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 LottoPoster Forums : NUMBER SETS TO PLAY FROM DIFFERENT METHODS : History Methods
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Colin F
Lotto Systems Tester Creator & Analyst
Lotto Systems Tester Creator & Analyst
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Quote Colin F Replybullet Topic: Lotto History Absence and Occurrence Myths Exposed
    Posted: November 10 2010 at 9:24pm
There are two myths that I became aware of around 2000 in my study of Lotto numbers and a third a bit later on-
  1. The errant notion that there are beneficial Upper Limits for Absence of Integers in a Lotto game.
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  2. The belief that Integer Distribution will even out as the number of draws increases.
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  3. The absurdity of specifying a reduced Pool for a given Lotto game without giving the lines played and thinking this entitles credit to be taken for any prize that falls in that reduced Pool without acknowledging that this is at usually the considerable cost of all combinations for the reduced Pool being played.
 The first myth is that there is some upper limit to the absence of an integer in a Lotto game. For the Pick 6 Pool 49 Classic Lotto Washington is a good example with the integer 32 not appearing for 85 draws from a previous highest absence in that game of 36. The average absence for an integer is around 7. Is 85 the limit? Nah! It can easily go well over the 100 mark. (Multiply 8.16 by Monte Carlo 1913 26 Blacks in succession factor of 13 to get 104)
 
The second myth is that as the number of draws increases so the integer occurrence will become closer to the average. For 49 draws it is possible, but most unlikely to have an equal distribution of 6 occurrences for each integer giving a theoretical average per draw of 0.1224489. The chances of an even distribution happening are greater at 49 draws than at any number of draws after that.
 
The average occurrence per draw at 20682 draws is pretty spot on varying from 0.1117880 to 0.124939561. However, as per the table below the Standard Deviation for the Occurrence per Integer at 1000 draws is 10.89 compared to 46.28 at 20,000 draws. The maximum Occurrence Difference is only 49 at 1000 draws but is 272 at 20,000 draws. This can hardly be interpreted as a trend towards evenness of distribution!  
 
Draws StDev AVEDEV Average Max Min Max Occur Diff
1000 10.89103961 8.82132 122.4490 152 103 49
2000 15.96200194 12.29571 244.8980 289 220 69
3000 18.78291779 13.62099 367.3469 411 318 93
4000 22.34696673 16.59142 489.7959 538 433 105
5000 26.35745692 19.72928 612.2449 688 538 150
6000 27.44731806 20.81799 734.6939 816 648 168
7000 28.47985324 21.20700 857.1429 947 765 182
8000 28.67760156 21.78759 979.5918 1045 880 165
9000 31.38305742 23.02124 1102.0408 1176 981 195
10000 34.81737922 26.90796 1224.4898 1302 1089 213
11000 34.64479121 25.49105 1346.9388 1431 1199 232
12000 37.08556919 27.13953 1469.3878 1555 1315 240
13000 38.91977460 30.58809 1591.8367 1675 1446 229
14000 39.56807619 31.18950 1714.2857 1803 1571 232
15000 41.09857513 31.29946 1836.7347 1918 1685 233
16000 42.64886221 32.07247 1959.1837 2059 1813 246
17000 47.26507701 35.73678 2081.6327 2203 1929 274
18000 47.53852862 36.53228 2204.0816 2339 2050 289
19000 45.37017902 35.15119 2326.5306 2462 2188 274
20000 46.28637116 36.18409 2448.9796 2584 2312 272
 
The third myth is seen most often in Lotto forums and newsgroups with predictionists giving say 20 integers in a Lotto game with a Pool of say 45 or 49. They rate their chances of success on the reduced Pool carrying on as if the Picking of 20 integers has somehow eliminated the balance of the Pool from consideration. They want to take credit for any prize without specifying the lines played.
 
Even if they specified all the 38,760 combinations possible for a pool of 20 integers in a Pick 6 game this represents only a 0.28% in a 6/49 game for 1st prize and 0.48% in a 6/45.
 
Colin Fairbrother
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