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Lottery Blackbody Radiation

Topic closed. 39 replies. Last post 4 months ago by Sunglasses.

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JADELottery's avatar - MeAtWork 03.PNG
The Quantum Master
West Concord, MN
United States
Member #21
December 7, 2001
3675 Posts
Offline
Posted: July 29, 2016, 6:27 pm - IP Logged

As we stated in our blog, we were asked a question by CARBOB about how long does it take for all numbers in a Pick 3 type lottery to be picked; both in a single column and overall.

It led to an interesting formula that is very similar to Blackbody Radiation.

We'll start with a simple Pick 1 example.

This can apply to any individual Pick 3 column.

In the Pick 1 selection, we keep track of the number selected at each drawing.

Below is a table showing the Draw, Picked number and the Tracked # Selection.

The example shows on the 24th drawing, all the numbers have been selected.

On the 25th draw, the cycle starts over and the Tracking begins again.

Draw

Pick 1

Tracked # Selection

0

1

2

3

4

5

6

7

8

9

1

3

·

·

·

1

·

·

·

·

·

·

2

4

·

·

·

1

1

·

·

·

·

·

3

1

·

1

·

1

1

·

·

·

·

·

4

4

·

1

·

1

2

·

·

·

·

·

5

1

·

2

·

1

2

·

·

·

·

·

6

1

·

3

·

1

2

·

·

·

·

·

7

1

·

4

·

1

2

·

·

·

·

·

8

6

·

4

·

1

2

·

1

·

·

·

9

9

·

4

·

1

2

·

1

·

·

1

10

2

·

4

1

1

2

·

1

·

·

1

11

8

·

4

1

1

2

·

1

·

1

1

12

2

·

4

2

1

2

·

1

·

1

1

13

2

·

4

3

1

2

·

1

·

1

1

14

3

·

4

3

2

2

·

1

·

1

1

15

0

1

4

3

2

2

·

1

·

1

1

16

8

1

4

3

2

2

·

1

·

2

1

17

1

1

5

3

2

2

·

1

·

2

1

18

8

1

5

3

2

2

·

1

·

3

1

19

9

1

5

3

2

2

·

1

·

3

2

20

2

1

5

4

2

2

·

1

·

3

2

21

9

1

5

4

2

2

·

1

·

3

3

22

4

1

5

4

2

3

·

1

·

3

3

23

5

1

5

4

2

3

1

1

·

3

3

24

7

1

5

4

2

3

1

1

1

3

3

25

8

·

·

·

·

·

·

·

·

1

·

26

1

·

1

·

·

·

·

·

·

1

·

27

6

·

1

·

·

·

·

1

·

1

·

28

3

·

1

·

1

·

·

1

·

1

·

29

0

1

1

·

1

·

·

1

·

1

·

30

1

1

2

·

1

·

·

1

·

1

·

31

2

1

2

1

1

·

·

1

·

1

·

32

9

1

2

1

1

·

·

1

·

1

1

Continues...

Presented 'AS IS' and for Entertainment Purposes Only.
Any gain or loss is your responsibility.
Use at your own risk.

Order is a Subset of Chaos
Knowledge is Beyond Belief
Wisdom is Not Censored
Douglas Paul Smallish
Jehocifer

    JADELottery's avatar - MeAtWork 03.PNG
    The Quantum Master
    West Concord, MN
    United States
    Member #21
    December 7, 2001
    3675 Posts
    Offline
    Posted: July 29, 2016, 6:39 pm - IP Logged

    The next step was to gather a frequency of draws when the cycle ends.

    In the previous example, it was the 24th draw.

    We ran a simulation for Millions of draws to obtain a Million data set of end draw cycles.

    Below is a table of our obtained data for this run.

    The table shows there is a minimum of 10 draws; which is to be expected since there are only 10 numbers 0 to 9 that can be selected.

    The Peak appears to be at 24 draws.

    Next we will look at the graph of the data.

     

