16-reel slot machines 3f632y
1. Case A – the same number of stops and symbol distribution on the reels
1.7 A specific symbol at least three times
The probability of this events 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.
Table of values for the probability of a specific symbol occurring at least three times on a payline
c |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
t |
|||||||
20 |
0.00048125 |
0.0037 |
0.01198125 |
0.0272 |
0.05078125 |
0.0837 |
0.12648125 |
22 |
0.000362851 |
0.002800355 |
0.009105423 |
0.020763609 |
0.038953111 |
0.064544772 |
0.098102076 |
24 |
0.00028031 |
0.002170139 |
0.007080078 |
0.016203704 |
0.030517578 |
0.05078125 |
0.077537254 |
26 |
0.000221018 |
0.001715626 |
0.005612986 |
0.012884703 |
0.024344823 |
0.040649837 |
0.062298677 |
28 |
0.000177335 |
0.001379633 |
0.004524482 |
0.010412328 |
0.019726481 |
0.033033111 |
0.05078125 |
30 |
0.000144444 |
0.001125926 |
0.0037 |
0.008533333 |
0.016203704 |
0.0272 |
0.041922222 |
32 |
0.000119209 |
0.000930786 |
0.003064156 |
0.007080078 |
0.01347065 |
0.022659302 |
0.035000801 |
34 |
9.95259E-05 |
0.000778247 |
0.002565971 |
0.005938626 |
0.011318261 |
0.019073047 |
0.029517277 |
36 |
8.39478E-05 |
0.000657293 |
0.002170139 |
0.005029721 |
0.009600409 |
0.016203704 |
0.025118241 |
38 |
7.14582E-05 |
0.000560155 |
0.001851678 |
0.004297082 |
0.008212894 |
0.013881109 |
0.021549194 |
40 |
6.13281E-05 |
0.00048125 |
0.001592578 |
0.0037 |
0.007080078 |
0.01198125 |
0.018623828 |
42 |
5.30257E-05 |
0.000416493 |
0.001379633 |
0.00320854 |
0.006146166 |
0.010412328 |
0.016203704 |
44 |
4.61568E-05 |
0.000362851 |
0.001203011 |
0.002800355 |
0.005369393 |
0.009105423 |
0.014184535 |
46 |
4.04247E-05 |
0.000318038 |
0.001055287 |
0.002458539 |
0.004718081 |
0.008008119 |
0.012486778 |
48 |
3.56038E-05 |
0.00028031 |
0.000930786 |
0.002170139 |
0.00416791 |
0.007080078 |
0.011049059 |
50 |
0.00003152 |
0.00024832 |
0.00082512 |
0.00192512 |
0.0037 |
0.00628992 |
0.00982352 |
52 |
2.80376E-05 |
0.000221018 |
0.000734858 |
0.001715626 |
0.003299544 |
0.005612986 |
0.008772479 |
54 |
2.50498E-05 |
0.000197576 |
0.000657293 |
0.001535448 |
0.00295482 |
0.005029721 |
0.007865995 |
56 |
2.24719E-05 |
0.000177335 |
0.000590269 |
0.001379633 |
0.002656466 |
0.004524482 |
0.007080078 |
58 |
2.02359E-05 |
0.000159767 |
0.000532055 |
0.001244201 |
0.002396943 |
0.004084657 |
0.006395354 |
60 |
1.8287E-05 |
0.000144444 |
0.00048125 |
0.001125926 |
0.002170139 |
0.0037 |
0.005796065 |
62 |
1.65806E-05 |
0.00013102 |
0.000436712 |
0.001022175 |
0.001971057 |
0.003362133 |
0.005269304 |
64 |
1.508E-05 |
0.000119209 |
0.000397503 |
0.000930786 |
0.00179559 |
0.003064156 |
0.004804432 |
66 |
1.37551E-05 |
0.000108776 |
0.000362851 |
0.000849972 |
0.001640339 |
0.002800355 |
0.00439263 |
68 |
1.2581E-05 |
9.95259E-05 |
0.000332111 |
0.000778247 |
0.001502476 |
0.002565971 |
0.004026542 |
70 |
1.15369E-05 |
9.12953E-05 |
0.000304748 |
0.000714369 |
0.001379633 |
0.002357018 |
0.0037 |
72 |
1.06051E-05 |
8.39478E-05 |
0.00028031 |
0.000657293 |
0.001269821 |
0.002170139 |
0.00340781 |
74 |
9.77104E-06 |
7.7368E-05 |
0.000258416 |
0.000606138 |
0.001171357 |
0.002002496 |
