Discharging Reoccurrence Distribution
Reference - Average Rate of Reoccurrence Distribution, Generalized Average Rate of Reoccurrence
Discharge Reoccurrence - y = (d / m2 ) e -(x / m )
d - total number of draws
m - average rate of reoccurrence
x - draw difference or Dd between two draw occurrences of the same number
y - the approximate frequency of reoccurrence for a given draw difference or Dd for a given draw count d
The discharge reoccurrence function can be used to calculate the approximate frequency distribution of reoccurrence (a.k.a skip, hit). For reference, the Wisconsin Megabucks lottery, a 6/49 lottery, will be used as an example. The first 1500 draws will be used to calculate the function's values. As an example, looking at the draw occurrences for the number 1 in column 1 at a draw count of 1500, the draw occurrences are listed below in Table 1; column 2. Using this information, a Dd or draw difference can be extracted, Table 1; column 3. Column 6 of Table 1 shows the frequency count of Dd and column 7 of Table 1 shows the calculated frequency for the 1500 draws. The values for d and m come from the draw count and average rate of reoccurrence.
d = 1500
m = Ar(49,6,1,1) » 8.17
x = Dd (ref. Table 1; column 5)
y = (1500 / (8.17)2 ) e -(Dd / 8.17 ) (ref. Table 1; column 7)
Table 1
Index | Draw Occurrence | Dd | | Dd | Actual Frequency | Calculated Frequency |
1 | 16 | | | 1 | 18 | 19.90 |
2 | 41 | 25 | | 2 | 15 | 17.61 |
3 | 51 | 10 | | 3 | 16 | 15.58 |
4 | 53 | 2 | | 4 | 21 | 13.78 |
5 | 59 | 6 | | 5 | 16 | 12.19 |
6 | 69 | 10 | | 6 | 15 | 10.79 |
7 | 72 | 3 | | 7 | 7 | 9.54 |
8 | 76 | 4 | | 8 | 9 | 8.44 |
9 | 81 | 5 | | 9 | 8 | 7.47 |
10 | 83 | 2 | | 10 | 9 | 6.61 |
11 | 102 | 19 | | 11 | 7 | 5.85 |
12 | 106 | 4 | | 12 | 4 | 5.17 |
13 | 133 | 27 | | 13 | 1 | 4.58 |
14 | 143 | 10 | | 14 | 4 | 4.05 |
15 | 149 | 6 | | 15 | 1 | 3.58 |
16 | 160 | 11 | | 16 | 1 | 3.17 |
17 | 166 | 6 | | 17 | 1 | 2.81 |
18 | 167 | 1 | | 18 | 1 | 2.48 |
19 | 172 | 5 | | 19 | 1 | 2.20 |
20 | 174 | 2 | | 20 | 2 | 1.94 |
21 | 185 | 11 | | 21 | 3 | 1.72 |
22 | 193 | 8 | | 22 | 4 | 1.52 |
23 | 196 | 3 | | 23 | 1 | 1.35 |
24 | 206 | 10 | | 24 | 1 | 1.19 |
25 | 227 | 21 | | 25 | 3 | 1.05 |
26 | 247 | 20 | | 26 | 2 | 0.93 |
27 | 249 | 2 | | 27 | 2 | 0.82 |
28 | 252 | 3 | | 28 | 0 | 0.73 |
29 | 255 | 3 | | 29 | 1 | 0.65 |
30 | 257 | 2 | | 30 | 0 | 0.57 |
31 | 258 | 1 | | 31 | 1 | 0.51 |
32 | 259 | 1 | | 32 | 0 | 0.45 |
33 | 269 | 10 | | 33 | 1 | 0.40 |
34 | 276 | 7 | | 34 | 0 | 0.35 |
35 | 293 | 17 | | 35 | 0 | 0.31 |
36 | 301 | 8 | | 36 | 0 | 0.27 |
37 | 326 | 25 | | 37 | 0 | 0.24 |
38 | 329 | 3 | | 38 | 0 | 0.21 |
39 | 335 | 6 | | 39 | 0 | 0.19 |
40 | 345 | 10 | | 40 | 0 | 0.17 |
41 | 395 | 50 | | 41 | 0 | 0.15 |
42 | 404 | 9 | | 42 | 0 | 0.13 |
43 | 435 | 31 | | 43 | 0 | 0.12 |
44 | 440 | 5 | | 44 | 0 | 0.10 |
45 | 454 | 14 | | 45 | 0 | 0.09 |
46 | 457 | 3 | | 46 | 0 | 0.08 |
47 | 462 | 5 | | 47 | 0 | 0.07 |
48 | 483 | 21 | | 48 | 0 | 0.06 |
49 | 484 | 1 | | 49 | 0 | 0.06 |
50 | 487 | 3 | | 50 | 1 | 0.05 |
51 | 493 | 6 | | | | |
52 | 498 | 5 | | | | |