    Draws

    Pick 1 Tracked # Selection Frequency

    0

    0

    1

    0

    2

    0

    3

    0

    4

    0

    5

    0

    6

    0

    7

    0

    8

    0

    9

    0

    10

    344

    11

    1605

    12

    4306

    13

    7962

    14

    12670

    15

    19266

    16

    24277

    17

    29919

    18

    34560

    19

    38797

    20

    41426

    21

    43395

    22

    45105

    23

    44710

    24

    45240

    25

    43409

    26

    42265

    27

    40858

    28

    38108

    29

    36519

    30

    34598

    31

    31914

    32

    29250

    33

    27122

    34

    25506

    35

    23658

    36

    21466

    37

    19721

    38

    18198

    39

    16430

    40

    15337

    41

    14041

    42

    12429

    43

    11339

    44

    10231

    45

    8885

    46

    8500

    47

    7532

    48

    6914

    49

    5965

    50

    5333

    51

    4974

    52

    4461

    53

    4077

    54

    3847

    55

    3361

    56

    2983

    57

    2857

    58

    2536

    59

    2289

    60

    1979

    61

    1828

    62

    1573

    63

    1559

    64

    1076

    65

    1207

    66

    974

    67

    950

    68

    926

    69

    787

    70

    599

    71

    586

    72

    548

    73

    469

    74

    477

    75

    416

    76

    342

    77

    280

    78

    299

    79

    189

    80

    228

    81

    208

    82

    219

    83

    139

    84

    184

    85

    141

    86

    107

    87

    144

    88

    113

    89

    75

    90

    76

    91

    64

    92

    77

    93

    104

    94

    61

    95

    28

    96

    54

    97

    58

    98

    59

    99

    32

    100

    18

    101

    28

    102

    26

    103

    10

    104

    29

    105

    20

    106

    14

    107

    16

    108

    10

    109

    7

    110

    8

    111

    7

    112

    6

    113

    21

    114

    4

    115

    0

    116

    10

    117

    3

    118

    0

    119

    0

    120

    10

    121

    0

    122

    6

    123

    0

    124

    3

    125

    0

    126

    0

    127

    0

    128

    3

    129

    0

    130

    0

    131

    0

    132

    0

    133

    3

    134

    0

    135

    0

    136

    3

    137

    0

    138

    0

    139

    0

    140

    5

     

    Continues ...

    Presented 'AS IS' and for Entertainment Purposes Only.
    Any gain or loss is your responsibility.
    Use at your own risk.

    Order is a Subset of Chaos
    Knowledge is Beyond Belief
    Wisdom is Not Censored
    Douglas Paul Smallish
    Jehocifer

      JADELottery's avatar - MeAtWork 03.PNG
      The Quantum Master
      West Concord, MN
      United States
      Member #21
      December 7, 2001
      3675 Posts
      Offline
      Posted: July 29, 2016, 6:48 pm - IP Logged

      In the graph of the Tracked # Selections, we can see the frequency is skewed to the low end and tapers off to the high end.

       

       

      This graph looks very similar to a natural phenomenon know as Blackbody Radiation.

      Below is a graph of the Planck Radiation Formula.

       

       

      We tried to curve fit this formula to the data, but it did not fit very well.

      We had to come up with a different variation that looks nearly the same as the Planck Formula.

      Continues ...

      Presented 'AS IS' and for Entertainment Purposes Only.
      Any gain or loss is your responsibility.
      Use at your own risk.

      Order is a Subset of Chaos
      Knowledge is Beyond Belief
      Wisdom is Not Censored
      Douglas Paul Smallish
      Jehocifer

        JADELottery's avatar - MeAtWork 03.PNG
        The Quantum Master
        West Concord, MN
        United States
        Member #21
        December 7, 2001
        3675 Posts
        Offline
        Posted: July 29, 2016, 7:20 pm - IP Logged

        The formula expression we had to used is as follows.

         

        This expression fit the data far better.

        Using the expression we curve fit it and found the values for αβγ and δ

        The graph next shows the bar graph and the curve fit probability function.

         

         

        Continues ...

        Presented 'AS IS' and for Entertainment Purposes Only.
        Any gain or loss is your responsibility.
        Use at your own risk.

        Order is a Subset of Chaos
        Knowledge is Beyond Belief
        Wisdom is Not Censored
        Douglas Paul Smallish
        Jehocifer

          JADELottery's avatar - MeAtWork 03.PNG
          The Quantum Master
          West Concord, MN
          United States
          Member #21
          December 7, 2001
          3675 Posts
          Offline
          Posted: July 29, 2016, 7:26 pm - IP Logged

          The coefficients for the Pick 1 probability are:

          Coefficients

          Pick 1

          α

          -966.93367803712

          β

          30.6458275075256

          γ

          -0.165505462399517

          δ

          -0.105317939314043

           

          These plugged in the probability function gives the following graph.

           

          Continues ...

          Presented 'AS IS' and for Entertainment Purposes Only.
          Any gain or loss is your responsibility.
          Use at your own risk.

          Order is a Subset of Chaos
          Knowledge is Beyond Belief
          Wisdom is Not Censored
          Douglas Paul Smallish
          Jehocifer

            Avatar

            United States
            Member #139779
            March 3, 2013
            115 Posts
            Offline
            Posted: July 29, 2016, 7:32 pm - IP Logged

            The formula expression we had to used is as follows.

             

            This expression fit the data far better.

            Using the expression we curve fit it and found the values for αβγ and δ

            The graph next shows the bar graph and the curve fit probability function.