0.003145574 |
76 |
9.02219E-06 |
7.14582E-05 |
0.000238743 |
0.000560155 |
0.001082813 |
0.001851678 |
0.002909552 |
78 |
8.34795E-06 |
6.61353E-05 |
0.000221018 |
0.000518708 |
0.00100297 |
0.001715626 |
0.002696551 |
80 |
7.73926E-06 |
6.13281E-05 |
0.000205005 |
0.00048125 |
0.000930786 |
0.001592578 |
0.002503833 |
82 |
7.18833E-06 |
5.69758E-05 |
0.000190502 |
0.000447313 |
0.000865364 |
0.001481017 |
0.002329041 |
84 |
6.68847E-06 |
5.30257E-05 |
0.000177335 |
0.000416493 |
0.000805931 |
0.001379633 |
0.002170139 |
86 |
6.23391E-06 |
4.94325E-05 |
0.000165354 |
0.00038844 |
0.000751817 |
0.001287293 |
0.002025363 |
88 |
5.81962E-06 |
4.61568E-05 |
0.000154428 |
0.000362851 |
0.00070244 |
0.001203011 |
0.001893178 |
90 |
5.44124E-06 |
4.31642E-05 |
0.000144444 |
0.00033946 |
0.000657293 |
0.001125926 |
0.001772245 |
92 |
5.09497E-06 |
4.04247E-05 |
0.000135303 |
0.000318038 |
0.000615933 |
0.001055287 |
0.001661393 |
94 |
4.77746E-06 |
3.79123E-05 |
0.000126917 |
0.00029838 |
0.000577971 |
0.000990434 |
0.001559592 |
96 |
4.4858E-06 |
3.56038E-05 |
0.000119209 |
0.00028031 |
0.000543065 |
0.000930786 |
0.001465939 |
98 |
4.2174E-06 |
3.3479E-05 |
0.000112114 |
0.000263669 |
0.000510913 |
0.000875832 |
0.001379633 |
100 |
0.00000397 |
0.00003152 |
0.00010557 |
0.00024832 |
0.00048125 |
0.00082512 |
0.00129997 |
102 |
3.74157E-06 |
2.97109E-05 |
9.95259E-05 |
0.000234139 |
0.000453839 |
0.000778247 |
0.001226322 |
104 |
3.53034E-06 |
2.80376E-05 |
9.39344E-05 |
0.000221018 |
0.000428471 |
0.000734858 |
0.001158131 |
106 |
3.33471E-06 |
2.64876E-05 |
8.87541E-05 |
0.000208859 |
0.000404958 |
0.000694634 |
0.001094903 |
108 |
3.15328E-06 |
2.50498E-05 |
8.39478E-05 |
0.000197576 |
0.000383134 |
0.000657293 |
0.001036194 |
110 |
2.98477E-06 |
2.37142E-05 |
7.94823E-05 |
0.000187091 |
0.000362851 |
0.00062258 |
0.000981606 |
112 |
2.82806E-06 |
2.24719E-05 |
7.5328E-05 |
0.000177335 |
0.000343974 |
0.000590269 |
0.000930786 |
114 |
2.68212E-06 |
2.13149E-05 |
7.14582E-05 |
0.000168246 |
0.000326384 |
0.000560155 |
0.000883413 |
116 |
2.54606E-06 |
2.02359E-05 |
6.7849E-05 |
0.000159767 |
0.000309973 |
0.000532055 |
0.000839201 |
118 |
2.41905E-06 |
1.92286E-05 |
6.44788E-05 |
0.000151848 |
0.000294644 |
0.000505803 |
0.000797889 |
120 |
2.30035E-06 |
1.8287E-05 |
6.13281E-05 |
0.000144444 |
0.00028031 |
0.00048125 |
0.000759245 |
122 |
2.18929E-06 |
1.74059E-05 |
5.83794E-05 |
0.000137514 |
0.00026689 |
0.00045826 |
0.000723056 |
124 |
2.08526E-06 |
1.65806E-05 |
5.56168E-05 |
0.00013102 |
0.000254313 |
0.000436712 |
0.00068913 |
126 |
1.98772E-06 |
1.58066E-05 |
5.30257E-05 |
0.000124929 |
0.000242514 |
0.000416493 |
0.000657293 |
128 |
1.89617E-06 |
1.508E-05 |
5.05932E-05 |
0.000119209 |
0.000231434 |
0.000397503 |
0.000627387 |
130 |
1.81016E-06 |
1.43973E-05 |
4.83071E-05 |
0.000113834 |
0.000221018 |
0.000379651 |
0.000599268 |
132 |
1.72927E-06 |
1.37551E-05 |
4.61568E-05 |
0.000108776 |
0.000211218 |
0.000362851 |
0.000572804 |
134 |
1.65313E-06 |
1.31506E-05 |
4.41322E-05 |
0.000104014 |
0.000201989 |
0.000347028 |
0.000547876 |
136 |
1.5814E-06 |
1.2581E-05 |
4.22242E-05 |
9.95259E-05 |
0.00019329 |
0.000332111 |
0.000524373 |
