16-reel slot machines

1. Case A the same number of stops and symbol distribution on the reels

         1.3  Event   A specific symbol exactly three times

            The probability of  is given in the following table, where t is the number of stops of a reel and c is the distribution of that symbol on a reel. The values of t are listed in increments of 2, ranging from 20 to 200, and the values of c range from 1 to 7.

             Table of values for the probability of a specific symbol occurring three times on a payline 

c

1

2

3

4

5

6

7

t

20

0.00000625

0.0001

0.00050625

0.0016

0.00390625

0.0081

0.01500625

22

4.26883E-06

6.83013E-05

0.000345776

0.001092822

0.002668021

0.005532409

0.010249471

24

3.01408E-06

4.82253E-05

0.000244141

0.000771605

0.001883801

0.00390625

0.00723681

26

2.1883E-06

3.50128E-05

0.000177252

0.000560204

0.001367687

0.002836035

0.005254105

28

1.62693E-06

2.60308E-05

0.000131781

0.000416493

0.001016829

0.002108496

0.00390625

30

1.23457E-06

1.97531E-05

0.0001

0.000316049

0.000771605

0.0016

0.002964198

32

9.53674E-07

1.52588E-05

7.72476E-05

0.000244141

0.000596046

0.001235962

0.002289772

34

7.48315E-07

1.1973E-05

6.06135E-05

0.000191569

0.000467697

0.000969816

0.001796704

36

5.95374E-07

9.52599E-06

4.82253E-05

0.000152416

0.000372109

0.000771605

0.001429493

38

4.79585E-07

7.67336E-06

3.88464E-05

0.000122774

0.000299741

0.000621542

0.001151484

40

3.90625E-07

0.00000625

3.16406E-05

0.0001

0.000244141

0.00050625

0.000937891

42

3.21368E-07

5.14189E-06

2.60308E-05

8.22702E-05

0.000200855

0.000416493

0.000771605

44

2.66802E-07

4.26883E-06

2.1611E-05

6.83013E-05

0.000166751

0.000345776

0.000640592

46

2.23341E-07

3.57346E-06

1.80906E-05

5.71753E-05

0.000139588

0.00028945

0.000536242

48

1.8838E-07

3.01408E-06

1.52588E-05

4.82253E-05

0.000117738

0.000244141

0.000452301

50

0.00000016

0.00000256

0.00001296

0.00004096

0.0001

0.00020736

0.00038416

52

1.36769E-07

2.1883E-06

1.10783E-05

3.50128E-05

8.54804E-05

0.000177252

0.000328382

54

1.17605E-07

1.88168E-06

9.52599E-06

3.01068E-05

7.3503E-05

0.000152416

0.000282369

56

1.01683E-07

1.62693E-06

8.23631E-06

2.60308E-05

6.35518E-05

0.000131781

0.000244141

58

8.83666E-08

1.41387E-06

7.15769E-06

2.26218E-05

5.52291E-05

0.000114523

0.000212168

60

7.71605E-08

1.23457E-06

0.00000625

1.97531E-05

4.82253E-05

0.0001

0.000185262

62

6.76758E-08

1.08281E-06

5.48174E-06

1.7325E-05

4.22974E-05

8.77078E-05

0.00016249

64

5.96046E-08

9.53674E-07

4.82798E-06

1.52588E-05

3.72529E-05

7.72476E-05

0.000143111

66

5.27017E-08

8.43226E-07

4.26883E-06

1.34916E-05

3.29385E-05

6.83013E-05

0.000126537

68

4.67697E-08

7.48315E-07

3.78834E-06

1.1973E-05

2.9231E-05

6.06135E-05

0.000112294

70

4.16493E-08

6.66389E-07

3.37359E-06

1.06622E-05

2.60308E-05

5.39775E-05

0.0001

72

3.72109E-08

5.95374E-07

3.01408E-06