             

             

            Continues ...

            Is this the same or similar as the wave add in you made for excel 2007?

              JADELottery's avatar - MeAtWork 03.PNG
              The Quantum Master
              West Concord, MN
              United States
              Member #21
              December 7, 2001
              3675 Posts
              Offline
              Posted: July 29, 2016, 7:35 pm - IP Logged

              Using the coefficients and probability function we can now calculate the maximum frequency draws that it takes to draw all the numbers in a single column.

              This works out to be about 22.732498 draws.

              In addition, here are other points of interest in the data we sampled.

               

              ·

              Draws

              Minimum

              10

              Peak

              22.732498

              Mode

              24

              Median

              27

              Mean

              29.283008

              Maximum

              140

               

               

              Continues ...

              Presented 'AS IS' and for Entertainment Purposes Only.
              Any gain or loss is your responsibility.
              Use at your own risk.

              Order is a Subset of Chaos
              Knowledge is Beyond Belief
              Wisdom is Not Censored
              Douglas Paul Smallish
              Jehocifer

                JADELottery's avatar - MeAtWork 03.PNG
                The Quantum Master
                West Concord, MN
                United States
                Member #21
                December 7, 2001
                3675 Posts
                Offline
                Posted: July 29, 2016, 7:36 pm - IP Logged

                Is this the same or similar as the wave add in you made for excel 2007?

                This is something new.

                Presented 'AS IS' and for Entertainment Purposes Only.
                Any gain or loss is your responsibility.
                Use at your own risk.

                Order is a Subset of Chaos
                Knowledge is Beyond Belief
                Wisdom is Not Censored
                Douglas Paul Smallish
                Jehocifer

                  Avatar

                  United States
                  Member #139779
                  March 3, 2013
                  115 Posts
                  Offline
                  Posted: July 29, 2016, 7:50 pm - IP Logged

                  I have been trying to follow your research. So far it has led me to test skip ranges for single digits. this does tell when to best play the number. working with the 2007 add in I found that groups of 5 worked best. I was not having much luck with straight number runs but it did work better with box digit tracking. Are you going to make a new add in for this method? I find this very interesting and appreciate your work on this. I wonder how this formula in this thread would look when applied to digit skips?

                  Thank you.

                    Sunglasses's avatar - nicebear
                    Zaperlopopotam
                    Belgium
                    Member #173932
                    March 26, 2016
                    976 Posts
                    Offline
                    Posted: July 29, 2016, 7:51 pm - IP Logged

                    Using the coefficients and probability function we can now calculate the maximum frequency draws that it takes to draw all the numbers in a single column.

                    This works out to be about 22.732498 draws.

                    In addition, here are other points of interest in the data we sampled.

                     

                    ·

                    Draws

                    Minimum

                    10

                    Peak

                    22.732498

                    Mode

                    24

                    Median

                    27

                    Mean

                    29.283008

                    Maximum

                    140

                     

                     

                    Continues ...

                    I'd suggest to set the maximum to 140 to lifetime of the game.

                      JADELottery's avatar - MeAtWork 03.PNG
                      The Quantum Master
                      West Concord, MN
                      United States
                      Member #21
                      December 7, 2001
                      3675 Posts
                      Offline
                      Posted: July 29, 2016, 7:52 pm - IP Logged

                      We expanded this tracking to all the Pick 3 numbers and were excited to find the same formula worked for the Pick 3 overall tracking.

                      Below is an example of the tracking.

                      In this example, we can see all the numbers are picked by draw 8.

                      Then the cycle starts over and the next complete selection is at draw 18 or 10 draws to select all numbers.