138 |
1.51376E-06 |
1.20439E-05 |
4.04247E-05 |
9.52922E-05 |
0.000185084 |
0.000318038 |
0.000502195 |
140 |
1.44992E-06 |
1.15369E-05 |
3.87261E-05 |
9.12953E-05 |
0.000177335 |
0.000304748 |
0.00048125 |
142 |
1.38962E-06 |
1.10579E-05 |
3.71212E-05 |
8.75188E-05 |
0.000170013 |
0.000292188 |
0.000461454 |
144 |
1.33261E-06 |
1.06051E-05 |
3.56038E-05 |
8.39478E-05 |
0.000163088 |
0.00028031 |
0.000442728 |
148 |
1.22763E-06 |
9.77104E-06 |
3.28084E-05 |
7.7368E-05 |
0.000150328 |
0.000258416 |
0.00040821 |
150 |
1.17926E-06 |
9.38667E-06 |
0.00003152 |
7.43348E-05 |
0.000144444 |
0.00024832 |
0.00039229 |
152 |
1.13339E-06 |
9.02219E-06 |
3.02982E-05 |
7.14582E-05 |
0.000138864 |
0.000238743 |
0.000377188 |
154 |
1.08988E-06 |
8.67635E-06 |
2.91387E-05 |
6.87281E-05 |
0.000133568 |
0.000229653 |
0.000362851 |
156 |
1.04856E-06 |
8.34795E-06 |
2.80376E-05 |
6.61353E-05 |
0.000128537 |
0.000221018 |
0.000349231 |
158 |
1.0093E-06 |
8.03593E-06 |
2.69913E-05 |
6.36712E-05 |
0.000123756 |
0.000212811 |
0.000336285 |
160 |
9.71985E-07 |
7.73926E-06 |
2.59964E-05 |
6.13281E-05 |
0.000119209 |
0.000205005 |
0.00032397 |
162 |
9.36482E-07 |
7.45701E-06 |
2.50498E-05 |
5.90986E-05 |
0.000114882 |
0.000197576 |
0.000312249 |
164 |
9.02688E-07 |
7.18833E-06 |
2.41486E-05 |
5.69758E-05 |
0.000110762 |
0.000190502 |
0.000301087 |
166 |
8.70501E-07 |
6.9324E-06 |
2.32902E-05 |
5.49535E-05 |
0.000106837 |
0.000183761 |
0.000290451 |
168 |
8.39825E-07 |
6.68847E-06 |
2.24719E-05 |
5.30257E-05 |
0.000103095 |
0.000177335 |
0.00028031 |
170 |
8.10575E-07 |
6.45586E-06 |
2.16916E-05 |
5.11871E-05 |
9.95259E-05 |
0.000171205 |
0.000270635 |
172 |
7.82667E-07 |
6.23391E-06 |
2.09469E-05 |
4.94325E-05 |
9.61195E-05 |
0.000165354 |
0.0002614 |
174 |
7.56025E-07 |
6.02202E-06 |
2.02359E-05 |
4.77572E-05 |
9.28667E-05 |
0.000159767 |
0.000252581 |
176 |
7.30579E-07 |
5.81962E-06 |
1.95568E-05 |
4.61568E-05 |
8.97591E-05 |
0.000154428 |
0.000244154 |
178 |
7.06263E-07 |
5.62619E-06 |
1.89077E-05 |
4.4627E-05 |
8.67886E-05 |
0.000149325 |
0.000236098 |
180 |
6.83013E-07 |
5.44124E-06 |
1.8287E-05 |
4.31642E-05 |
8.39478E-05 |
0.000144444 |
0.000228392 |
182 |
6.60773E-07 |
5.26431E-06 |
1.76932E-05 |
4.17645E-05 |
8.12295E-05 |
0.000139774 |
0.000221018 |
184 |
6.39488E-07 |
5.09497E-06 |
1.71249E-05 |
4.04247E-05 |
7.86274E-05 |
0.000135303 |
0.000213958 |
186 |
6.19108E-07 |
4.93281E-06 |
1.65806E-05 |
3.91417E-05 |
7.61352E-05 |
0.00013102 |
0.000207196 |
188 |
5.99585E-07 |
4.77746E-06 |
1.60591E-05 |
3.79123E-05 |
7.37473E-05 |
0.000126917 |
0.000200715 |
190 |
5.80873E-07 |
4.62857E-06 |
1.55593E-05 |
3.67339E-05 |
7.14582E-05 |
0.000122982 |
0.000194502 |
192 |
5.62933E-07 |
4.4858E-06 |
1.508E-05 |
3.56038E-05 |
6.92628E-05 |
0.000119209 |
0.000188543 |
194 |
5.45723E-07 |
4.34884E-06 |
1.46202E-05 |
3.45197E-05 |
6.71565E-05 |
0.000115589 |
0.000182824 |
196 |
5.29208E-07 |
4.2174E-06 |
1.41789E-05 |
3.3479E-05 |
6.51346E-05 |
0.000112114 |
0.000177335 |
198 |
5.13353E-07 |
4.09121E-06 |
1.37551E-05 |
3.24798E-05 |
6.31932E-05 |
0.000108776 |
0.000172063 |
200 |
4.98125E-07 |
0.00000397 |
1.33481E-05 |
0.00003152 |
6.13281E-05 |
0.00010557 |
0.000166998 |