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

2. Case B – different numbers of stops and symbol distributions on the reels

The probability of

, where

are the basic probabilities of that symbol occurring on the reels respectively. In the particular case when two of the three reels have the same number of stops and the same distribution of symbols, the probability of

, where

is the basic probability of that symbol occurring on one of the two similar reels and

is the basic probability of that symbol occurring on the third reel. This particular formula returns the following table of values, where the values of the basic probabilities are listed in increments of 0.005, ranging from 0.005 to 0.100, and each table lists seven values of

Tables of values for the probability of a specific symbol occurring twice on a payline

	0.005	0.010	0.015	0.020	0.025	0.030	0.035
	0.005	0.010	0.015	0.020	0.025	0.030	0.035
0.005	0.000074625	0.00012425	0.000173875	0.0002235	0.000273125	0.00032275	0.000372375
0.01	0.0001985	0.000297	0.0003955	0.000494	0.0005925	0.000691	0.0007895
0.015	0.000371625	0.00051825	0.000664875	0.0008115	0.000958125	0.00110475	0.001251375
0.02	0.000594	0.000788	0.000982	0.001176	0.00137	0.001564	0.001758
0.025	0.000865625	0.00110625	0.001346875	0.0015875	0.001828125	0.00206875	0.002309375
0.03	0.0011865	0.001473	0.0017595	0.002046	0.0023325	0.002619	0.0029055
0.035	0.001556625	0.00188825	0.002219875	0.0025515	0.002883125	0.00321475	0.003546375
0.04	0.001976	0.002352	0.002728	0.003104	0.00348	0.003856	0.004232
0.045	0.002444625	0.00286425	0.003283875	0.0037035	0.004123125	0.00454275	0.004962375
0.05	0.0029625	0.003425	0.0038875	0.00435	0.0048125	0.005275	0.0057375
0.055	0.003529625	0.00403425	0.004538875	0.0050435	0.005548125	0.00605275	0.006557375
0.06	0.004146	0.004692	0.005238	0.005784	0.00633	0.006876	0.007422
0.065	0.004811625	0.00539825	0.005984875	0.0065715	0.007158125	0.00774475	0.008331375
0.07	0.0055265	0.006153	0.0067795	0.007406	0.0080325	0.008659	0.0092855
0.075	0.006290625	0.00695625	0.007621875	0.0082875	0.008953125	0.00961875	0.010284375
0.08	0.007104	0.007808	0.008512	0.009216	0.00992	0.010624	0.011328
0.085	0.007966625	0.00870825	0.009449875	0.0101915	0.010933125	0.01167475	0.012416375
0.09	0.0088785	0.009657	0.0104355	0.011214	0.0119925	0.012771	0.0135495
0.095	0.009839625	0.01065425	0.011468875	0.0122835	0.013098125	0.01391275	0.014727375
0.1	0.01085	0.0117	0.01255	0.0134	0.01425	0.0151	0.01595