                      Draw

                      Pick 3

                      Tracked # Selection

                      A

                      B

                      C

                      0

                      1

                      2

                      3

                      4

                      5

                      6

                      7

                      8

                      9

                      1

                      2

                      6

                      8

                      ·

                      ·

                      1

                      ·

                      ·

                      ·

                      1

                      ·

                      1

                      ·

                      2

                      0

                      1

                      6

                      1

                      1

                      1

                      ·

                      ·

                      ·

                      2

                      ·

                      1

                      ·

                      3

                      6

                      4

                      0

                      2

                      1

                      1

                      ·

                      1

                      ·

                      3

                      ·

                      1

                      ·

                      4

                      0

                      0

                      8

                      4

                      1

                      1

                      ·

                      1

                      ·

                      3

                      ·

                      2

                      ·

                      5

                      5

                      5

                      6

                      4

                      1

                      1

                      ·

                      1

                      2

                      4

                      ·

                      2

                      ·

                      6

                      1

                      5

                      1

                      4

                      3

                      1

                      ·

                      1

                      3

                      4

                      ·

                      2

                      ·

                      7

                      9

                      7

                      2

                      4

                      3

                      2

                      ·

                      1

                      3

                      4

                      1

                      2

                      1

                      8

                      0

                      3

                      4

                      5

                      3

                      2

                      1

                      2

                      3

                      4

                      1

                      2

                      1

                      9

                      0

                      9

                      2

                      1

                      ·

                      1

                      ·

                      ·

                      ·

                      ·

                      ·

                      ·

                      1

                      10

                      6

                      3

                      8

                      1

                      ·

                      1

                      1

                      ·

                      ·

                      1

                      ·

                      1

                      1

                      11

                      9

                      0

                      9

                      2

                      ·

                      1

                      1

                      ·

                      ·

                      1

                      ·

                      1

                      3

                      12

                      6

                      7

                      5

                      2

                      ·

                      1

                      1

                      ·

                      1

                      2

                      1

                      1

                      3

                      13

                      9

                      3

                      6

                      2

                      ·

                      1

                      2

                      ·

                      1

                      3

                      1

                      1

                      4

                      14

                      3

                      6

                      2

                      2

                      ·

                      2

                      3

                      ·

                      1

                      4

                      1

                      1

                      4

                      15

                      4

                      5

                      9

                      2

                      ·

                      2

                      3

                      1

                      2

                      4

                      1

                      1

                      5

                      16

                      8

                      4

                      7

                      2

                      ·

                      2

                      3

                      2

                      2

                      4

                      2

                      2

                      5

                      17

                      8

                      3

                      6

                      2

                      ·

                      2

                      4

                      2

                      2

                      5

                      2

                      3

                      5

                      18

                      9

                      1

                      2

                      2

                      1

                      3

                      4

                      2

                      2

                      5

                      2

                      3

                      6

                      19

                      0

                      3

                      5

                      1

                      ·

                      ·

                      1

                      ·

                      1

                      ·

                      ·

                      ·

                      ·

                      20

                      4

                      1

                      6

                      1

                      1

                      ·

                      1

                      1

                      1

                      1

                      ·

                      ·

                      ·

                      21

                      3

                      8

                      7

                      1

                      1

                      ·

                      2

                      1

                      1

                      1

                      1

                      1

                      ·

                      22

                      6

                      6

                      9

                      1

                      1

                      ·

                      2

                      1

                      1

                      3

                      1

                      1

                      1

                      23

                      3

                      5

                      4

                      1

                      1

                      ·

                      3

                      2

                      2

                      3

                      1

                      1

                      1

                      24

                      2

                      9

                      2

                      1

                      1

                      2

                      3

                      2

                      2

                      3

                      1

                      1

                      2

                      25

                      0

                      0

                      8

                      2

                      ·

                      ·

                      ·

                      ·

                      ·

                      ·

                      ·

                      1

                      ·

                      26

                      0

                      1

                      5

                      3

                      1

                      ·

                      ·

                      ·

                      1

                      ·

                      ·

                      1

                      ·

                      27

                      8

                      3

                      2

                      3

                      1

                      1

                      1

                      ·

                      1

                      ·

                      ·

                      2

                      ·

                      28

                      3

                      3

                      4

                      3

                      1

                      1

                      3

                      1

                      1

                      ·

                      ·

                      2

                      ·

                      29

                      8

                      6

                      0

                      4

                      1

                      1

                      3

                      1

                      1

                      1

                      ·

                      3

                      ·

                      30

                      3

                      7

                      0

                      5

                      1

                      1

                      4

                      1

                      1

                      1

                      1

                      3

                      ·

                      31

                      2

                      3

                      3

                      5

                      1

                      2

                      6

                      1

                      1

                      1

                      1

                      3

                      ·

                      32

                      6

                      7

                      7

                      5

                      1

                      2

                      6

                      1

                      1

                      2

                      3

                      3

                      ·

                       

                      Continues ...

                      Presented 'AS IS' and for Entertainment Purposes Only.
                      Any gain or loss is your responsibility.
                      Use at your own risk.

                      Order is a Subset of Chaos
                      Knowledge is Beyond Belief
                      Wisdom is Not Censored
                      Douglas Paul Smallish
                      Jehocifer

                        JADELottery's avatar - MeAtWork 03.PNG
                        The Quantum Master
                        West Concord, MN
                        United States
                        Member #21
                        December 7, 2001
                        3675 Posts
                        Offline
                        Posted: July 29, 2016, 7:56 pm - IP Logged

                        Knowing this formula works for Pick 3, we completed it for Pick 1 to Pick 5.

                        Below is a table of the frequency data we sampled.

