The mathematics of Slots 232q13 Probabilities - 3-reel: A specific symbol at least twice on a payline in case A

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 twice on a payline

c	1	2	3	4	5	6	7
t	1	2	3	4	5	6	7
20	0.00725	0.028	0.06075	0.104	0.15625	0.216	0.28175
22	0.00601052	0.02329076	0.05071375	0.08715252	0.13148009	0.1825695	0.23929376
24	0.00506366	0.01967593	0.04296875	0.07407407	0.11212384	0.15625	0.20558449
26	0.00432408	0.01684115	0.03686846	0.06372326	0.0967228	0.13518434	0.17842513
28	0.00373542	0.01457726	0.03197886	0.05539359	0.08427478	0.1180758	0.15625
30	0.00325926	0.01274074	0.028	0.04859259	0.07407407	0.104	0.13792593
32	0.00286865	0.01123047	0.02471924	0.04296875	0.06561279	0.09228516	0.12261963
34	0.00254427	0.00997354	0.0219825	0.03826583	0.05851822	0.08243436	0.10970894
36	0.00227195	0.00891632	0.01967593	0.03429355	0.052512	0.07407407	0.09872257
38	0.00204111	0.00801866	0.01771395	0.0309083	0.047383	0.06691938	0.08929873
40	0.00184375	0.00725	0.01603125	0.028	0.04296875	0.06075	0.08115625
42	0.00167369	0.00658676	0.01457726	0.02548321	0.03914264	0.05539359	0.07407407
44	0.00152611	0.00601052	0.01331236	0.02329076	0.03580485	0.05071375	0.0678766
46	0.00139722	0.0055067	0.01220515	0.02136928	0.03287581	0.04660146	0.06242295
48	0.001284	0.00506366	0.01123047	0.01967593	0.03029152	0.04296875	0.0575991
50	0.001184	0.004672	0.010368	0.018176	0.028	0.039744	0.053312
52	0.00109524	0.00432408	0.00960116	0.01684115	0.02595869	0.03686846	0.04948509
54	0.00101611	0.00401362	0.00891632	0.01564802	0.0241325	0.03429355	0.04605497
56	0.00094524	0.00373542	0.0083022	0.01457726	0.02249226	0.03197886	0.04296875
58	0.00088154	0.00348518	0.0077494	0.01361269	0.02101357	0.02989052	0.04018205
60	0.00082407	0.00325926	0.00725	0.01274074	0.01967593	0.028	0.03765741
62	0.00077205	0.00305461	0.00679735	0.01194992	0.01846195	0.02628311	0.03536303
64	0.00072479	0.00286865	0.0063858	0.01123047	0.01735687	0.02471924	0.03327179
66	0.00068175	0.00269917	0.00601052	0.01057406	0.01634805	0.02329076	0.03136044
68	0.00064243	0.00254427	0.00566736	0.00997354	0.01542464	0.0219825	0.02960895
70	0.00060641	0.00240233	0.00535277	0.00942274	0.01457726	0.02078134	0.028
72	0.00057335	0.00227195	0.00506366	0.00891632	0.0137978	0.01967593	0.02651856
74	0.00054291	0.0021519	0.00479735	0.00844965	0.01307919	0.01865635	0.02515152
76	0.00051483	0.00204111	0.0045515	0.00801866	0.01241526	0.01771395	0.02388741
78	0.00048888	0.00193867	0.00432408	0.00761982	0.0118006	0.01684115	0.02271616
80	0.00046484	0.00184375	0.00411328	0.00725	0.01123047	0.01603125	0.02162891
82	0.00044254	0.00175563	0.00391753	0.00690646	0.01070066	0.01527836	0.02061781
84	0.0004218	0.00167369	0.00373542	0.00658676	0.01020746	0.01457726	0.01967593
86	0.00040248	0.00159734	0.00356572	0.00628875	0.00974757	0.0139233	0.01879709
88	0.00038446	0.00152611	0.00340733	0.00601052	0.00931806	0.01331236	0.01797579
90	0.00036763	0.00145953	0.00325926	0.00575034	0.00891632	0.01274074	0.01720713
92	0.00035187	0.00139722	0.00312063	0.0055067	0.00854001	0.01220515	0.01648671
94	0.00033711	0.00133882	0.00299067	0.00527821	0.00818701	0.01170261	0.01581056
96	0.00032326	0.001284	0.00286865	0.00506366	0.00785545	0.01123047	0.01517515
98	0.00031024	0.00123248	0.00275395	0.00486192	0.00754363	0.01078632	0.01457726
100	0.000298	0.001184	0.002646	0.004672	0.00725	0.010368	0.014014
102	0.00028647	0.00113833	0.00254427	0.00449299	0.00697319	0.00997354	0.01348275
104	0.00027559	0.00109524	0.0024483	0.00432408	0.00671192	0.00960116	0.01298112
106	0.00026532	0.00105456	0.00235765	0.00416451	0.00646507	0.00924925	0.01250697
108	0.00025561	0.00101611	0.00227195	0.00401362	0.00623158	0.00891632	0.01205831
110	0.00024643	0.00097971	0.00219083	0.00387077	0.00601052	0.00860105	0.01163336