9.52599E-06

2.32568E-05

4.82253E-05

8.93433E-05

74

3.33483E-08

5.33572E-07

2.70121E-06

8.53715E-06

2.08427E-05

4.32193E-05

8.00692E-05

76

2.99741E-08

4.79585E-07

2.4279E-06

7.67336E-06

1.87338E-05

3.88464E-05

7.19677E-05

78

2.7016E-08

4.32257E-07

2.1883E-06

6.9161E-06

1.6885E-05

3.50128E-05

6.48655E-05

80

2.44141E-08

3.90625E-07

1.97754E-06

0.00000625

1.52588E-05

3.16406E-05

5.86182E-05

82

2.21179E-08

3.53887E-07

1.79155E-06

5.66219E-06

1.38237E-05

2.86648E-05

5.31052E-05

84

2.00855E-08

3.21368E-07

1.62693E-06

5.14189E-06

1.25534E-05

2.60308E-05

4.82253E-05

86

1.82813E-08

2.925E-07

1.48078E-06

4.68E-06

1.14258E-05

2.36925E-05

4.38933E-05

88

1.66751E-08

2.66802E-07

1.35069E-06

4.26883E-06

1.0422E-05

2.1611E-05

4.0037E-05

90

1.52416E-08

2.43865E-07

1.23457E-06

3.90184E-06

9.52599E-06

1.97531E-05

3.6595E-05

92

1.39588E-08

2.23341E-07

1.13066E-06

3.57346E-06

8.72426E-06

1.80906E-05

3.35151E-05

94

1.28082E-08

2.04931E-07

1.03747E-06

3.2789E-06

8.00513E-06

1.65994E-05

3.07525E-05

96

1.17738E-08

1.8838E-07

9.53674E-07

3.01408E-06

7.3586E-06

1.52588E-05

2.82688E-05

98

1.08417E-08

1.73467E-07

8.78174E-07

2.77546E-06

6.77604E-06

1.40508E-05

2.60308E-05

100

0.00000001

0.00000016

0.00000081

0.00000256

0.00000625

0.00001296

0.00002401

102

9.23845E-09

1.47815E-07

7.48315E-07

2.36504E-06

5.77403E-06

1.1973E-05

2.21815E-05

104

8.54804E-09

1.36769E-07

6.92391E-07

2.1883E-06

5.34253E-06

1.10783E-05

2.05238E-05

106

7.92094E-09

1.26735E-07

6.41596E-07

2.02776E-06

4.95059E-06

1.02655E-05

1.90182E-05

108

7.3503E-09

1.17605E-07

5.95374E-07

1.88168E-06

4.59394E-06

9.52599E-06

1.76481E-05

110

6.83013E-09

1.09282E-07

5.53241E-07

1.74851E-06

4.26883E-06

8.85185E-06

1.63992E-05

112

6.35518E-09

1.01683E-07

5.1477E-07

1.62693E-06

3.97199E-06

8.23631E-06

1.52588E-05

114

5.9208E-09

9.47328E-08

4.79585E-07

1.51573E-06

3.7005E-06

7.67336E-06

1.42158E-05

116

5.52291E-09

8.83666E-08

4.47356E-07

1.41387E-06

3.45182E-06

7.15769E-06

1.32605E-05

118

5.15789E-09

8.25262E-08

4.17789E-07

1.32042E-06

3.22368E-06

6.68462E-06

1.23841E-05

120

4.82253E-09

7.71605E-08

3.90625E-07

1.23457E-06

3.01408E-06

0.00000625

1.15789E-05

122

4.51399E-09

7.22239E-08

3.65633E-07

1.15558E-06

2.82124E-06

5.85013E-06

1.08381E-05

124

4.22974E-09

6.76758E-08

3.42609E-07

1.08281E-06

2.64358E-06

5.48174E-06

1.01556E-05

126

3.96751E-09

6.34801E-08

3.21368E-07

1.01568E-06

2.47969E-06

5.14189E-06

9.52599E-06

128

3.72529E-09

5.96046E-08

3.01749E-07

9.53674E-07

2.32831E-06

4.82798E-06

8.94442E-06

130

3.50128E-09

5.60204E-08

2.83604E-07

8.96327E-07

2.1883E-06

4.53766E-06

8.40657E-06

132

3.29385E-09

5.27017E-08

2.66802E-07

8.43226E-07

2.05866E-06

4.26883E-06

7.90854E-06

134

3.10156E-09

4.9625E-08

2.51227E-07

7.94E-07

1.93848E-06

4.01963E-06

7.44686E-06

136

2.9231E-09

4.67697E-08

