It happened on October 21, 2006 in The United Kingdom National Lottery. It generated some buzz around the world, because the lotto players were also professors! The players themselves stated that they used mathematics in designing their strategy. Actually, only one or two of the lottery club members were real professors ...
They had organized a lottery syndicate. The syndicate consisted of 17 staff members at Bradford University and College in Britain. The group started playing lotto together since 1994. They hadn't had spectacular success up until this year. They applied their winning strategy (playing all the lotto numbers) for the past four years only.
"We just thought that if all the numbers are in use, we must have a good chance of winning and it has proved so, though you never really think it will happen to you, " syndicate leader said.
Apparently, they played 17 tickets (17 lotto-6 combinations) in the 6 of 49 lotto game played in Britain. That amount of tickets - 17 - looks somehow odd (pun intended)!
I'll tell you the real mathematical story right here. I have been doing similar lottery strategies since the early 1990's. I call this type of lotto playing SHUFFLE. Nobody contests the fact that I was the first lottery analyst to come up with the idea and also the software. Matter of fact, my lotto shuffling software is still the only one sporting the feature.
It resembles shuffling a deck of cards. All the cards remain in the deck. In my shuffling method, all lotto numbers remain in the deck, as it were. We play the numbers in 9 groups of 6 numbers apiece. If we play only 8 tickets, we miss one number: 49. Thus, we add lotto number 49 in the 9th line, and then complete the ticket by adding five numbers previously selected. The simplest method is shown - but it is strongly recommended not to play such tickets!
49, 1, 8, 15, 22, 30
I also released special software to handle LOTTO SHUFFLING. The programs have been freeware since no later than 1994:
The shuffling feature was added to far more powerful software, including freeware. There are two integrated lotto packages that boast the lotto-shuffling feature:
The feature is present in the POWER532.EXE and POWER632.EXE programs. The improvement went even higher: The Bright lotto software packages. Shuffling all lotto numbers is present in the Combine.exe programs. Here is a good example of playing all lotto 6/49 numbers as generated by Combine6.exe:
25 43 41 47 32 3
2 20 12 8 33 14
27 31 24 16 36 22
6 48 15 9 4 29
13 11 1 46 17 23
7 18 34 44 42 19
10 26 35 38 5 49
39 21 37 45 28 40
30 25 20 24 4 23
The cluster represents the group that contains all the lotto '6 of 49' numbers, which are unique, except for the last ticket. The last combination repeats 5 of the lotto numbers previously generated: 1 number from line #1, 1 from line 2, 1 from line 3, 1 from line 4, and 1 from line 5. By the way, none of the lines in a cluster repeat any 6-number groups from past lotto drawings. In a vast majority of cases, no past lotto combination will repeat in hundreds of thousands of drawings!
I am NOT saying that the British syndicate used my strategy. I did NOT expressly give any player or group of players exact strategies of applying the lotto shuffle. But they might have had knowledge of the shuffle feature in my lotto software.Chances are good for that happening. My free software has a pretty large following worldwide. A number of visitors are referred to my web site via searches such as 'sixline lotto' or 'ion saliu six-line lottery groups' or 'lotto shuffle'.
Of course, IP addresses can be matched in the web server log files for quite some time back. I want to stress that my software is totally free no strings attached. It is free you win, all winnings are yours. Besides, the shuffle strategy applied by the professors is quite illogical. Why 17 tickets? Just 9 6-number combinations were needed. If they played two clusters, then 18 lotto tickets should have been played! Looks like they eliminated the last line in the second cluster so that every player played one ticket! Lucky they didn't eliminate the winning ticket!
Or, perhaps they were very efficient! A lotto 6/49 cluster consists of 8 6-number combinations. So they added two clusters to have 16 full 6-liners. The line #9 in each cluster consists of one number. They put together the two numbers in the last lines and added four more unique numbers. Thus, they came up with 17 tickets or one ticket per player. Payment-wise, that is; they played the tickets together.
The story reopened my appetite for my shuffling strategy. Granted, the early computers were inept at handling this type of combination generating strategy. The computer must be adequately fast to handle such a daunting task. Generating all the lotto clusters in lexicographic order involves very complex mathematics and very difficult computer science. Even the fast computers of today allow for random generation only; hence the term shuffle.