112	0.00023773	0.00094524	0.00211399	0.00373542	0.00580101	0.0083022	0.01123047
114	0.00022949	0.00091256	0.00204111	0.00360705	0.00560226	0.00801866	0.01084814
116	0.00022167	0.00088154	0.00197194	0.00348518	0.00541356	0.0077494	0.010485
118	0.00021424	0.00085208	0.00190623	0.00336938	0.00523423	0.00749346	0.01013979
120	0.00020718	0.00082407	0.00184375	0.00325926	0.00506366	0.00725	0.00981134
122	0.00020046	0.00079742	0.00178429	0.00315445	0.00490129	0.00701821	0.00949859
124	0.00019406	0.00077205	0.00172766	0.00305461	0.00474661	0.00679735	0.00920056
126	0.00018796	0.00074786	0.00167369	0.00295944	0.00459914	0.00658676	0.00891632
128	0.00018215	0.00072479	0.0016222	0.00286865	0.00445843	0.0063858	0.00864506
130	0.0001766	0.00070278	0.00157305	0.00278198	0.00432408	0.0061939	0.00838598
132	0.00017131	0.00068175	0.00152611	0.00269917	0.00419571	0.00601052	0.00813837
134	0.00016624	0.00066165	0.00148123	0.00262	0.00407297	0.00583516	0.00790157
136	0.0001614	0.00064243	0.00143831	0.00254427	0.00395555	0.00566736	0.00767495
138	0.00015677	0.00062403	0.00139722	0.00247177	0.00384312	0.0055067	0.00745794
140	0.00015233	0.00060641	0.00135787	0.00240233	0.00373542	0.00535277	0.00725
142	0.00014808	0.00058953	0.00132016	0.00233578	0.00363219	0.0052052	0.00705064
144	0.00014401	0.00057335	0.001284	0.00227195	0.00353317	0.00506366	0.00685938
148	0.00013634	0.00054291	0.00121599	0.0021519	0.00334691	0.00479735	0.00649949
150	0.00013274	0.00052859	0.001184	0.00209541	0.00325926	0.004672	0.00633007
152	0.00012928	0.00051483	0.00115325	0.00204111	0.003175	0.0045515	0.00616719
154	0.00012595	0.00050161	0.00112369	0.0019889	0.00309397	0.0044356	0.00601052
156	0.00012275	0.00048888	0.00109524	0.00193867	0.003016	0.00432408	0.00585974
158	0.00011967	0.00047664	0.00106787	0.00189032	0.00294094	0.0042167	0.00571456
160	0.0001167	0.00046484	0.0010415	0.00184375	0.00286865	0.00411328	0.00557471
162	0.00011384	0.00045348	0.00101611	0.00179888	0.00279899	0.00401362	0.00543993
164	0.00011109	0.00044254	0.00099162	0.00175563	0.00273184	0.00391753	0.00530997
166	0.00010843	0.00043198	0.00096802	0.00171392	0.00266708	0.00382485	0.00518462
168	0.00010587	0.0004218	0.00094524	0.00167369	0.00260459	0.00373542	0.00506366
170	0.0001034	0.00041197	0.00092326	0.00163485	0.00254427	0.00364909	0.00494688
172	0.00010101	0.00040248	0.00090204	0.00159734	0.00248602	0.00356572	0.00483409
174	9.8709E-05	0.00039332	0.00088154	0.00156112	0.00242975	0.00348518	0.00472511
176	9.6482E-05	0.00038446	0.00086174	0.00152611	0.00237537	0.00340733	0.00461978
178	9.433E-05	0.0003759	0.00084259	0.00149226	0.0023228	0.00333206	0.00451793
180	9.225E-05	0.00036763	0.00082407	0.00145953	0.00227195	0.00325926	0.00441941
182	9.0237E-05	0.00035962	0.00080616	0.00142787	0.00222275	0.00318882	0.00432408
184	8.829E-05	0.00035187	0.00078883	0.00139722	0.00217513	0.00312063	0.0042318
186	8.6404E-05	0.00034437	0.00077205	0.00136755	0.00212903	0.00305461	0.00414244
188	8.4579E-05	0.00033711	0.00075579	0.00133882	0.00208438	0.00299067	0.00405588
190	8.2811E-05	0.00033008	0.00074005	0.00131098	0.00204111	0.00292871	0.00397201
192	8.1098E-05	0.00032326	0.00072479	0.001284	0.00199918	0.00286865	0.00389071
194	7.9437E-05	0.00031665	0.00071	0.00125784	0.00195853	0.00281043	0.00381188
196	7.7827E-05	0.00031024	0.00069566	0.00123248	0.00191911	0.00275395	0.00373542
198	7.6265E-05	0.00030403	0.00068175	0.00120788	0.00188086	0.00269917	0.00366124
200	0.00007475	0.000298	0.00066825	0.001184	0.00184375	0.002646	0.00358925

Find the probability of a cherry occurring at least twice on a payline of a 3-reel slot machine with 34 stops on each reel, having 3 cherries on each reel.

We look in the table, at the intersection of row t = 34 with column c = 3 and find the probability P = 0.0219825 = 2.19825%.