                         

                        One Million Tracked # Selections 0-9

                        Draws

                        Pick 1

                        Pick 2

                        Pick 3

                        Pick 4

                        Pick 5

                        0

                        0

                        0

                        0

                        0

                        0

                        1

                        0

                        0

                        0

                        0

                        0

                        2

                        0

                        0

                        0

                        0

                        3995

                        3

                        0

                        0

                        0

                        24378

                        173281

                        4

                        0

                        0

                        14907

                        148658

                        301168

                        5

                        0

                        629

                        73153

                        220812

                        232686

                        6

                        0

                        8813

                        131099

                        199469

                        137767

                        7

                        0

                        29338

                        153688

                        147390

                        74468

                        8

                        0

                        55532

                        145563

                        98287

                        38103

                        9

                        0

                        76909

                        123660

                        62752

                        19275

                        10

                        344

                        91148

                        96463

                        38486

                        9677

                        11

                        1605

                        95825

                        73743

                        23778

                        4769

                        12

                        4306

                        93583

                        53976

                        14387

                        2403

                        13

                        7962

                        86657

                        38879

                        8607

                        1229

                        14

                        12670

                        76938

                        27920

                        5262

                        585

                        15

                        19266

                        67279

                        19803

                        3085

                        291

                        16

                        24277

                        57428

                        13978

                        1881

                        147

                        17

                        29919

                        48065

                        9847

                        1120

                        75

                        18

                        34560

                        39763

                        6899

                        659

                        36

                        19

                        38797

                        32691

                        5012

                        412

                        15

                        20

                        41426

                        26565

                        3379

                        247

                        15

                        21

                        43395

                        21883

                        2446

                        140

                        13

                        22

                        45105

                        17873

                        1615

                        82

                        0

                        23

                        44710

                        14162

                        1207

                        41

                        1

                        24

                        45240

                        11759

                        805

                        25

                        1

                        25

                        43409

                        9422

                        601

                        17

                        0

                        26

                        42265

                        7546

                        395

                        8

                        0

                        27

                        40858

                        6082

                        293

                        9

                        0

                        28

                        38108

                        4787

                        207

                        1

                        0

                        29

                        36519

                        3939

                        134

                        3

                        0

                        30

                        34598

                        3066

                        110

                        0

                        0

                        31

                        31914

                        2464

                        65

                        1

                        0

                        32

                        29250

                        1950

                        37

                        2

                        0

                        33

                        27122

                        1609

                        32

                        0

                        0

                        34

                        25506

                        1254

                        21

                        1

                        0

                        35

                        23658

                        1006

                        18

                        0

                        0

                        36

                        21466

                        854

                        11

                        0

                        0

                        37

                        19721

                        632

                        7

                        0

                        0

                        38

                        18198

                        519

                        5

                        0

                        0

                        39

                        16430

                        372

                        5

                        0

                        0

                        40

                        15337

                        335

                        8

                        0

                        0

                        41

                        14041

                        258

                        3

                        0

                        0

                        42

                        12429

                        209

                        1

                        0

                        0

                        43

                        11339

                        157

                        0

                        0

                        0

                        44

                        10231

                        126

                        2

                        0

                        0

                        45

                        8885

                        124

                        0

                        0

                        0

                        46

                        8500

                        91

                        1

                        0

                        0

                        47

                        7532

                        65

                        1

                        0

                        0

                        48

                        6914

                        50

                        0

                        0

                        0

                        49

                        5965

                        57

                        0

                        0

                        0

                        50

                        5333

                        36

                        0

                        0

                        0

                        51

                        4974

                        35

                        1

                        0

                        0

                        52

                        4461

                        25

                        0

                        0

                        0

                        53

                        4077

                        21

                        0

                        0

                        0

                        54

                        3847

                        15

                        0

                        0

                        0

                        55

                        3361

                        10

                        0

                        0

                        0

                        56

                        2983

                        14

                        0

                        0

                        0

                        57

                        2857

                        2

                        0

                        0

                        0

                        58

                        2536

                        2

                        0

                        0

                        0

                        59

                        2289

                        7

                        0

                        0

                        0

                        60

                        1979

                        2

                        0

                        0

                        0

                        61

                        1828

                        4

                        0

                        0

                        0

                        62

                        1573

                        5

                        0

                        0

                        0

                        63

                        1559

                        2

                        0

                        0

                        0

                        64

                        1076

                        0

                        0

                        0

                        0

                        65

                        1207

                        0

                        0

                        0

                        0

                        66

                        974

                        2

                        0

                        0

                        0

                        67

                        950

                        0

                        0

                        0

                        0

                        68

                        926

                        1

                        0

                        0

                        0

                        69

                        787

                        0

                        0

                        0

                        0

                        70

                        599

                        2

                        0

                        0

                        0

                        71

                        586

