Colin Fairbrother

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whether other than through sheer luck the odds can be bettered.

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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 6743 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
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