	0.040	0.045	0.050	0.055	0.060	0.065	0.070
	0.040	0.045	0.050	0.055	0.060	0.065	0.070
0.005	0.000422	0.000471625	0.00052125	0.000570875	0.0006205	0.000670125	0.00071975
0.01	0.000888	0.0009865	0.001085	0.0011835	0.001282	0.0013805	0.001479
0.015	0.001398	0.001544625	0.00169125	0.001837875	0.0019845	0.002131125	0.00227775
0.02	0.001952	0.002146	0.00234	0.002534	0.002728	0.002922	0.003116
0.025	0.00255	0.002790625	0.00303125	0.003271875	0.0035125	0.003753125	0.00399375
0.03	0.003192	0.0034785	0.003765	0.0040515	0.004338	0.0046245	0.004911
0.035	0.003878	0.004209625	0.00454125	0.004872875	0.0052045	0.005536125	0.00586775
0.04	0.004608	0.004984	0.00536	0.005736	0.006112	0.006488	0.006864
0.045	0.005382	0.005801625	0.00622125	0.006640875	0.0070605	0.007480125	0.00789975
0.05	0.0062	0.0066625	0.007125	0.0075875	0.00805	0.0085125	0.008975
0.055	0.007062	0.007566625	0.00807125	0.008575875	0.0090805	0.009585125	0.01008975
0.06	0.007968	0.008514	0.00906	0.009606	0.010152	0.010698	0.011244
0.065	0.008918	0.009504625	0.01009125	0.010677875	0.0112645	0.011851125	0.01243775
0.07	0.009912	0.0105385	0.011165	0.0117915	0.012418	0.0130445	0.013671
0.075	0.01095	0.011615625	0.01228125	0.012946875	0.0136125	0.014278125	0.01494375
0.08	0.012032	0.012736	0.01344	0.014144	0.014848	0.015552	0.016256
0.085	0.013158	0.013899625	0.01464125	0.015382875	0.0161245	0.016866125	0.01760775
0.09	0.014328	0.0151065	0.015885	0.0166635	0.017442	0.0182205	0.018999
0.095	0.015542	0.016356625	0.01717125	0.017985875	0.0188005	0.019615125	0.02042975
0.1	0.0168	0.01765	0.0185	0.01935	0.0202	0.02105	0.0219

	0.075	0.080	0.085	0.090	0.095	0.100	0.105
	0.075	0.080	0.085	0.090	0.095	0.100	0.105
0.005	0.000769375	0.000819	0.000868625	0.00091825	0.000967875	0.0010175	0.001067125
0.01	0.0015775	0.001676	0.0017745	0.001873	0.0019715	0.00207	0.0021685
0.015	0.002424375	0.002571	0.002717625	0.00286425	0.003010875	0.0031575	0.003304125
0.02	0.00331	0.003504	0.003698	0.003892	0.004086	0.00428	0.004474
0.025	0.004234375	0.004475	0.004715625	0.00495625	0.005196875	0.0054375	0.005678125
0.03	0.0051975	0.005484	0.0057705	0.006057	0.0063435	0.00663	0.0069165
0.035	0.006199375	0.006531	0.006862625	0.00719425	0.007525875	0.0078575	0.008189125
0.04	0.00724	0.007616	0.007992	0.008368	0.008744	0.00912	0.009496
0.045	0.008319375	0.008739	0.009158625	0.00957825	0.009997875	0.0104175	0.010837125
0.05	0.0094375	0.0099	0.0103625	0.010825	0.0112875	0.01175	0.0122125
0.055	0.010594375	0.011099	0.011603625	0.01210825	0.012612875	0.0131175	0.013622125
0.06	0.01179	0.012336	0.012882	0.013428	0.013974	0.01452	0.015066
0.065	0.013024375	0.013611	0.014197625	0.01478425	0.015370875	0.0159575	0.016544125
0.07	0.0142975	0.014924	0.0155505	0.016177	0.0168035	0.01743	0.0180565
0.075	0.015609375	0.016275	0.016940625	0.01760625	0.018271875	0.0189375	0.019603125
0.08	0.01696	0.017664	0.018368	0.019072	0.019776	0.02048	0.021184
0.085	0.018349375	0.019091	0.019832625	0.02057425	0.021315875	0.0220575	0.022799125
0.09	0.0197775	0.020556	0.0213345	0.022113	0.0228915	0.02367	0.0244485
0.095	0.021244375	0.022059	0.022873625	0.02368825	0.024502875	0.0253175	0.026132125
0.1	0.02275	0.0236	0.02445	0.0253	0.02615	0.027	0.02785

Find the probability of two cherries occurring on a payline of a 3-reel slot machine having 72, 72, and 72 stops on reels 1, 2, and 3 respectively and 4, 2, and 2 cherries on these reels respectively.

We have here the particular case of the same number of stops and the same distribution of the cherry symbol on two reels (2 and 3).

and

. We consider Table 2 and look at the intersection of column

with rows

and

. We find the probabilities 0.003271875 and 0.0040515 that bound the sought probability. We can take for instance 0.0036 = 0.36% as an approximation. For the exact result, apply directly the explicit probability formula that returned the tables.