                        0

                        0

                        0

                        0

                        72

                        548

                        0

                        0

                        0

                        0

                        73

                        469

                        1

                        0

                        0

                        0

                        74

                        477

                        0

                        0

                        0

                        0

                        75

                        416

                        0

                        0

                        0

                        0

                        76

                        342

                        0

                        0

                        0

                        0

                        77

                        280

                        0

                        0

                        0

                        0

                        78

                        299

                        0

                        0

                        0

                        0

                        79

                        189

                        0

                        0

                        0

                        0

                        80

                        228

                        0

                        0

                        0

                        0

                        81

                        208

                        0

                        0

                        0

                        0

                        82

                        219

                        0

                        0

                        0

                        0

                        83

                        139

                        0

                        0

                        0

                        0

                        84

                        184

                        0

                        0

                        0

                        0

                        85

                        141

                        0

                        0

                        0

                        0

                        86

                        107

                        0

                        0

                        0

                        0

                        87

                        144

                        0

                        0

                        0

                        0

                        88

                        113

                        0

                        0

                        0

                        0

                        89

                        75

                        0

                        0

                        0

                        0

                        90

                        76

                        0

                        0

                        0

                        0

                        91

                        64

                        0

                        0

                        0

                        0

                        92

                        77

                        0

                        0

                        0

                        0

                        93

                        104

                        0

                        0

                        0

                        0

                        94

                        61

                        0

                        0

                        0

                        0

                        95

                        28

                        0

                        0

                        0

                        0

                        96

                        54

                        0

                        0

                        0

                        0

                        97

                        58

                        0

                        0

                        0

                        0

                        98

                        59

                        0

                        0

                        0

                        0

                        99

                        32

                        0

                        0

                        0

                        0

                        100

                        18

                        0

                        0

                        0

                        0

                        101

                        28

                        0

                        0

                        0

                        0

                        102

                        26

                        0

                        0

                        0

                        0

                        103

                        10

                        0

                        0

                        0

                        0

                        104

                        29

                        0

                        0

                        0

                        0

                        105

                        20

                        0

                        0

                        0

                        0

                        106

                        14

                        0

                        0

                        0

                        0

                        107

                        16

                        0

                        0

                        0

                        0

                        108

                        10

                        0

                        0

                        0

                        0

                        109

                        7

                        0

                        0

                        0

                        0

                        110

                        8

                        0

                        0

                        0

                        0

                        111

                        7

                        0

                        0

                        0

                        0

                        112

                        6

                        0

                        0

                        0

                        0

                        113

                        21

                        0

                        0

                        0

                        0

                        114

                        4

                        0

                        0

                        0

                        0

                        115

                        0

                        0

                        0

                        0

                        0

                        116

                        10

                        0

                        0

                        0

                        0

                        117

                        3

                        0

                        0

                        0

                        0

                        118

                        0

                        0

                        0

                        0

                        0

                        119

                        0

                        0

                        0

                        0

                        0

                        120

                        10

                        0

                        0

                        0

                        0

                        121

                        0

                        0

                        0

                        0

                        0

                        122

                        6

                        0

                        0

                        0

                        0

                        123

                        0

                        0

                        0

                        0

                        0

                        124

                        3

                        0

                        0

                        0

                        0

                        125

                        0

                        0

                        0

                        0

                        0

                        126

                        0

                        0

                        0

                        0

                        0

                        127

                        0

                        0

                        0

                        0

                        0

                        128

                        3

                        0

                        0

                        0

                        0

                        129

                        0

                        0

                        0

                        0

                        0

                        130

                        0

                        0

                        0

                        0

                        0

                        131

                        0

                        0

                        0

                        0

                        0

                        132

                        0

                        0

                        0

                        0

                        0

                        133

                        3

                        0

                        0

                        0

                        0

                        134

                        0

                        0

                        0

                        0

                        0

                        135

                        0

                        0

                        0

                        0

                        0

                        136

                        3

                        0

                        0

                        0

                        0

                        137

                        0

                        0

                        0

                        0

                        0

                        138

                        0

                        0

                        0

                        0

                        0

                        139

                        0

                        0

                        0

                        0

                        0

                        140

                        5

                        0

                        0

                        0

                        0

                         

                         

                         

                        Continues ...

                        Presented 'AS IS' and for Entertainment Purposes Only.
                        Any gain or loss is your responsibility.
                        Use at your own risk.

                        Order is a Subset of Chaos
                        Knowledge is Beyond Belief
                        Wisdom is Not Censored
                        Douglas Paul Smallish
                        Jehocifer

                          JADELottery's avatar - MeAtWork 03.PNG
                          The Quantum Master
                          West Concord, MN
                          United States
                          Member #21
                          December 7, 2001
                          3675 Posts
                          Offline
                          Posted: July 29, 2016, 7:59 pm - IP Logged

                          The coefficients worked out to the following.

