Written by Ion Saliu on July 25, 2001.
• I have received some interesting feedback in response to Most powerful lottery strategy? Pairs, pairings, frequency, lotto 'Wonder-grid'. I have rewarded the authors as promised. They received the pick-4 software. Unfortunately, LOTWON4 is not of much use to those who live in jurisdictions without pick 3/4 lottery games. A promise is a promise, so I added an option to the reward system. An author can now choose to receive a more potent UTIL-6.EXE - the collection of utilities for lotto-6 games.
The most useful capability of the new UTIL-6.EXE is related to what I called in a previous post the lottery "wonder-grid". I also call it the "magical wheel" - for there is no better method of "wheeling" lotto numbers. I briefly presented the strategy in my post "Re: An experiment in mutual cooperation/A 'wonder' lotto strategy?" The idea is to play every lotto number plus its 'top five pairings'. If the game has 49 numbers, we play 49 combinations. That is, a 49-ticket wheel. The UTIL-6.EXE currently on my download site creates a file with the frequencies of all the pairs in a lotto game. The frequencies are sorted in descending order, i.e. from the most frequent pairing to the least frequent one. That version of the program, however, does not create a file that can be used directly as a lotto wheel (e.g. 49 lines of 6 numbers each). It is not too hard to create such a file manually, using copy-and-paste.
The new UTIL-6.EXE creates the lotto wheel automatically. Moreover, the program offers a lot more choices. It defaults now to an optimal range of analysis. The user has the option to select how many lottery 'worst pairings' to save to file. Or, how many 'best pairings' to write to disk, and also at what point to start. The user can choose, for example, to write to file the 'top 7 pairings' beginning with the 3rd best pair, instead of the very best (first) one.
I did a test. I generated a data file for a lotto 49/6 game. I ran UTIL-6 and created a WHEEL-49 file consisting of each lotto number followed by its 'best 5' pairings. The file looks like this:
Lotto number 7 was best paired with #15 (6 times in 147 drawings), #22 (5 times), #41 (5 times), #6 (4 times), #20 (4 times). That amounts to 24 times out of 90 appearances of all pairings for number 7. Or, number 7 was paired with its 'top 5' in 27% of the cases! Meanwhile, number 7 was not paired at all (i.e. in 147 drawings) with 6 other lotto numbers! Here is the fragment of PAIRS6 (that shows the frequency of all pairs in a lotto game):
I ran then UTIL-6 and selected the option 'W – check for Winners'. To my positive astonishment, the 49-line lotto WHEEL49 had 76 '4 of 6' winners (1 in 5) and 4 '5 of 6' winners (1 in 100) in 400 drawings analyzed! That's serious leverage if you consider that people are astonished by static lotto 49/6 wheels assuring '3 of 6' in 160+ lines! I don't even bother to check for '3 of 6' winners. I am sure, there is a ton of them, and I mean hundreds!
The winning report is at the end of this message. You can do it for yourself, with a real lotto drawing file. I am sure that real drawing files are even more biased than random combination files. You'll see serious bias in the report. The lines starting with lotto number 7 had 6 hits. Meanwhile, there was no hit for lotto number 12 and its 'top 5 pairings'.
How is it possible for a 49-line wheel to yield far better results than a 160-line static lottery wheel? The answer is in 'static'. A static wheel considers all number patterns to be probabilistically and statistically EQUAL all the time. That's the fundamental sin. FFG proves that the probability of appearance is determined by the AGE of the last appearance. For example, a lotto number is more likely to repeat (to be drawn again) after a skip equal to/less than its median. For a lotto 49/6 game: a lotto number will repeat after 6 misses in at least 50% of the cases. Look at the skip chart for number 6:
In 14 of its 24 hits, the lotto number 6 waited 5 or fewer drawings between hits (58%). (A skip of 0 is another way of saying that the number came out in consecutive drawings.)
There are many other patterns that show the same discrepancy. You may want to look at a simpler lottery game, such as pick-3. Some combinations come out 10 times in 1000 draws, while other combinations do not come out within the same range. The static sin considers that all combinations will come out with an equal frequency because they have the same probability 1/N. You will never ever see a random event (such a lottery game) showing equal frequencies among its elements. Now you understand why a 160-line WHEEL49 is far less efficient than the dynamic WHEEL49 created by UTIL-6. The 160-line static wheel combines number 7 with numbers like 44, 35, 29, 21, 42, 11. Those numbers came out ZERO times paired with number 7.
