16-reel slot machines

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

1.1  Event  – A specific symbol four 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 four 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