–
A specific symbol exactly twice3-reel slot machines
1. Case A – the same number of stops and symbol distribution on the reels
1.3 Event –
A specific symbol exactly twice
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 twice on a payline
|
c |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
|
t |
|||||||
|
20 |
0.007125 |
0.027 |
0.057375 |
0.096 |
0.140625 |
0.189 |
0.238875 |
|
22 |
0.0059166 |
0.02253944 |
0.04817806 |
0.081142 |
0.1197408 |
0.162284 |
0.20708114 |
|
24 |
0.00499132 |
0.01909722 |
0.04101563 |
0.06944444 |
0.1030816 |
0.140625 |
0.18077257 |
|
26 |
0.00426718 |
0.01638598 |
0.03533227 |
0.06008193 |
0.08961083 |
0.12289486 |
0.15890988 |
|
28 |
0.00368987 |
0.01421283 |
0.03074891 |
0.05247813 |
0.07858054 |
0.10823615 |
0.140625 |
|
30 |
0.00322222 |
0.01244444 |
0.027 |
0.04622222 |
0.06944444 |
0.096 |
0.12522222 |
|
32 |
0.00283813 |
0.01098633 |
0.02389526 |
0.04101563 |
0.0617981 |
0.08569336 |
0.1121521 |
|
34 |
0.00251883 |
0.00977 |
0.02129554 |
0.03663749 |
0.05533788 |
0.07693873 |
0.10098209 |
|
36 |
0.00225051 |
0.00874486 |
0.01909722 |
0.03292181 |
0.04983282 |
0.06944444 |
0.09137088 |
|
38 |
0.00202289 |
0.00787287 |
0.0172219 |
0.02974194 |
0.04510497 |
0.06298294 |
0.08304782 |
|
40 |
0.00182813 |
0.007125 |
0.01560938 |
0.027 |
0.04101563 |
0.057375 |
0.07579688 |
|
42 |
0.00166019 |
0.00647878 |
0.01421283 |
0.02461937 |
0.03745546 |
0.05247813 |
0.06944444 |
|
44 |
0.00151437 |
0.0059166 |
0.0129954 |
0.02253944 |
0.03433743 |
0.04817806 |
0.06385002 |
|
46 |
0.00138695 |
0.00542451 |
0.01192776 |
0.02071176 |
0.0315916 |
0.04438235 |
0.05889907 |
|
48 |
0.00127496 |
0.00499132 |
0.01098633 |
0.01909722 |
0.02916124 |
0.04101563 |
0.05449761 |
|
50 |
0.001176 |
0.004608 |
0.010152 |
0.017664 |
0.027 |
0.038016 |
0.050568 |
|
52 |
0.00108813 |
0.00426718 |
0.00940914 |
0.01638598 |
0.0250697 |
0.03533227 |
0.04704569 |
|
54 |
0.00100975 |
0.00396281 |
0.00874486 |
0.01524158 |
0.02333867 |
0.03292181 |
0.0438767 |
|
56 |
0.00093955 |
0.00368987 |
0.00814846 |
0.01421283 |
0.02178048 |
0.03074891 |
0.04101563 |
|
58 |
0.00087642 |
0.00344418 |
0.00761101 |
0.01328468 |
0.02037291 |
0.02878347 |
0.03842408 |
|
60 |
0.00081944 |
0.00322222 |
0.007125 |
0.01244444 |
0.01909722 |
0.027 |
0.03606944 |
|
62 |
0.00076785 |
0.00302105 |
0.00668407 |
0.01168138 |
0.01793746 |
0.02537679 |
0.03392384 |
|
64 |
0.00072098 |
0.00283813 |
0.00628281 |
0.01098633 |
0.01688004 |
0.02389526 |
0.03196335 |
|
66 |
0.00067827 |
0.00267134 |
0.0059166 |
0.01035145 |
0.01591326 |
0.02253944 |
0.03016738 |
|
68 |
0.00063925 |
0.00251883 |
0.00558149 |
0.00977 |
0.0150271 |
0.02129554 |
0.02851809 |
|
70 |
0.0006035 |
0.00237901 |
0.00527405 |
0.00923615 |
0.01421283 |
0.0201516 |
0.027 |
|
72 |
0.00057067 |
0.00225051 |
0.00499132 |
0.00874486 |
0.0134629 |
0.01909722 |
0.0255996 |
|
74 |
0.00054044 |
0.00213215 |
0.00473072 |
0.00829171 |
0.01277071 |
0.01812331 |
0.02430508 |
|
76 |
0.00051256 |
0.00202289 |
0.00448999 |
0.00787287 |
0.0121305 |
0.0172219 |
0.02310605 |
|
78 |
0.00048677 |
0.00192181 |
0.00426718 |