There are two opposite opinions when it comes to randomness. There are those who say randomness is synonymous with agnosticism. "It is random therefore we cannot know it."
Then, there are those who say: "Everything has a rule, therefore there is no randomness."
I believe the truth is: "Everything is random". Everything in the Universe, the Universe itself is the result of RANDOM INTERACTION BETWEEN FORCES. Randomness represents fairness in its purest form. Randomness is logical. Randomness is the only solution to the logical absurdity I call "Deus ex machina" (the god in the machinery). In old times, there were very surprising conclusions to stage plays. The "god in the machinery" explained the totally unexpected surprise. Unfortunately, even today, when knowledge has reached dizzyingly high peaks, humans still explain the Universe by deus ex machina. It is the gnoseological (related to knowledge) root of religion. The ontological (related to being) root of religion is in the FearSurvival essential principle. Fear of gods is Fear in its most frightening form. Eternal life provided by gods is the ultimate form of Survival.
1 15 46 47 18 19
2 21 16 25 29 33
3 23 29 31 42 48
4 8 32 41 12 30
5 9 10 29 30 31
6 28 14 15 25 9
7 15 22 41 6 20
8 15 33 24 17 4
9 26 6 33 48 15
10 33 25 15 42 1
…………
Etc.
Number: 7 Hits: 18 ( 12.2 %)
With #: 15 22 41 6 20 10 12 30 32 33 36 2 14 23 24 25 26 4 17 18 19 37 38 9 43 48 49 1 16 34 5 3 13 39 40 27 28 45 46 47 8 31 44 35 29 21 42 11
Hits: 6 5 5 4 4 3 3 3 3 3 3 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0
Pairs total: 90
Number: 8 Hits: 20 ( 13.6 %)
With #: 15 33 24 17 4 19 22 12 26 13 39 45 46 49 21 11 3 25 1 27 30 31 32 6 38 16 41 9 10 20 34 36 37 28 29 5 42 43 44 14 7 47 48 23 35 2 40 18
Hits: 7 6 5 5 4 3 3 3 3 3 3 3 3 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0
Pairs total: 100
Number: 6 (22 hits)
* Skips: 30 2 0 4 0 6 19 0 2 0 0 3 2 5 7 11 1 2 6 4 8 6
Sorted Skips: 0 0 0 0 0 1 2 2 2 2 3 4 4 5 6 6 6 7 8 11 19 30
* Median Skip: 3
LOTTO-6 Winning Number Checking
Files: MOST6 -> Lotto DATA-6
Line Numbers 6 5 4
no. Checked Winners Winners Winners
------------------------------------------------------------------------
1 1 15 46 47 18 19 in line # 100
1 1 15 46 47 18 19 in line # 117
2 2 21 16 25 29 33 in line # 15
2 2 21 16 25 29 33 in line # 20
3 3 23 29 31 42 48 in line # 222
4 4 8 32 41 12 30 in line # 75
...
7 7 15 22 41 6 20 in line # 87
7 7 15 22 41 6 20 in line # 106
7 7 15 22 41 6 20 in line # 142
...
16 16 2 17 13 21 23 in line # 20
17 17 33 20 8 27 28 in line # 2
18 18 33 2 6 9 26 in line # 26
18 18 33 2 6 9 26 in line # 35
...
20 20 17 25 28 6 7 in line # 87
20 20 17 25 28 6 7 in line # 224
21 21 2 25 27 28 31 in line # 20
...
33 33 8 17 10 9 18 in line # 7
35 35 41 29 46 10 11 in line # 90
35 35 41 29 46 10 11 in line # 122
35 35 41 29 46 10 11 in line # 138
36 36 25 20 7 16 17 in line # 87
36 36 25 20 7 16 17 in line # 93
37 37 14 25 48 42 38 in line # 145
...
44 44 6 20 26 28 34 in line # 39
45 45 33 15 20 25 26 in line # 61
45 45 33 15 20 25 26 in line # 372
46 46 29 13 1 41 2 in line # 90
46 46 29 13 1 41 2 in line # 122
47 47 43 11 15 20 34 in line # 71
48 48 9 37 41 14 19 in line # 380
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