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Discharging Reoccurrence Distribution

Topic closed. 2 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 9, 2006, 9:51 am - IP Logged

Discharging Reoccurrence Distribution

    Reference - Average Rate of Reoccurrence Distribution, Generalized Average Rate of Reoccurrence

    Discharge Reoccurrence - y = (d / m2 ) e -(x / m )

      d - total number of draws
      m - average rate of reoccurrence
      x - draw difference or Dd between two draw occurrences of the same number
      y - the approximate frequency of reoccurrence for a given draw difference or Dd for a given draw count d

The discharge reoccurrence function can be used to calculate the approximate frequency distribution of reoccurrence (a.k.a skip, hit). For reference, the Wisconsin Megabucks lottery, a 6/49 lottery, will be used as an example. The first 1500 draws will be used to calculate the function's values. As an example, looking at the draw occurrences for the number 1 in column 1 at a draw count of 1500, the draw occurrences are listed below in Table 1; column 2. Using this information, a Dd or draw difference can be extracted, Table 1; column 3. Column 6 of Table 1 shows the frequency count of Dd and column 7 of Table 1 shows the calculated frequency for the 1500 draws. The values for d and m come from the draw count and average rate of reoccurrence.

          d = 1500
          m = Ar(49,6,1,1) » 8.17
          x = Dd      (ref. Table 1; column 5)

          y = (1500 / (8.17)2 ) e -(Dd / 8.17 )      (ref. Table 1; column 7)

                                              Table 1

Index

Draw Occurrence

Dd

 

Dd

Actual Frequency

Calculated Frequency

1

16

 

 

1

18

19.90

2

41

25

 

2

15

17.61

3

51

10

 

3

16

15.58

4

53

2

 

4

21

13.78

5

59

6

 

5

16

12.19

6

69

10

 

6

15

10.79

7

72

3

 

7

7

9.54

8

76

4

 

8

9

8.44

9

81

5

 

9

8

7.47

10

83

2

 

10

9

6.61

11

102

19

 

11

7

5.85

12

106

4

 

12

4

5.17

13

133

27

 

13

1

4.58

14

143

10

 

14

4

4.05

15

149

6

 

15

1

3.58

16

160

11

 

16

1

3.17

17

166

6

 

17

1

2.81

18

167

1

 

18

1

2.48

19

172

5

 

19

1

2.20

20

174

2

 

20

2

1.94

21

185

11

 

21

3

1.72

22

193

8

 

22

4

1.52

23

196

3

 

23

1

1.35

24

206

10

 

24

1

1.19

25

227

21

 

25

3

1.05

26

247

20

 

26

2

0.93

27

249

2

 

27

2

0.82

28

252

3

 

28

0

0.73

29

255

3

 

29

1

0.65

30

257

2

 

30

0

0.57

31

258

1

 

31

1

0.51

32

259

1

 

32

0

0.45

33

269

10

 

33

1

0.40

34

276

7

 

34

0

0.35

35

293

17

 

35

0

0.31

36

301

8

 

36

0

0.27

37

326

25

 

37

0

0.24

38

329

3

 

38

0

0.21

39

335

6

 

39

0

0.19

40

345

10

 

40

0

0.17

41

395

50

 

41

0

0.15

42

404

9

 

42

0

0.13

43

435

31

 

43

0

0.12

44

440

5

 

44

0

0.10

45

454

14

 

45

0

0.09

46

457

3

 

46

0

0.08

47

462

5

 

47

0

0.07

48

483

21

 

48

0

0.06

49

484

1

 

49

0

0.06

50

487

3

 

50

1

0.05

51

493

6

 

 

 

 

52

498

5

 

 

 

 

53

506

8

 

 

 

 

54

509

3

 

 

 

 

55

513

4

 

 

 

 

56

515

2

 

 

 

 

57

529

14

 

 

 

 

58

533

4

 

 

 

 

59

541

8

 

 

 

 

60

548

7

 

 

 

 

61

551

3

 

 

 

 

62

558

7

 

 

 

 

63

562

4

 

 

 

 

64

564

2

 

 

 

 

65

576

12

 

 

 

 

66

601

25

 

 

 

 

67

627

26

 

 

 

 

68

631

4

 

 

 

 

69

637

6

 

 

 

 

70

638

1

 

 

 

 

71

646

8

 

 

 

 

72

668

22

 

 

 

 

73

690

22

 

 

 

 

74

699

9

 

 

 

 

75

700

1

 

 

 

 

76

701

1

 

 

 

 

77

712

11

 

 

 

 

78

714

2

 

 

 

 

79

716

2

 

 

 

 

80

719

3

 

 

 

 

81

724

5

 

 

 

 

82

726

2

 

 

 

 

83

730

4

 

 

 

 

84

735

5

 

 

 

 

85

742

7

 

 

 

 

86

748

6

 

 

 

 

87

760

12

 

 

 

 

88

772

12

 

 

 

 

89

778

6

 

 

 

 

