The methodology I have been espousing for some time is:

Use the full pool of integers for the game. eg 45 or 49 .

Produce a set of numbers that does not have repeat combinations of the integers if they are paid on in the game. eg Unique 3's ™ .

Maximize the coverage (ie next best play without unnecessary optimization techniques) of the main winning combinations for combinations of 2 of the integers if they are paid on eg Powerball or 3 of the integers for the Pick 6 type games.

I deliberately chose to produce a progressively increasing coverage set where previous lines remain the same. While a marginal increase can be made in coverage through optimization techniques for a given number of combinations this does not necessarily increase the yield.

An example template follows for the Pool 25, Pick 6 West Virginia Cash 25 Lotto game. The odds are 1:177,100 for 1st prize which pays $25,000, 1:1554 for 2nd prize which pays $250, 1:69 for 3rd prize which pays $10 and 1:9 for 4th prize which pays $1.00. Cost of entry is $1 per line so playing the first 8 lines of the cover randomized per game draw you should average out to a win of some sort per draw albeit as low as 10% of what you have outlaid. It is important that you retain the order of the blocks for what you play - with the integers randomized of course.

The first important point to note is that the coverage as shown in the second table below is measuring the progress towards a certain win per draw which is not necessarily just 1 Three; it could be 2 Threes or 3 Threes or a Four.The second point is that this is not the end of the line; one could just as easily have set a cover goal of a minimum 2 Three wins per draw.

For the set shown if you play 9 lines per draw you should average at least 1 Three win per draw, if you play 18 lines per draw you should average 2 Three wins per draw, if 27 3 Threes etc.

If you played the 37 lines apart from being guaranteed at least 1 Three win per draw you have an 85% chance of averaging $14 in winnings or a percentage return of 38%. Here is a short summary.

Prize Group Combinations % Chance Cum %Chance

1 Four & 0 to 9 Threes 73188 41.33 41.33

5 Threes 26928 15.20 56.53

4 Threes 23224 13.11 69.64

6 Threes 17445 9.85 79.49

3 Threes 10640 6.01 85.50

2 Fours & 0 to 7 Threes 10629 6.01 91.50

7 Threes 6533 3.69 65.19

1 Five & 0 to 6 Threes 4218 2.38 97.57

2 Threes 2324 1.31 98.89

8 Threes 1378 0.78 99.67

1 Three 227 0.13 99.79

9 Threes 160 0.09 99.88

3 Fours & 0 To 3 Threes 153 0.09 99.97

1 Six 37 0.02 99.99

10 Threes 16 0.01 100.00

As you can see you have a better chance of getting a Five and overall a 99.87% chance of getting something other than a solitary Three win. Interestingly, instead of 1st prize being the lowest chances of success group with 37 possible winning combinations for the draw that will give this there is a group that pays 10 Threes with only 16.

It is up to you how much you want to spend per draw but with my method as you increase the number of combinations played so your chances of getting a higher prize increase proportionately. This kind of distribution is referred to as normal, Gaussian or bell curve and is the most appropriate where money is paid and a return on average obtained, albeit in Lotto for state run games around the 15% to 30% for the two or sometimes three lowest prize levels.

A distorted Wheel or Cover can be done in 22 combs with duplicate Threes which is constructed to give more lower prizes in the warped notion of guaranteeing a single Three win in a lower number of combinations. You need look no further than the two largest groupings to assess its inferiority when the first 22 combs of my set are compared with those of the distorted cover - mine has a 28.6% chance of a Four win (worth 5 Threes) with up to 5 extra Threes and 24.3% for 3 Threes whereas the distorted Cover has 24.1% for just 1 Three and 21.99 for 2 Threes. How did they get away spreading this nonsense for so long?

C(25,6,3,6)=37 (Unique 3's™, Maximized Coverage)

Line Block Coverage Cum Coverage % Cum Coverage

1 01 02 03 04 05 06 22060 22060 12.45623

2 07 08 09 10 11 12 21660 43720 24.68661

3 13 14 15 16 17 18 21260 64980 36.69113

4 19 20 21 22 23 24 20860 85840 48.46979

5 01 02 07 13 19 25 13420 99260 56.04743

6 03 04 08 14 20 25 12277 111537 62.97967

7 05 06 09 15 21 25 11134 122671 69.26651

8 10 11 16 17 22 23 10176 132847 75.01242

9 01 03 10 12 18 24 8510 141357 79.81761

10 02 05 11 12 14 24 6131 147488 83.27950

11 04 06 07 08 18 22 5904 153392 86.61321

12 09 12 16 17 19 20 4836 158228 89.34387

13 03 08 13 15 21 23 4106 162334 91.66233

14 04 10 11 13 15 20 2802 165136 93.24449

15 01 07 09 14 21 23 2590 167726 94.70694

16 02 06 08 16 17 24 2083 169809 95.88311

17 05 11 18 19 23 25 1799 171608 96.89892

18 03 05 07 15 16 22 1276 172884 97.61942

19 02 04 10 17 18 21 1023 173907 98.19706

20 06 09 12 13 14 22 952 174859 98.73461

21 01 04 15 17 24 25 563 175422 99.05251

22 01 05 08 10 19 20 444 175866 99.30320

23 03 06 07 11 19 20 349 176215 99.50028

24 02 09 15 18 22 23 266 176481 99.65047

25 11 12 13 16 21 25 230 176711 99.78035

26 04 05 07 09 13 24 142 176853 99.86053

27 06 10 14 16 19 25 100 176853 99.91699

28 02 06 12 20 23 25 50 177003 99.94522

29 01 03 08 09 17 22 36 177039 99.96555

30 04 12 14 15 19 23 25 177064 99.97967

31 01 06 16 18 20 21 15 177079 99.98814

32 03 05 10 13 17 25 8 177087 99.99265

33 08 10 14 15 22 24 6 177093 99.99604

34 03 11 14 18 21 22 4 177097 99.99830

35 01 06 11 13 23 24 1 177098 99.99887

36 02 07 14 17 20 22 1 177099 99.99943

37 03 09 16 23 24 25 1 177100 100.00000

The most dramatic results will be seen in the short term with more prizes if you previously played System entries (Full Wheels) or other Covers or Wheels with guarantees with high repetition of the subset threes, fours and fives. Over random selections there is a discernible improvement but more to the point is the knowledge that you have done the best possible in improving your chances of winning a prize.

Regarding First Prize as long as your lines are different, then any line is just as good as any other. Only con-artists claim credit for supplying numbers that win first prizes.

Regards

Colin Fairbrother

This article first published on the web 23/1/2009 and has been viewed 7311 times. The author may be contacted at fairbros@bigpond.com. To generate sets of Lotto numbers to play for most Lotto games around the world go to LottoToWin ^{®} where for a US$5.00 annual subscription you can store the numbers as well, to check later for wins. The numbers produced have no duplicate subset combinations of two integers (if applicable) or three integers, use all the integers for the particular Lotto game and maximize the coverage of the potential winning main number. The articles on this site have been selected from the many at the forum LottoPoster