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Brief presentation.

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First things first. You might want to know the odds. Correctly, the term used should always be PROBABILITY. The lottery and lotto games have a multitude of possibilities or cases. Each case has a specific probability, precisely calculated by mathematical formulas.

The probability can be calculated in three ways: ‘exactly’, ‘at least’ and ‘at most’. The differences are more than subtle: The differences are essential.

For example, given a “lotto” game consisting of 9 numbers. You play a “lotto wheel or system” consisting of 9 numbers. The probability to get EXACTLY ’4 of 6’ winners with a 9-number wheel in a lotto-6 game is 0 (zero). Such an event is impossible!

However, the probability to get AT LEAST ’4 of 6’ winners with a 9-number wheel in a lotto-6 game is 1: Certainty! Further, the probability to get AT LEAST ’4 of 6’ winners with a 9-number wheel in a lotto ‘6 of 49’ (notice the difference!) game is ‘1 in 135’.

Examples of probabilities for a lotto ‘6 winners of 49 numbers’:

 The odds calculated as EXACTLY in a lotto game '6/49':

~ 0 of 6 in 6 from 49  -> 1 in 2.29

~ 1 of 6 in 6 from 49  -> 1 in 2.42

~ 2 of 6 in 6 from 49  -> 1 in 7.55

~ 3 of 6 in 6 from 49  -> 1 in 56.66

~ 4 of 6 in 6 from 49  -> 1 in 1032.4

~ 5 of 6 in 6 from 49  -> 1 in 54200.84

~ 6 of 6 in 6 from 49  -> 1 in 13983816

 The odds calculated as AT LEAST in a lotto game '649':

~ 0 of 6 in 6 from 49  -> 1 in 1

~ 1 of 6 in 6 from 49  -> 1 in 1.77

~ 2 of 6 in 6 from 49  -> 1 in 6.62

~ 3 of 6 in 6 from 49  -> 1 in 53.66

~ 4 of 6 in 6 from 49  -> 1 in 1013.03

~ 5 of 6 in 6 from 49  -> 1 in 53991.57

~ 6 of 6 in 6 from 49  -> 1 in 13983816

You may also choose to play a POOL of numbers (i.e. a lotto system or a lottery wheel). Let’s take the most efficient size of the pool: 18 lotto numbers. You will find at saliu.com two great lotto wheels for 18 numbers: in 45 combinations, and 51 lines, respectively. Search for ‘lotto wheels’ at the site, or google the term (then select saliu.com in the results list). If you really want to wheel your lotto numbers, you should always apply only those two lottery wheels.

The odds calculated as EXACTLY in a lotto game '6/49':

~ 0 of 6 in 18 from 49  -> 1 in 18.99

~ 1 of 6 in 18 from 49  -> 1 in 4.57

~ 2 of 6 in 18 from 49  -> 1 in 2.9

~ 3 of 6 in 18 from 49  -> 1 in 3.81

~ 4 of 6 in 18 from 49  -> 1 in 9.83

~ 5 of 6 in 18 from 49  -> 1 in 52.65

~ 6 of 6 in 18 from 49  -> 1 in 753.28

 The odds calculated as AT LEAST in a lotto game '6/49':

~ 0 of 6 in 18 from 49  -> 1 in 1

~ 1 of 6 in 18 from 49  -> 1 in 1.06

~ 2 of 6 in 18 from 49  -> 1 in 1.37

~ 3 of 6 in 18 from 49  -> 1 in 2.6

~ 4 of 6 in 18 from 49  -> 1 in 8.19

~ 5 of 6 in 18 from 49  -> 1 in 49.21

~ 6 of 6 in 18 from 49  -> 1 in 753.28

Examples of probabilities for Powerball or Mega Millions ('Big Game') lottos:

 The odds calculated as EXACTLY in a Powerball game

 '5/55 AND 1/42':

