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Average Rate of Reoccurrence Distribution

Topic closed. 7 replies. Last post 10 years ago by JADELottery.

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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: November 7, 2006, 1:11 pm - IP Logged

Average Rate of Reoccurrence Distribution

    Reference - Combinatorial Distribution

    Average Rate of Reoccurrence Distribution - Ar(n,r,c,z) = C(n,r) / D(n,r,c,z)

The average rate of reoccurrence is the average number of draws or index counts between random selections of n items take r at a time. This is directly related to common terms of Skip, Hit. The average rate of reoccurrence will be used in another function to describe a generalized rate of reoccurrence for all items in a combinatorial random selection. Here's an example of 49 numbers taken 6 at a time, n = 49 and r = 6. Looking at item or number 5 in column 1, the number 5 will on average reoccur about once every 12.88 selections or draws in column 1.

 

 

 

C

 

 

 

Z

1

2

3

4

5

6

1

8.17

 

 

 

 

 

2

9.12

78.40

 

 

 

 

3

10.20

42.85

921.20

 

 

 

4

11.45

31.28

328.49

14125.07

 

 

5

12.88

25.75

175.98

3695.51

317814.00

 

6

14.53

22.66

113.31

1548.60

65041.00

13983816.00

7

16.44

20.82

81.21

812.07

22196.53

2330636.00

8

18.66

19.73

62.47

487.24

9744.82

665896.00

9

21.25

19.13

50.55

320.14

4994.22

249711.00

10

24.29

18.89

42.50

224.66

2845.71

110982.67

11

27.86

18.94

36.84

165.76

1752.36

55491.33

12

32.08

19.25

32.72

127.25

1145.28

30268.00

13

37.09

19.78

29.67

100.89

784.73

17656.33

14

43.08

20.54

27.39

82.18

558.79

10865.44

15

50.26

21.54

25.68

68.48

410.88

6984.92

16

58.92

22.78

24.41

58.21

310.44

4656.62

17

69.44

24.30

23.49

50.34

240.11

3201.42

18

82.30

26.14

22.87

44.22

189.53

2259.83

19

98.13

28.35

22.51

39.40

152.33

1632.10

20

117.75

30.99

22.38

35.54

124.41

1202.60

21

142.29

34.15

22.47

32.45

103.08

901.95

22

173.22

37.94

22.77

29.95

86.54

687.20

23

212.58

42.52

23.28

27.94

73.53

531.02

24

263.20

48.06

24.03

26.32

63.17

415.58

25

329.00

54.83

25.03

25.03

54.83

329.00

26

415.58

63.17

26.32

24.03

48.06

263.20

27

531.02

73.53

27.94

23.28

42.52

212.58

28

687.20

86.54

29.95

22.77

37.94

173.22

29

901.95

103.08

32.45

22.47

34.15

142.29

30

1202.60

124.41

35.54

22.38

30.99

117.75

31

1632.10

152.33

39.40

22.51

28.35

98.13

32

2259.83

189.53

44.22

22.87

26.14

82.30

33

3201.42

240.11

50.34

23.49

24.30

69.44

34

4656.62

310.44

58.21

24.41

22.78

58.92

35

6984.92

410.88

68.48

25.68

21.54

50.26

36

10865.44

558.79

82.18

27.39

20.54

43.08

37

17656.33

784.73

100.89

29.67

19.78

37.09

38

30268.00

1145.28

127.25

32.72

19.25

32.08

39

55491.33

1752.36

165.76

36.84

18.94

27.86

40

110982.67

2845.71

224.66

42.50

18.89

24.29

41

249711.00

4994.22

320.14

50.55

19.13

21.25

42

665896.00

9744.82

487.24

62.47

19.73

18.66

43

2330636.00

22196.53

812.07

81.21

20.82

16.44

44

13983816.00

65041.00

1548.60

113.31

22.66

14.53

45

 

317814.00

3695.51

175.98

25.75

12.88

46

 

 

14125.07

328.49

31.28

11.45

47

 

 

 

921.20

42.85

10.20

48

 

 

 

 

78.40

9.12

49

 

 

 

 

 

8.17

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 #32007
    February 6, 2006
    57 Posts
    Offline
    Posted: November 7, 2006, 2:01 pm - IP Logged

    I love the list. Is it good for every state? Would make for a great referance tool.