                          One Million Tracked # Selections 0-9

                          Coefficients

                          Pick 1

                          Pick 2

                          Pick 3

                          Pick 4

                          Pick 5

                          α

                          -966.93367803712

                          -288.229657414759

                          -112.848634704551

                          -60.9196072763659

                          -45.5856415845385

                          β

                          30.6458275075256

                          26.4269626065139

                          12.9474585211997

                          8.68322021541142

                          11.5743576972091

                          γ

                          -0.165505462399517

                          -0.00183622361668888

                          1.05332367290803

                          1.76921742869347

                          1.45813918513947

                          δ

                          -0.105317939314043

                          -0.212279140684865

                          -0.354411199971372

                          -0.522830929386791

                          -0.679029762719017

                           

                          Continues ...

                          Presented 'AS IS' and for Entertainment Purposes Only.
                          Any gain or loss is your responsibility.
                          Use at your own risk.

                          Order is a Subset of Chaos
                          Knowledge is Beyond Belief
                          Wisdom is Not Censored
                          Douglas Paul Smallish
                          Jehocifer

                            JADELottery's avatar - MeAtWork 03.PNG
                            The Quantum Master
                            West Concord, MN
                            United States
                            Member #21
                            December 7, 2001
                            3675 Posts
                            Offline
                            Posted: July 29, 2016, 8:03 pm - IP Logged

                            Here are the points of interest for Pick 1 to Pick 5.

                             

                            ·

                            Draws

                            Pick 1

                            Pick 2

                            Pick 3

                            Pick 4

                            Pick 5

                            Minimum

                            10

                            5

                            4

                            3

                            2

                            Peak

                            22.732498

                            11.031043

                            7.202824

                            5.261479

                            4.031870

                            Mode

                            24

                            11

                            7

                            5

                            4

                            Median

                            27

                            13

                            8

                            6

                            5

                            Mean

                            29.283008

                            14.131397

                            9.047672

                            6.483503

                            4.933889

                            Maximum

                            140

                            73

                            51

                            34

                            24

                             

                            Continues ...

                            Presented 'AS IS' and for Entertainment Purposes Only.
                            Any gain or loss is your responsibility.
                            Use at your own risk.

                            Order is a Subset of Chaos
                            Knowledge is Beyond Belief
                            Wisdom is Not Censored
                            Douglas Paul Smallish
                            Jehocifer

                              JADELottery's avatar - MeAtWork 03.PNG
                              The Quantum Master
                              West Concord, MN
                              United States
                              Member #21
                              December 7, 2001
                              3675 Posts
                              Offline
                              Posted: July 29, 2016, 8:14 pm - IP Logged

                              This formula is not restricted to just Daily Pick games.

                              We applied it to Mega Millions and Powerball.

                              Below is a tracked # selection data sample run for both.

                               