90

791

13

 

 

 

 

91

812

21

 

 

 

 

92

823

11

 

 

 

 

93

833

10

 

 

 

 

94

837

4

 

 

 

 

95

843

6

 

 

 

 

96

848

5

 

 

 

 

97

866

18

 

 

 

 

98

875

9

 

 

 

 

99

885

10

 

 

 

 

100

893

8

 

 

 

 

101

894

1

 

 

 

 

102

914

20

 

 

 

 

103

918

4

 

 

 

 

104

927

9

 

 

 

 

105

937

10

 

 

 

 

106

970

33

 

 

 

 

107

986

16

 

 

 

 

108

987

1

 

 

 

 

109

996

9

 

 

 

 

110

999

3

 

 

 

 

111

1005

6

 

 

 

 

112

1008

3

 

 

 

 

113

1012

4

 

 

 

 

114

1015

3

 

 

 

 

115

1021

6

 

 

 

 

116

1023

2

 

 

 

 

117

1028

5

 

 

 

 

118

1052

24

 

 

 

 

119

1056

4

 

 

 

 

120

1061

5

 

 

 

 

121

1075

14

 

 

 

 

122

1081

6

 

 

 

 

123

1087

6

 

 

 

 

124

1101

14

 

 

 

 

125

1113

12

 

 

 

 

126

1117

4

 

 

 

 

127

1121

4

 

 

 

 

128

1125

4

 

 

 

 

129

1128

3

 

 

 

 

130

1132

4

 

 

 

 

131

1141

9

 

 

 

 

132

1146

5

 

 

 

 

133

1147

1

 

 

 

 

134

1149

2

 

 

 

 

135

1150

1

 

 

 

 

136

1155

5

 

 

 

 

137

1164

9

 

 

 

 

138

1170

6

 

 

 

 

139

1174

4

 

 

 

 

140

1185

11

 

 

 

 

141

1211

26

 

 

 

 

142

1215

4

 

 

 

 

143

1230

15

 

 

 

 

144

1238

8

 

 

 

 

145

1239

1

 

 

 

 

146

1241

2

 

 

 

 

147

1246

5

 

 

 

 

148

1253

7

 

 

 

 

149

1254

1

 

 

 

 

150

1276

22

 

 

 

 

151

1277

1

 

 

 

 

152

1280

3

 

 

 

 

153

1291

11

 

 

 

 

154

1297

6

 

 

 

 

155

1298

1

 

 

 

 

156

1299

1

 

 

 

 

157

1306

7

 

 

 

 

158

1314

8

 

 

 

 

159

1318

4

 

 

 

 

160

1327

9

 

 

 

 

161

1350

23

 

 

 

 

162

1357

7

 

 

 

 

163

1361

4

 

 

 

 

164

1363

2

 

 

 

 

165

1374

11

 

 

 

 

166

1382

8

 

 

 

 

167

1385

3

 

 

 

 

168

1390

5

 

 

 

 

169

1391

1

 

 

 

 

170

1393

2

 

 

 

 

171

1398

5

 

 

 

 

172

1420

22

 

 

 

 

173

1449

29

 

 

 

 

174

1476

27

 

 

 

 

175

1480

4

 

 

 

 

176

1485

5

 

 

 

 

177

1489

4

 

 

 

 

178

1490

1

 

 

 

 

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: November 9, 2006, 10:33 am - IP Logged

    Here's an example for the number 5 in column 1 of Wisconsin Megabucks 6/49 lottery:

        d = 1500
        m = Ar(49,6,1,5) » 12.88
        x = Dd

        y = (1500 / (12.88)2 ) e -(x / 12.88)

     

    Index

    Draw Occurrence

    Dd

     

    Dd

    Actual Frequency

    Calculated Frequency

    1

    14

     

     

    1

    9

    8.37

    2

    24

    10

     

    2

    11

    7.74

    3

    27

    3

     

    3

    6

    7.16

    4

    34

    7

     

    4

    7

    6.63

    5

    73

    39

     

    5

    7

    6.13

    6

    100

    27

     

    6

    11

    5.67

    7

    108

    8

     

    7

    9

    5.25

    8

    121

    13

     

    8

    6

    4.86

    9

    132

    11

     

    9

    3

    4.50

    10

    140

    8

     

    10

    4

    4.16

    11

    161

    21

     

    11

    4

    3.85

    12

    162

    1

     

    12

    3

    3.56

    13

    204

    42

     

    13

    4

    3.30

    14

    205

    1

     

    14

    4

    3.05

    15

    220

    15

     

    15

    4

    2.82

    16

    224

    4

     

    16

    4

    2.61

    17

    238

    14

     

    17

    3

    2.42

    18

    240

    2

     

    18

    3

    2.24

    19

    242

    2

     

    19

    1

    2.07

    20

    248

    6

     

    20

    2

    1.91

    21

    274

    26

     

    21

    1

    1.77

    22

    275

    1

     

    22

    2

    1.64

    23

    280

    5

     