~ 0 of 5 in 5 from 55  AND  0 of 1 in 1 from 42  -> 1 in 1.68

~ 0 of 5 in 5 from 55  AND  1 of 1 in 1 from 42  -> 1 in 68.96

~ 1 of 5 in 5 from 55  AND  0 of 1 in 1 from 42  -> 1 in 3.09

~ 1 of 5 in 5 from 55  AND  1 of 1 in 1 from 42  -> 1 in 126.88

~ 2 of 5 in 5 from 55  AND  0 of 1 in 1 from 42  -> 1 in 18.18

~ 2 of 5 in 5 from 55  AND  1 of 1 in 1 from 42  -> 1 in 745.45

~ 3 of 5 in 5 from 55  AND  0 of 1 in 1 from 42  -> 1 in 290.91

~ 3 of 5 in 5 from 55  AND  1 of 1 in 1 from 42  -> 1 in 11927.18

~ 4 of 5 in 5 from 55  AND  0 of 1 in 1 from 42  -> 1 in 14254.44

~ 4 of 5 in 5 from 55  AND  1 of 1 in 1 from 42  -> 1 in 584431.85

~ 5 of 5 in 5 from 55  AND  0 of 1 in 1 from 42  -> 1 in 3563608.83

~ 5 of 5 in 5 from 55  AND  1 of 1 in 1 from 42  -> 1 in 146107962

 The odds calculated as AT LEAST in a Powerball game

 '5/55 AND 1/42':

~ 0 of 5 in 5 from 55  AND  0 of 1 in 1 from 42  -> 1 in 1

~ 0 of 5 in 5 from 55  AND  1 of 1 in 1 from 42  -> 1 in 42

~ 1 of 5 in 5 from 55  AND  0 of 1 in 1 from 42  -> 1 in 2.56

~ 1 of 5 in 5 from 55  AND  1 of 1 in 1 from 42  -> 1 in 107.43

~ 2 of 5 in 5 from 55  AND  0 of 1 in 1 from 42  -> 1 in 16.68

~ 2 of 5 in 5 from 55  AND  1 of 1 in 1 from 42  -> 1 in 700.75

~ 3 of 5 in 5 from 55  AND  0 of 1 in 1 from 42  -> 1 in 278.28

~ 3 of 5 in 5 from 55  AND  1 of 1 in 1 from 42  -> 1 in 11687.7

~ 4 of 5 in 5 from 55  AND  0 of 1 in 1 from 42  -> 1 in 13859.61

~ 4 of 5 in 5 from 55  AND  1 of 1 in 1 from 42  -> 1 in 582103.43

~ 5 of 5 in 5 from 55  AND  0 of 1 in 1 from 42  -> 1 in 3478761

~ 5 of 5 in 5 from 55  AND  1 of 1 in 1 from 42  -> 1 in 146107962

II • •

After we know the “odds” (probabilities) correctly, we are ready to generate optimized random combinations for any lotto and lottery games. The great online application (random number generator) also offers sensible advice.

“It is recommended to run a generator several times ~ before attempting to play! The probability is higher as you compress the time.

Also, be mindful of 'Ion Saliu's Paradox of N Trials', as presented on saliu.com/formula.htm . Rather than playing one or few combinations every draw, save the money and play more combinations, more rarely.  The winning probability increases by as much as 37% ~ for the same cost!”

The superiorly randomized numbers (combinations) certainly increase the winning chance for the player. The combination generators employ intelligent inner filters. The filters are math-based restrictions that eliminate combinations with poor statistics.  You would certainly wait your entire life and never see a lotto 6 combination such as 1-2-3-4-5-6. There are thousands of lotto games (from a historical perspective). I wonder why none of them has drawn such a "popular" lotto combination (or, newest term, ComboNation -- plural is CombosNations)? You know, this is a Universal occurrence, mind you. Why are there NO perfect shapes in the Universe? You know, shapes such as perfect lines, or circles, or spheres, or cones… Only Randomness is Almighty!

Lotto 649, 6-number combinations:

  12  21  33  35  37  49

   2   5   8  26  33  41

   3  27  34  39  46  47

   8  12  30  35  38  40

  11  14  23  36  44  47

  18  20  32  34  40  44

   5  10  13  19  39  45

   3  21  28  32  36  48

   1   6   8  11  17  32

   5  17  25  26  33  43

Powerball ‘5 of 55 and 1 of 42’ (no pools) combinations:

  14  28  33  42  43   21

  12  24  39  52  53    3

   4   9  15  18  45   18

   2  14  33  46  54   42

   9  31  37  39  50   26

   6   7   8  23  28   16

   5  28  30  33  47   22

   7  12  22  23  49    1

   7  13  14  28  29    1

  15  19  32  45  49    3