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Discharging Reoccurrence Distribution

Topic closed. 2 replies. Last post 10 years ago by JADELottery.

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The Quantum Master
West Concord, MN
United States
Member #21
December 7, 2001
3675 Posts
Offline
 Posted: November 9, 2006, 9:51 am - IP Logged

Discharging Reoccurrence Distribution

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

Presented 'AS IS' and for Entertainment Purposes Only.
Any gain or loss is your responsibility.

Order is a Subset of Chaos
Knowledge is Beyond Belief
Wisdom is Not Censored
Douglas Paul Smallish
Jehocifer

The Quantum Master
West Concord, MN
United States
Member #21
December 7, 2001
3675 Posts
Offline
 Posted: November 9, 2006, 10:33 am - IP Logged

Here's an example for the number 5 in column 1 of Wisconsin Megabucks 6/49 lottery:

d = 1500
m = Ar(49,6,1,5) » 12.88
x = Dd

y = (1500 / (12.88)2 ) e -(x / 12.88)

 Index Draw Occurrence Dd Dd Actual Frequency Calculated Frequency 1 14 1 9 8.37 2 24 10 2 11 7.74 3 27 3 3 6 7.16 4 34 7 4 7 6.63 5 73 39 5 7 6.13 6 100 27 6 11 5.67 7 108 8 7 9 5.25 8 121 13 8 6 4.86 9 132 11 9 3 4.50 10 140 8 10 4 4.16 11 161 21 11 4 3.85 12 162 1 12 3 3.56 13 204 42 13 4 3.30 14 205 1 14 4 3.05 15 220 15 15 4 2.82 16 224 4 16 4 2.61 17 238 14 17 3 2.42 18 240 2 18 3 2.24 19 242 2 19 1 2.07 20 248 6 20 2 1.91 21 274 26 21 1 1.77 22 275 1 22 2 1.64 23 280 5 23 0 1.52 24 298 18 24 0 1.40 25 302 4 25 2 1.30 26 311 9 26 1 1.20 27 315 4 27 1 1.11 28 325 10 28 0 1.03 29 328 3 29 0 0.95 30 336 8 30 0 0.88 31 338 2 31 2 0.81 32 346 8 32 1 0.75 33 371 25 33 0 0.70 34 375 4 34 0 0.65 35 382 7 35 0 0.60 36 385 3 36 1 0.55 37 399 14 37 0 0.51 38 411 12 38 1 0.47 39 443 32 39 2 0.44 40 449 6 40 0 0.41 41 460 11 41 0 0.37 42 467 7 42 1 0.35 43 473 6 43 0 0.32 44 481 8 44 1 0.30 45 495 14 45 0 0.27 46 550 55 46 0 0.25 47 560 10 47 0 0.24 48 577 17 48 0 0.22 49 593 16 49 0 0.20 50 600 7 50 0 0.19 51 620 20 51 0 0.17 52 630 10 52 0 0.16 53 641 11 53 0 0.15 54 648 7 54 0 0.14 55 654 6 55 2 0.13 56 655 1 57 660 5 58 691 31 59 693 2 60 698 5 61 711 13 62 749 38 63 750 1 64 764 14 65 769 5 66 784 15 67 786 2 68 792 6 69 793 1 70 799 6 71 800 1 72 809 9 73 814 5 74 820 6 75 821 1 76 828 7 77 841 13 78 856 15 79 859 3 80 868 9 81 923 55 82 931 8 83 948 17 84 952 4 85 968 16 86 971 3 87 977 6 88 995 18 89 1002 7 90 1046 44 91 1077 31 92 1097 20 93 1114 17 94 1130 16 95 1166 36 96 1173 7 97 1192 19 98 1194 2 99 1200 6 100 1205 5 101 1220 15 102 1224 4 103 1226 2 104 1232 6 105 1271 39 106 1287 16 107 1288 1 108 1290 2 109 1292 2 110 1294 2 111 1312 18 112 1324 12 113 1329 5 114 1351 22 115 1364 13 116 1376 12 117 1380 4 118 1405 25 119 1408 3 120 1419 11 121 1426 7 122 1432 6 123 1454 22 124 1456 2

Presented 'AS IS' and for Entertainment Purposes Only.
Any gain or loss is your responsibility.

Order is a Subset of Chaos
Knowledge is Beyond Belief
Wisdom is Not Censored
Douglas Paul Smallish
Jehocifer

The Quantum Master
West Concord, MN
United States
Member #21
December 7, 2001
3675 Posts
Offline
 Posted: December 2, 2006, 7:14 am - IP Logged

Presented 'AS IS' and for Entertainment Purposes Only.
Any gain or loss is your responsibility.