    Good job.

    Dragon Dreamer

      Avatar

      United States
      Member #32007
      February 6, 2006
      57 Posts
      Offline
      Posted: November 7, 2006, 2:06 pm - IP Logged

      Need one for 39 numbers.

      I am not that great in math to figure it out my-self.

      Dragon Dreamer

        JADELottery's avatar - MeAtWork 03.PNG
        The Quantum Master
        West Concord, MN
        United States
        Member #21
        December 7, 2001
        3675 Posts
        Offline
        Posted: November 7, 2006, 2:25 pm - IP Logged

        Need one for 39 numbers.

        I am not that great in math to figure it out my-self.

        Dragon Dreamer

         

         

         

        C

         

         

         

        Z

        1

        2

        3

        4

        5

        6

        1

        6.50

         

         

         

         

         

        2

        7.48

        49.40

         

         

         

         

        3

        8.65

        27.69

        456.95

         

         

         

        4

        10.05

        20.77

        166.16

        5483.40

         

         

        5

        11.73

        17.59

        90.87

        1453.93

        95959.50

         

        6

        13.75

        15.95

        59.80

        617.92

        19773.47

        3262623.00

        7

        16.20

        15.12

        43.85

        328.89

        6797.13

        543770.50

        8

        19.20

        14.81

        34.56

        200.47

        3007.03

        155363.00

        9

        22.89

        14.88

        28.70

        133.93

        1553.63

        58261.13

        10

        27.47

        15.26

        24.80

        95.67

        892.89

        25893.83

        11

        33.20

        15.93

        22.13

        71.93

        554.87

        12946.92

        12

        40.41

        16.90

        20.28

        56.33

        366.18

        7061.95

        13

        49.60

        18.19

        19.01

        45.63

        253.51

        4119.47

        14

        61.41

        19.84

        18.19

        38.03

        182.52

        2535.06

        15

        76.76

        21.93

        17.71

        32.48

        135.81

        1629.68

        16

        96.96

        24.56

        17.55

        28.34

        103.92

        1086.45

        17

        123.89

        27.88

        17.65

        25.22

        81.48

        746.94

        18

        160.33

        32.07

        18.04

        22.85

        65.28

        527.25

        19

        210.44

        37.41

        18.71

        21.04

        53.31

        380.79

        20

        280.58

        44.30

        19.69

        19.69

        44.30

        280.58

        21

        380.79

        53.31

        21.04

        18.71

        37.41

        210.44

        22

        527.25

        65.28

        22.85

        18.04

        32.07

        160.33

        23

        746.94

        81.48

        25.22

        17.65

        27.88

        123.89

        24

        1086.45

        103.92

        28.34

        17.55

        24.56

        96.96

        25

        1629.68

        135.81

        32.48

        17.71

        21.93

        76.76

        26

        2535.06

        182.52

        38.03

        18.19

        19.84

        61.41

        27

        4119.47

        253.51

        45.63

        19.01

        18.19

        49.60

        28

        7061.95

        366.18

        56.33

        20.28

        16.90

        40.41

        29

        12946.92

        554.87

        71.93

        22.13

        15.93

        33.20

        30

        25893.83

        892.89

        95.67

        24.80

        15.26

        27.47

        31

        58261.13

        1553.63

        133.93

        28.70

        14.88

        22.89

        32

        155363.00

        3007.03

        200.47

        34.56

        14.81

        19.20

        33

        543770.50

        6797.13

        328.89

        43.85

        15.12

        16.20

        34

        3262623.00

        19773.47

        617.92

        59.80

        15.95

        13.75

        35

         