0.00748495 |
0.0115372 |
0.01638598 |
0.02199337 |
|
80 |
0.00046289 |
0.00182813 |
0.00406055 |
0.007125 |
0.01098633 |
0.01560938 |
0.02095898 |
|
82 |
0.00044072 |
0.00174112 |
0.00386856 |
0.00679038 |
0.01047395 |
0.01488661 |
0.01999572 |
|
84 |
0.00042011 |
0.00166019 |
0.00368987 |
0.00647878 |
0.00999656 |
0.01421283 |
0.01909722 |
|
86 |
0.00040091 |
0.00158477 |
0.00352327 |
0.00618813 |
0.00955105 |
0.01358371 |
0.01825783 |
|
88 |
0.00038299 |
0.00151437 |
0.00336771 |
0.0059166 |
0.00913464 |
0.0129954 |
0.01747247 |
|
90 |
0.00036626 |
0.00144856 |
0.00322222 |
0.00566255 |
0.00874486 |
0.01244444 |
0.01673663 |
|
92 |
0.00035059 |
0.00138695 |
0.00308596 |
0.00542451 |
0.00837948 |
0.01192776 |
0.01604622 |
|
94 |
0.00033591 |
0.00132919 |
0.00295816 |
0.00520116 |
0.00803651 |
0.01144255 |
0.0153976 |
|
96 |
0.00032213 |
0.00127496 |
0.00283813 |
0.00499132 |
0.00771417 |
0.01098633 |
0.01478746 |
|
98 |
0.00030918 |
0.00122398 |
0.00272527 |
0.00479392 |
0.00741082 |
0.01055683 |
0.01421283 |
|
100 |
0.000297 |
0.001176 |
0.002619 |
0.004608 |
0.007125 |
0.010152 |
0.013671 |
|
102 |
0.00028552 |
0.00113079 |
0.00251883 |
0.00443268 |
0.00685539 |
0.00977 |
0.01315953 |
|
104 |
0.0002747 |
0.00108813 |
0.00242429 |
0.00426718 |
0.0066008 |
0.00940914 |
0.0126762 |
|
106 |
0.00026448 |
0.00104784 |
0.00233498 |
0.00411078 |
0.00636012 |
0.00906789 |
0.01221898 |
|
108 |
0.00025482 |
0.00100975 |
0.00225051 |
0.00396281 |
0.00613235 |
0.00874486 |
0.01178603 |
|
110 |
0.00024568 |
0.0009737 |
0.00217055 |
0.00382269 |
0.0059166 |
0.00843877 |
0.01137566 |
|
112 |
0.00023702 |
0.00093955 |
0.00209477 |
0.00368987 |
0.00571204 |
0.00814846 |
0.01098633 |
|
114 |
0.00022882 |
0.00090716 |
0.00202289 |
0.00356385 |
0.00551789 |
0.00787287 |
0.01061663 |
|
116 |
0.00022103 |
0.00087642 |
0.00195465 |
0.00344418 |
0.00533348 |
0.00761101 |
0.01026526 |
|
118 |
0.00021363 |
0.00084721 |
0.0018898 |
0.00333043 |
0.00515815 |
0.007362 |
0.00993103 |
|
120 |
0.0002066 |
0.00081944 |
0.00182813 |
0.00322222 |
0.00499132 |
0.007125 |
0.00961285 |
|
122 |
0.00019991 |
0.00079302 |
0.00176942 |
0.0031192 |
0.00483245 |
0.00689926 |
0.0093097 |
|
124 |
0.00019354 |
0.00076785 |
0.0017135 |
0.00302105 |
0.00468105 |
0.00668407 |
0.00902066 |
|
126 |
0.00018746 |
0.00074386 |
0.00166019 |
0.00292745 |
0.00453665 |
0.00647878 |
0.00874486 |
|
128 |
0.00018167 |
0.00072098 |
0.00160933 |
0.00283813 |
0.00439882 |
0.00628281 |
0.0084815 |
|
130 |
0.00017615 |
0.00069914 |
0.00156076 |
0.00275284 |
0.00426718 |
0.00609558 |
0.00822986 |
|
132 |
0.00017087 |
0.00067827 |
0.00151437 |
0.00267134 |
0.00414136 |
0.0059166 |
0.00798924 |
|
134 |
0.00016583 |
0.00065833 |
0.00147001 |
0.0025934 |
0.00402102 |
0.00574539 |
0.00775902 |
|
136 |
0.000161 |
0.00063925 |
0.00142757 |
0.00251883 |
0.00390585 |
0.00558149 |
0.00753859 |
|
138 |
0.00015639 |
0.00062099 |
0.00138695 |
0.00244742 |
0.00379556 |
0.00542451 |
0.00732742 |
|
140 |
0.00015197 |
0.0006035 |
0.00134803 |
0.00237901 |
0.00368987 |
0.00527405 |
0.007125 |
|
142 |
0.00014773 |
0.00058674 |