                              One Million Tracked # Selections

                              Draws

                              Mega Millions

                              Powerball

                              P5

                              MM

                              P5

                              PB

                              0

                              0

                              0

                              0

                              0

                              1

                              0

                              0

                              0

                              0

                              2

                              0

                              0

                              0

                              0

                              3

                              0

                              0

                              0

                              0

                              4

                              0

                              0

                              0

                              0

                              5

                              0

                              0

                              0

                              0

                              6

                              0

                              0

                              0

                              0

                              7

                              0

                              0

                              0

                              0

                              8

                              0

                              0

                              0

                              0

                              9

                              0

                              0

                              0

                              0

                              10

                              0

                              0

                              0

                              0

                              11

                              0

                              0

                              0

                              0

                              12

                              0

                              0

                              0

                              0

                              13

                              0

                              0

                              0

                              0

                              14

                              0

                              0

                              0

                              0

                              15

                              0

                              6

                              0

                              0

                              16

                              0

                              21

                              0

                              0

                              17

                              0

                              53

                              0

                              0

                              18

                              0

                              168

                              0

                              0

                              19

                              0

                              470

                              0

                              0

                              20

                              0

                              982

                              0

                              0

                              21

                              0

                              1671

                              0

                              0

                              22

                              0

                              2511

                              0

                              0

                              23

                              0

                              4031

                              0

                              0

                              24

                              0

                              5264

                              0

                              0

                              25

                              0

                              7190

                              0

                              0

                              26

                              0

                              8643

                              3

                              0

                              27

                              0

                              11155

                              8

                              0

                              28

                              0

                              12608

                              11

                              0

                              29

                              0

                              15605

                              32

                              0

                              30

                              0

                              17408

                              61

                              0

                              31

                              8

                              19214

                              106

                              0

                              32

                              8

                              20884

                              245

                              0

                              33

                              25

                              22715

                              425

                              0

                              34

                              88

                              23963

                              747

                              0

                              35

                              134

                              25091

                              1133

                              12

                              36

                              285

                              26388

                              1786

                              0

                              37

                              366

                              27319

                              2575

                              36

                              38

                              718

                              27779

                              3702

                              24

                              39

                              1006

                              27975

                              4729

                              70

                              40

                              1581

                              28542

                              6435

                              146

                              41

                              2064

                              28161

                              7556

                              127

                              42

                              2869

                              28541

                              9333

                              321

                              43

                              3732

                              28112

                              11083

                              302

                              44

                              4865

                              27377

                              13536

                              442

                              45

                              6270

                              27127

                              15633

                              537

                              46

                              7434

                              25827

                              16868

                              1030

                              47

                              8842

                              25596

                              18930

                              913

                              48

                              10051

                              24616

                              21102

                              1338

                              49

                              12102

                              23820

                              22873

                              1356

                              50

                              13269

                              22724

                              23745

                              1891

                              51

                              15383

                              21957

                              25158

                              1978

                              52

                              16758

                              21502

                              26565

                              2566

                              53

                              18215

                              20001

                              27424

                              2995

                              54

                              20223

                              19208

                              27559

                              3253

                              55

                              20613

                              17998

                              28846

                              3931

                              56

                              22067

                              17909

                              28569

                              4051

                              57

                              23735

                              17046

                              28395

                              5022

                              58

                              24333

                              15877

                              28384

                              5282

                              59

                              24971

                              15429

                              27849

                              5979

                              60

                              25600

                              13804

                              26908

                              6655

                              61

                              26338

                              13253

                              27360

                              7002

                              62

                              25844

                              12853

                              26291

                              7782

                              63

                              26228

                              11885

                              25557

                              8786

                              64

                              26364

                              11389

                              24957

                              9426

                              65

                              25300

                              10759

                              24921

                              9427

                              66

                              25959

                              10012

                              23606

                              10125

                              67

                              25278

                              9633

                              21904

                              10666

                              68

                              25136

                              8838

                              22117

                              11952

                              69

                              24567

                              8398

                              20746

                              11962

                              70

                              24367

                              8143

                              19513

                              12203

                              71

                              23037

                              7349

                              18453

                              13058

                              72

                              22396

                              6791

                              18200

                              13282

                              73

                              21372

                              6413

                              16654

                              13705

                              74

                              20769

                              6228

                              16193

                              13050

                              75

                              19621

                              5888

                              15325

                              14416

                              76

                              19264

                              5298

                              14519

                              14426

                              77

                              17935

                              5123

                              13719

                              14956

                              78

                              17884

                              4603

                              12327

                              15210

                              79

                              16991

                              4450

                              12096

                              15250

                              80

                              15732

                              4117

                              10988

                              15151

                              81

                              15975

                              3858

                              10298

                              15340

                              82

                              14931

                              3754

                              9727

                              15700

                              83

                              14226

                              3311

                              8978

                              15412

                              84

                              12918

                              3115

                              8675

                              15023

                              85

                              12416

                              2772

                              8106

                              15243

                              86

                              11848

                              2732

                              7546

                              15816

                              87

                              11129

                              2532

                              7212

                              15356

                              88

                              9995

                              2440

                              6760

                              15153

                              89

                              9565

                              2329

                              6324

                              15671

                              90

                              9433

                              2022

                              5665

                              14222

                              91

                              8685

                              1988

                              5360

                              14353

                              92

                              8218

                              1776

                              4952

                              14211

                              93

                              7697

                              1704

                              4703

                              14911

                              94

                              7062

                              1496

                              4690

                              14660

                              95

                              6969

                              1548

                              4195

                              13699

                              96

                              6370

                              1311

                              3707

                              13853

                              97

                              5987

                              1413

                              3382

                              14235

                              98

                              5797

                              1246

                              3186

                              13164

                              99

                              5257

                              1212

                              3193

                              13521

                              100

                              4945

                              1039

                              2844

                              12957

                              101

                              4526

                              1019

                              2460

                              12246

                              102

                              4364

                              816

                              2358

                              12244

                              103

                              4094

                              839

                              2268

                              11867

                              104

                              3910

                              909

                              2212

                              12305

                              105

                              3768

                              730

                              1983

                              11564

                              106

                              3467

                              703

                              1842

                              10381

                              107

                              3026

                              593

                              1728

                              11491

                              108

                              3069

                              590

                              1727

                              11378

                              109

                              2771

                              609

                              1401

                              10832

                              110

                              2482

                              509

                              1390