        95959.50

        1453.93

        90.87

        17.59

        11.73

        36

         

         

        5483.40

        166.16

        20.77

        10.05

        37

         

         

         

        456.95

        27.69

        8.65

        38

         

         

         

         

        49.40

        7.48

        39

         

         

         

         

         

        6.50

        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 #32007
          February 6, 2006
          57 Posts
          Offline
          Posted: November 7, 2006, 2:56 pm - IP Logged

          Thanks Doug.

          That was quick.

          Dragon Dreamer

            Bryan's avatar - Lottery-002.jpg
            Mid-Missouri
            United States
            Member #644
            August 31, 2002
            4271 Posts
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            Posted: November 7, 2006, 3:07 pm - IP Logged

            Doug,

            If you have time could you do one for 44 numbers?

            TIA,

            Bryan  :)

              JADELottery's avatar - MeAtWork 03.PNG
              The Quantum Master
              West Concord, MN
              United States
              Member #21
              December 7, 2001
              3675 Posts
              Offline
              Posted: November 7, 2006, 4:02 pm - IP Logged

              Doug,

              If you have time could you do one for 44 numbers?

              TIA,

              Bryan  :)

               

              1

              2

              3

              4

              5

              6

              1

              7.33

               

               

               

               

               

              2

              8.30

              63.07

               

               

               

               

              3

              9.42

              34.85

              662.20

               

               

               

              4

              10.73

              25.75

              238.16

              9050.07

               

               

              5

              12.26

              21.46

              128.73

              2381.60

              181001.33

               