0.00131073 |
0.00231342 |
0.00358853 |
0.00512977 |
0.00693084 |
|
144 |
0.00014367 |
0.00057067 |
0.00127496 |
0.00225051 |
0.00349131 |
0.00499132 |
0.00674451 |
|
148 |
0.00013604 |
0.00054044 |
0.00120767 |
0.00213215 |
0.00330836 |
0.00473072 |
0.00639369 |
|
150 |
0.00013244 |
0.00052622 |
0.001176 |
0.00207644 |
0.00322222 |
0.004608 |
0.00622844 |
|
152 |
0.00012899 |
0.00051256 |
0.00114556 |
0.00202289 |
0.00313941 |
0.00448999 |
0.00606952 |
|
154 |
0.00012568 |
0.00049942 |
0.00111629 |
0.00197138 |
0.00305975 |
0.00437646 |
0.0059166 |
|
156 |
0.00012248 |
0.00048677 |
0.00108813 |
0.00192181 |
0.00298308 |
0.00426718 |
0.00576939 |
|
158 |
0.00011941 |
0.00047461 |
0.00106102 |
0.00187409 |
0.00290925 |
0.00416194 |
0.0056276 |
|
160 |
0.00011646 |
0.00046289 |
0.00103491 |
0.00182813 |
0.00283813 |
0.00406055 |
0.00549097 |
|
162 |
0.00011361 |
0.0004516 |
0.00100975 |
0.00178383 |
0.00276959 |
0.00396281 |
0.00535925 |
|
164 |
0.00011086 |
0.00044072 |
0.0009855 |
0.00174112 |
0.0027035 |
0.00386856 |
0.00523221 |
|
166 |
0.00010821 |
0.00043023 |
0.00096212 |
0.00169993 |
0.00263975 |
0.00377763 |
0.00510964 |
|
168 |
0.00010566 |
0.00042011 |
0.00093955 |
0.00166019 |
0.00257823 |
0.00368987 |
0.00499132 |
|
170 |
0.0001032 |
0.00041034 |
0.00091777 |
0.00162182 |
0.00251883 |
0.00360513 |
0.00487706 |
|
172 |
0.00010082 |
0.00040091 |
0.00089674 |
0.00158477 |
0.00246146 |
0.00352327 |
0.00476668 |
|
174 |
9.8519E-05 |
0.0003918 |
0.00087642 |
0.00154897 |
0.00240603 |
0.00344418 |
0.00466 |
|
176 |
9.6299E-05 |
0.00038299 |
0.00085679 |
0.00151437 |
0.00235244 |
0.00336771 |
0.00455686 |
|
178 |
9.4153E-05 |
0.00037448 |
0.0008378 |
0.00148092 |
0.00230063 |
0.00329376 |
0.00445711 |
|
180 |
9.2078E-05 |
0.00036626 |
0.00081944 |
0.00144856 |
0.00225051 |
0.00322222 |
0.0043606 |
|
182 |
9.0071E-05 |
0.00035829 |
0.00080168 |
0.00141725 |
0.00220202 |
0.00315299 |
0.00426718 |
|
184 |
8.8129E-05 |
0.00035059 |
0.00078449 |
0.00138695 |
0.00215507 |
0.00308596 |
0.00417674 |
|
186 |
8.6249E-05 |
0.00034313 |
0.00076785 |
0.00135761 |
0.0021096 |
0.00302105 |
0.00408914 |
|
188 |
8.4429E-05 |
0.00033591 |
0.00075173 |
0.00132919 |
0.00206556 |
0.00295816 |
0.00400426 |
|
190 |
8.2665E-05 |
0.00032891 |
0.00073611 |
0.00130165 |
0.00202289 |
0.00289722 |
0.003922 |
|
192 |
8.0956E-05 |
0.00032213 |
0.00072098 |
0.00127496 |
0.00198152 |
0.00283813 |
0.00384225 |
|
194 |
7.93E-05 |
0.00031556 |
0.0007063 |
0.00124908 |
0.00194141 |
0.00278084 |
0.0037649 |
|
196 |
7.7694E-05 |
0.00030918 |
0.00069207 |
0.00122398 |
0.00190251 |
0.00272527 |
0.00368987 |
|
198 |
7.6136E-05 |
0.000303 |
0.00067827 |
0.00119963 |
0.00186476 |
0.00267134 |
0.00361706 |
|
200 |
7.4625E-05 |
0.000297 |
0.00066488 |
0.001176 |
0.00182813 |
0.002619 |
0.00354638 |
Example of using the table:
Find the probability of a plum occurring exactly twice on a payline of a 3-reel slot machine with 64 stops on each reel, having 7 plums on each reel.
We look at the intersection of row t = 64 with column c = 7 and find the probability P = 0.03196335= 3.196335%.