53 | 506 | 8 | | | | |
54 | 509 | 3 | | | | |
55 | 513 | 4 | | | | |
56 | 515 | 2 | | | | |
57 | 529 | 14 | | | | |
58 | 533 | 4 | | | | |
59 | 541 | 8 | | | | |
60 | 548 | 7 | | | | |
61 | 551 | 3 | | | | |
62 | 558 | 7 | | | | |
63 | 562 | 4 | | | | |
64 | 564 | 2 | | | | |
65 | 576 | 12 | | | | |
66 | 601 | 25 | | | | |
67 | 627 | 26 | | | | |
68 | 631 | 4 | | | | |
69 | 637 | 6 | | | | |
70 | 638 | 1 | | | | |
71 | 646 | 8 | | | | |
72 | 668 | 22 | | | | |
73 | 690 | 22 | | | | |
74 | 699 | 9 | | | | |
75 | 700 | 1 | | | | |
76 | 701 | 1 | | | | |
77 | 712 | 11 | | | | |
78 | 714 | 2 | | | | |
79 | 716 | 2 | | | | |
80 | 719 | 3 | | | | |
81 | 724 | 5 | | | | |
82 | 726 | 2 | | | | |
83 | 730 | 4 | | | | |
84 | 735 | 5 | | | | |
85 | 742 | 7 | | | | |
86 | 748 | 6 | | | | |
87 | 760 | 12 | | | | |
88 | 772 | 12 | | | | |
89 | 778 | 6 | | | | |
90 | 791 | 13 | | | | |
91 | 812 | 21 | | | | |
92 | 823 | 11 | | | | |
93 | 833 | 10 | | | | |
94 | 837 | 4 | | | | |
95 | 843 | 6 | | | | |
96 | 848 | 5 | | | | |
97 | 866 | 18 | | | | |
98 | 875 | 9 | | | | |
99 | 885 | 10 | | | | |
100 | 893 | 8 | | | | |
101 | 894 | 1 | | | | |
102 | 914 | 20 | | | | |
103 | 918 | 4 | | | | |
104 | 927 | 9 | | | | |
105 | 937 | 10 | | | | |
106 | 970 | 33 | | | | |
107 | 986 | 16 | | | | |
108 | 987 | 1 | | | | |
109 | 996 | 9 | | | | |
110 | 999 | 3 | | | | |
111 | 1005 | 6 | | | | |
112 | 1008 | 3 | | | | |
113 | 1012 | 4 | | | | |
114 | 1015 | 3 | | | | |
115 | 1021 | 6 | | | | |
116 | 1023 | 2 | | | | |
117 | 1028 | 5 | | | | |
118 | 1052 | 24 | | | | |
119 | 1056 | 4 | | | | |
120 | 1061 | 5 | | | | |
121 | 1075 | 14 | | | | |
122 | 1081 | 6 | | | | |
123 | 1087 | 6 | | | | |
124 | 1101 | 14 | | | | |
125 | 1113 | 12 | | | | |
126 | 1117 | 4 | | | | |
127 | 1121 | 4 | | | | |
128 | 1125 | 4 | | | | |
129 | 1128 | 3 | | | | |
130 | 1132 | 4 | | | | |
131 | 1141 | 9 | | | | |
132 | 1146 | 5 | | | | |
133 | 1147 | 1 | | | | |
134 | 1149 | 2 | | | | |
135 | 1150 | 1 | | | | |
136 | 1155 | 5 | | | | |
137 | 1164 | 9 | | | | |
138 | 1170 | 6 | | | | |
139 | 1174 | 4 | | | | |
140 | 1185 | 11 | | | | |
141 | 1211 | 26 | | | | |
142 | 1215 | 4 | | | | |
143 | 1230 | 15 | | | | |
144 | 1238 | 8 | | | | |
145 | 1239 | 1 | | | | |
146 | 1241 | 2 | | | | |
147 | 1246 | 5 | | | | |
148 | 1253 | 7 | | | | |
149 | 1254 | 1 | | | | |
150 | 1276 | 22 | | | | |
151 | 1277 | 1 | | | | |
152 | 1280 | 3 | | | | |
153 | 1291 | 11 | | | | |
154 | 1297 | 6 | | | | |
155 | 1298 | 1 | | | | |
156 | 1299 | 1 | | | | |
157 | 1306 | 7 | | | | |
158 | 1314 | 8 | | | | |
159 | 1318 | 4 | | | | |
160 | 1327 | 9 | | | | |
161 | 1350 | 23 | | | | |
162 | 1357 | 7 | | | | |
163 | 1361 | 4 | | | | |
164 | 1363 | 2 | | | | |
165 | 1374 | 11 | | | | |
166 | 1382 | 8 | | | | |
167 | 1385 | 3 | | | | |
168 | 1390 | 5 | | | | |
169 | 1391 | 1 | | | | |
170 | 1393 | 2 | | | | |
171 | 1398 | 5 | | | | |
172 | 1420 | 22 | | | | |
173 | 1449 | 29 | | | | |
174 | 1476 | 27 | | | | |
175 | 1480 | 4 | | | | |
176 | 1485 | 5 | | | | |
177 | 1489 | 4 | | | | |
178 | 1490 | 1 | | | | |