              6

              14.06

              19.13

              83.68

              1004.13

              37152.91

              7059052.00

              7

              16.19

              17.81

              60.57

              529.96

              12719.01

              1176508.67

              8

              18.72

              17.12

              47.08

              320.14

              5602.42

              336145.33

              9

              21.74

              16.85

              38.52

              211.86

              2881.25

              126054.50

              10

              25.37

              16.91

              32.77

              149.80

              1647.77

              56024.22

              11

              29.74

              17.25

              28.75

              111.41

              1018.62

              28012.11

              12

              35.05

              17.85

              25.88

              86.25

              668.47

              15279.33

              13

              41.55

              18.70

              23.79

              69.00

              460.02

              8912.94

              14

              49.54

              19.81

              22.29

              56.74

              329.09

              5484.89

              15

              59.44

              21.23

              21.23

              47.77

              243.17

              3526.00

              16

              71.83

              22.98

              20.52

              41.04

              184.70

              2350.67

              17

              87.44

              25.14

              20.11

              35.91

              143.65

              1616.08

              18

              107.31

              27.78

              19.96

              31.94

              114.08

              1140.76

              19

              132.86

              31.00

              20.06

              28.84

              92.28

              823.89

              20

              166.08

              34.96

              20.40

              26.39

              75.88

              607.07

              21

              209.78

              39.86

              20.98

              24.47

              63.35

              455.31

              22

              268.06

              45.95

              21.83

              22.98

              53.61

              346.90

              23

              346.90

              53.61

              22.98

              21.83

              45.95

              268.06

              24

              455.31

              63.35

              24.47

              20.98

              39.86

              209.78

              25

              607.07

              75.88

              26.39

              20.40

              34.96

              166.08

              26

              823.89

              92.28

              28.84

              20.06

              31.00

              132.86

              27

              1140.76

              114.08

              31.94

              19.96

              27.78

              107.31

              28

              1616.08

              143.65

              35.91

              20.11

              25.14

              87.44

              29

              2350.67

              184.70

              41.04

              20.52

              22.98

              71.83

              30

              3526.00

              243.17

              47.77

              21.23

              21.23

              59.44

              31

              5484.89

              329.09

              56.74

              22.29

              19.81

              49.54

              32

              8912.94

              460.02

              69.00

              23.79

              18.70

              41.55

              33

              15279.33

              668.47

              86.25

              25.88

              17.85

              35.05

              34

              28012.11

              1018.62

              111.41

              28.75

              17.25

              29.74

              35

              56024.22

              1647.77

              149.80

              32.77

              16.91

              25.37

              36

              126054.50

              2881.25

              211.86

              38.52

              16.85

              21.74

              37

              336145.33

              5602.42

              320.14

              47.08

              17.12

              18.72

              38

              1176508.67

              12719.01

              529.96

              60.57

              17.81

              16.19

              39

              7059052.00

              37152.91

              1004.13

              83.68

              19.13

              14.06

              40

               

              181001.33

              2381.60

              128.73

              21.46

              12.26

              41

               

               

              9050.07

              238.16

              25.75

              10.73

              42

               

               

               

              662.20

              34.85

              9.42

              43

               

               

               

               

              63.07

              8.30

              44

               

               

               

               

               

              7.33

              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: December 2, 2006, 5:30 am - IP Logged

                The average rate of reoccurrence shows why it's not a wise choice to bet on the combination {01, 02, 03, 04, 05, 06}. Yes, I'm fully aware the every combination has an equal probability of being drawn as a whole. However, there are sub numbers, combinations, and probabilities within the whole combination that determine the outcome of a combination. Looking at the number 6 and referring to the above table for a 6/49 lottery, the number 6 can occur in any of the 6 columns. Each column has a different rate of reoccurrence, shown below, Table 1.

                Table 1

                Z123456

                6

                14.53

                22.66

                113.31

                1548.60

                65041.00

                13983816.00

                The 1st column has an average rate of reoccurrence of 14.53 and the 6th column has an average rate of reoccurrence of 13983816.00. It shows the number 6 is more likely to reoccur in the 1st column than in the 6th column. The same is true for the other columns 2 through 5; with column 2 having a better reoccurrence and decreasing reoccurrence to the 5th column. The higher the number, the less likely it will reoccur in that column.

                There is also competition of reoccurrence between numbers in the 6th column. Shown below, Table 2, is the 6th column for the average rate of reoccurrence and the corresponding numbers. As the the number (Z) increases, the average rate of reoccurrence decreases in column 6. The number 49 has an average rate of reoccurrence in the 6th column of 8.17. This means the number 49 reoccurs on average about once every 8.17 draws. The number 6 in the 6th column reoccurs on average about once every 13983816.00 draws. Also, there are many other numbers with lesser rates, meaning they reoccur more often than the number 6 in the 6th column.

                Table 2

                Z

                6

                6

                13983816.00

                7

                2330636.00

                8

                665896.00

                9

                249711.00

                10

                110982.67

                11

                55491.33

                12

                30268.00

                13

                17656.33

                14

                10865.44

                15

                6984.92

                16

                4656.62

                17

                3201.42

                18

                2259.83

                19

                1632.10

                20

                1202.60

                21

                901.95

                22

                687.20

                23

                531.02

                24

                415.58

                25

                329.00

                26

                263.20

                27

                212.58

                28

                173.22

                29

                142.29

                30

                117.75

                31

                98.13

                32

                82.30

                33

                69.44

                34

                58.92

                35

                50.26

                36

                43.08

                37

                37.09

                38

                32.08

                39

                27.86

                40

                24.29

                41

                21.25

                42

                18.66

                43

                16.44

                44

                14.53

                45

                12.88

                46

                11.45

                47

                10.20

                48

                9.12

                49

                8.17

                Symmetry also shows there is an equally valid combination of {44, 45, 46, 47, 48, 49}. Yet, you don't hear many people boasting about how their going to play that combination; even though that combination has the same symmetric properties as the {01, 02, 03, 04, 05, 06} combination.

                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