2.36771E-07

7.48315E-07

1.82694E-06

3.78834E-06

7.01837E-06

138

2.7573E-09

4.41168E-08

2.23341E-07

7.05868E-07

1.72331E-06

3.57346E-06

6.62027E-06

140

2.60308E-09

4.16493E-08

2.1085E-07

6.66389E-07

1.62693E-06

3.37359E-06

0.00000625

142

2.4595E-09

3.9352E-08

1.99219E-07

6.29632E-07

1.53719E-06

3.18751E-06

5.90526E-06

144

2.32568E-09

3.72109E-08

1.8838E-07

5.95374E-07

1.45355E-06

3.01408E-06

5.58396E-06

148

2.08427E-09

3.33483E-08

1.68826E-07

5.33572E-07

1.30267E-06

2.70121E-06

5.00432E-06

150

1.97531E-09

3.16049E-08

0.00000016

5.05679E-07

1.23457E-06

0.00000256

4.74272E-06

152

1.87338E-09

2.99741E-08

1.51744E-07

4.79585E-07

1.17086E-06

2.4279E-06

4.49798E-06

154

1.77794E-09

2.8447E-08

1.44013E-07

4.55153E-07

1.11121E-06

2.30421E-06

4.26883E-06

156

1.6885E-09

2.7016E-08

1.36769E-07

4.32257E-07

1.05531E-06

2.1883E-06

4.05409E-06

158

1.60462E-09

2.56739E-08

1.29974E-07

4.10782E-07

1.00289E-06

2.07958E-06

3.85269E-06

160

1.52588E-09

2.44141E-08

1.23596E-07

3.90625E-07

9.53674E-07

1.97754E-06

3.66364E-06

162

1.45191E-09

2.32306E-08

1.17605E-07

3.71689E-07

9.07444E-07

1.88168E-06

3.48604E-06

164

1.38237E-09

2.21179E-08

1.11972E-07

3.53887E-07

8.63982E-07

1.79155E-06

3.31907E-06

166

1.31695E-09

2.10711E-08

1.06673E-07

3.37138E-07

8.23091E-07

1.70676E-06

3.16199E-06

168

1.25534E-09

2.00855E-08

1.01683E-07

3.21368E-07

7.8459E-07

1.62693E-06

3.01408E-06

170

1.1973E-09

1.91569E-08

9.69816E-08

3.0651E-07

7.48315E-07

1.55171E-06

2.87473E-06

172

1.14258E-09

1.82813E-08

9.25489E-08

2.925E-07

7.14112E-07

1.48078E-06

2.74333E-06

174

1.09095E-09

1.74551E-08

8.83666E-08

2.79282E-07

6.81841E-07

1.41387E-06

2.61936E-06

176

1.0422E-09

1.66751E-08

8.44179E-08

2.66802E-07

6.51372E-07

1.35069E-06

2.50231E-06

178

9.96139E-10

1.59382E-08

8.06873E-08

2.55012E-07

6.22587E-07

1.291E-06

2.39173E-06

180

9.52599E-10

1.52416E-08

7.71605E-08

2.43865E-07

5.95374E-07

1.23457E-06

2.28719E-06

182

9.11411E-10

1.45826E-08

7.38243E-08

2.33321E-07

5.69632E-07

1.18119E-06

2.1883E-06

184

8.72426E-10

1.39588E-08

7.06665E-08

2.23341E-07

5.45266E-07

1.13066E-06

2.0947E-06

186

8.35503E-10

1.33681E-08

6.76758E-08

2.13889E-07

5.2219E-07

1.08281E-06

2.00604E-06

188

8.00513E-10

1.28082E-08

6.48416E-08

2.04931E-07

5.00321E-07

1.03747E-06

1.92203E-06

190

7.67336E-10

1.22774E-08

6.21542E-08

1.96438E-07

4.79585E-07

9.94468E-07

1.84237E-06

192

7.3586E-10

1.17738E-08

5.96046E-08

1.8838E-07

4.59912E-07

9.53674E-07

1.7668E-06

194

7.05981E-10

1.12957E-08

5.71845E-08

1.80731E-07

4.41238E-07

9.14952E-07

1.69506E-06

196

6.77604E-10

1.08417E-08

5.48859E-08

1.73467E-07

4.23502E-07

8.78174E-07

1.62693E-06

198

6.50638E-10

1.04102E-08

5.27017E-08

1.66563E-07

4.06649E-07

8.43226E-07

1.56218E-06

200

6.25E-10

0.00000001

5.0625E-08

0.00000016

3.90625E-07

0.00000081

1.50063E-06