    23

    0

    1.52

    24

    298

    18

     

    24

    0

    1.40

    25

    302

    4

     

    25

    2

    1.30

    26

    311

    9

     

    26

    1

    1.20

    27

    315

    4

     

    27

    1

    1.11

    28

    325

    10

     

    28

    0

    1.03

    29

    328

    3

     

    29

    0

    0.95

    30

    336

    8

     

    30

    0

    0.88

    31

    338

    2

     

    31

    2

    0.81

    32

    346

    8

     

    32

    1

    0.75

    33

    371

    25

     

    33

    0

    0.70

    34

    375

    4

     

    34

    0

    0.65

    35

    382

    7

     

    35

    0

    0.60

    36

    385

    3

     

    36

    1

    0.55

    37

    399

    14

     

    37

    0

    0.51

    38

    411

    12

     

    38

    1

    0.47

    39

    443

    32

     

    39

    2

    0.44

    40

    449

    6

     

    40

    0

    0.41

    41

    460

    11

     

    41

    0

    0.37

    42

    467

    7

     

    42

    1

    0.35

    43

    473

    6

     

    43

    0

    0.32

    44

    481

    8

     

    44

    1

    0.30

    45

    495

    14

     

    45

    0

    0.27

    46

    550

    55

     

    46

    0

    0.25

    47

    560

    10

     

    47

    0

    0.24

    48

    577

    17

     

    48

    0

    0.22

    49

    593

    16

     

    49

    0

    0.20

    50

    600

    7

     

    50

    0

    0.19

    51

    620

    20

     

    51

    0

    0.17

    52

    630

    10

     

    52

    0

    0.16

    53

    641

    11

     

    53

    0

    0.15

    54

    648

    7

     

    54

    0

    0.14

    55

    654

    6

     

    55

    2

    0.13

    56

    655

    1

     

     

     

     

    57

    660

    5

     

     

     

     

    58

    691

    31

     

     

     

     

    59

    693

    2

     

     

     

     

    60

    698

    5

     

     

     

     

    61

    711

    13

     

     

     

     

    62

    749

    38

     

     

     

     

    63

    750

    1

     

     

     

     

    64

    764

    14

     

     

     

     

    65

    769

    5

     

     

     

     

    66

    784

    15

     

     

     

     

    67

    786

    2

     

     

     

     

    68

    792

    6

     

     

     

     

    69

    793

    1

     

     

     

     

    70

    799

    6

     

     

     

     

    71

    800

    1

     

     

     

     

    72

    809

    9

     

     

     

     

    73

    814

    5

     

     

     

     

    74

    820

    6

     

     

     

     

    75

    821

    1

     

     

     

     

    76

    828

    7

     

     

     

     

    77

    841

    13

     

     

     

     

    78

    856

    15

     

     

     

     

    79

    859

    3

     

     

     

     

    80

    868

    9

     

     

     

     

    81

    923

    55

     

     

     

     

    82

    931

    8

     

     

     

     

    83

    948

    17

     

     

     

     

    84

    952

    4

     

     

     

     

    85

    968

    16

     

     

     

     

    86

    971

    3

     

     

     

     

    87

    977

    6

     

     

     

     

    88

    995

    18

     

     

     

     

    89

    1002

    7

     

     

     

     

    90

    1046

    44

     

     

     

     

    91

    1077

    31

     

     

     

     

    92

    1097

    20

     

     

     

     

    93

    1114

    17

     

     

     

     

    94

    1130

    16

     

     

     

     

    95

    1166

    36

     

     

     

     

    96

    1173

    7

     

     

     

     

    97

    1192

    19

     

     

     

     

    98

    1194

    2

     

     

     

     

    99

    1200

    6

     

     

     

     

    100

    1205

    5

     

     

     

     

    101

    1220

    15

     

     

     

     

    102

    1224

    4

     

     

     

     

    103

    1226

    2

     

     

     

     

    104

    1232

    6

     

     

     

     

    105

    1271

    39

     

     

     

     

    106

    1287

    16

     

     

     

     

    107

    1288

    1

     

     

     

     

    108

    1290

    2

     

     

     

     

    109

    1292

    2

     

     

     

     

    110

    1294

    2

     

     

     

     

    111

    1312

    18

     

     

     

     

    112

    1324

    12

     

     

     

     

    113

    1329

    5

     

     

     

     

    114

    1351

    22

     

     

     

     

    115

    1364

    13

     

     

     

     

    116

    1376

    12

     

     

     

     

    117

    1380

    4

     

     

     

     

    118

    1405

    25

     

     

     

     

    119

    1408

    3

     

     

     

     

    120

    1419

    11

     

     

     

     

    121

    1426

    7

     

     

     

     

    122

    1432

    6

     

     

     

     

    123

    1454

    22

     

     

     

     

    124

    1456

    2

     

     

     

     

    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, 7:14 am - IP Logged

      WI Megabucks

      Wi Megabucks

      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