that there would be some constructive input from others but that has not been the case so I will in due course construct a different portal with a greater emphasis on presenting the information, rather than looking for input from others. I have done a complete makeover of LottoToWin to enable you to play and store these number sets so you can check for wins later and this will be uploaded to commence with the USA PowerBall configuration change in January 2009 from 55 to 59 main numbers and from 42 to 39 for the PowerBall. Practically all Lotto games around the world will be covered and the annual subscription will be a nominal $5.00.

ps 2 Here is a summary of each Number Set with 1 representing the worst: -

One Six combination is repeated 28 times; 98.13825% of Sixes uncovered.
.
Full System Eight or all the combinations of 6 integers from a Pool of 8; 95.30397% of Sixes Uncovered. How the Lottery Operators can promote the second worst style of play as increasing your chances of winning defies comprehension.
.
Cover or Wheel with Guarantee of a Five Win if 5 of the winning integers from a pool of 9 are obtained; despite allowing an extra 2 combinations to bring it up to 30 still 93.32568% of Sixes are uncovered. The abjectness and absurdity of this Cover is further revealed when it is realized that just 12 of the combinations maximized for coverage give the same uncovered percentage! Far from increasing the chances of getting a Five with a repeat of 54 of the Fives it decreases your chances not to mention the 624 Fours and 916 Threes repeated. The section of the mathematical community that espoused this Cover as being beneficial in Lotto and still continue to do so, should bow their heads in shame. The ignominy for the mathematical community at large is that exposure of this fraud was not done by one of their own but by yours truly, a competent database programmer guy that went to the trouble of checking things out.
.
One Five combination is repeated 28 times; 89.44119% of Sixes uncovered but still better than 5if5in9 Cover.
.
Cover or Wheel with Guarantee of a Four win if 4 of the winning integers from a pool of 11 are obtained; despite allowing an extra 4 combinations to bring it up to 32 still 88.25823% of Sixes are uncovered.
.
One Four combination is repeated 28 times; 83.99215% of Sixes uncovered but still better than a System play or both the 5if5in9 or 4if4in11 Covers.
.
C(14,6,4,5)=30
.
One Three combination is repeated 28 times; 73.48612% of Sixes uncovered but still better than a System play or the 5if5in9, 4if4in11 or 3if3in15 Covers.

.
Cover or Wheel with Guarantee of a Three win if 3 of the winning integers from a pool of 15 are obtained; despite allowing an extra 3 combinations to bring it up to 31 still 74.28749% of Sixes are uncovered. One Three combination is repeated 28 times; 73.48612% of Sixes uncovered but still better than a System play or the 5if5in9, 4if4in11 or 3if3in15 Covers.
.
C(24,6,3,5)=30
.
Cover or Wheel with Guarantee of a Three win if 4 of the winning integers from a pool of 19 are obtained; despite allowing an extra 2 combinations to bring it up to 30 still 69.60506% of Sixes are uncovered. For 28 of the combinations maximized for coverage of the Sixes the uncovered percentage rises to a whopping 91.15284%. Lordy, Lordy how can brain matter be so under utilized?
.
Cover or Wheel with Guarantee of a Three win if 6 of the winning integers from a pool of 28 are obtained; despite allowing an extra 3 combinations to bring it up to 31 still 65.485% of Sixes are uncovered.
.
Partial Cover to 28 combinations of 6 integers generated to give maximum coverage for 3if3in49 but only using pool of 48 to give 65.93677% of Sixes uncovered.
.
Good old Ramdom Selections - 2nd best and putting to shame all the nonsense that has been promoted since the 1980's with 60.33555% uncovered for the 28 combinations.
.
The best - 28 combinations with Unique Threes using the full pool of 49 and with coverage maximized to give only 54.25824% of Sixes uncovered.

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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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

Topic: ANALYSIS OF 15 LOTTO NUMBER SETS - WORST TO BEST
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