I run a faster computer now. I still can use a faster PC! I tried both the free lotto software (Pick632.EXE and Bright6) and my in-house software. The combination generator is slow even for cases with multiple-hit strategies.
I have a lottery data file (D6) with over 400,000 combinations (four hundred thousand). Most of you know that a D6 file consists of lotto- 6 real drawings on top of thousands of SIMulated lotto draws. I remember a time when the personal computers could barely handle data files with only 100 draws!
My free lotto software has this drawback that I fixed in version 4.0 of MDIEditor And Lotto WE: Inner filters. The inner filters cannot be disabled by the user. The frequency allowed by the inner filters is adequately statistics-wise - but not 100%. POWER632.EXE in Pick632.EXE automatically eliminates all the combinations in the D6 file - and then some. Deltas are applied to the past drawings as well. For example, this is a combination in the D6 lottery file:
6, 13, 26, 33, 38, 48
The following combinations will be eliminated (plus more!):
6, 13, 26, 33, 38, 48
5, 12, 25, 32, 37, 47
7, 14, 27, 34, 39, 49
My in-house lottery software can enable or disable the inner filters. The filter that eliminates all past combinations in the D6 file is also based on deltas, even tougher than in my freeware. That filter is 70% successful for an amount of over 400,000 lines in D6. That means that in 30% of the situations, the filter is lower than 400,000. The filter in my free lotto software is at least 80% successful.
In the free version -
The filter named FOUR reaches 1000 or more in many drawings. The filters FivR and FivS reach over 10,000 each in about 20% of the situations. If I run the SHUFFLE function in POWER632.EXE with D6 = 400,000 combinations and FivR = 10000 + FivS = 10000 the result is nothing! The program does not show a single cluster for a long run! There are at least 15 winning combinations every 100 lottery drawings! I know, my PC is at the minimum side of the speed spectrum today (733 MHz). I am certain (Saliu-certain, I should say!) that the above strategy should generate me a few lotto 6/49 clusters!
(Beginning 2008, my computer is a whole lot faster: Quad-core, 2.4 MHz, 4 GB RAM. It generates lotto combinations at high-speed; the amount of combinations is also higher.)
If I enable min_FOUR = 1000, the program generates some clusters, but slowly.
As I said, the TOTAL filter in my in-house loto software is a lot tougher. I only enable the deltas-past-draws and it moves very slowly. When I added FOUR to the fray - it all became very slow! Like a crocodile hunting the gods of the odds! I gotta be patient, like the lucky professors!
I discovered more evidence that the time of running is very important. That is, the probability to generate the winning combinations in the first few combinations is very low. I noticed with these types of runs: 1827 combinations and 914 combinations (actually, they were components of clusters). No duplicates encountered. The amount of winning combinations in the longest run is two times better than random play. The amount of winning combinations in the longest run is FOUR times better than the results in the low run (by comparison to the odds of winning).
That way I will say that patience is rewarded, especially for a strategy such as LOTTO SHUFFLE.
The winning lotto numbers were: 15, 18, 23, 31, 37, 49.
The combination passes the inner filters in LotWon lotto software or the inner filters in MDIEditor And Lotto WE.
V That puzzle or game that I don't care about Sudoku certainly shows resemblance to my lotto clusters. (No debate, the Sudoku thing came to life a few years after my lotto clustering or shuffling was offered in shareware software in 1990-1991. Sudoku came to prominence in 2005.) All the numbers in the cluster (or 9x9 Sudoku grid) are unique. My old-timer lotto buddies did not miss the resemblance. Of course, they wanted me to write the best software there is to generate every possible Sudoku grid. But, what for? I'd rather write software to generate every possible lotto cluster the effort can be worth millions, if not billions, of dollars over time.
The number of unique lotto clusters (groups containing all lotto numbers, all unique) is gigantically higher than total possible Sudoku grids. Today's computers are simply babies who can't walk, while asked to run Olympic dash races! I offered some accurate calculations regarding the number of possible lotto wheels transpositions (rotations, etc). Read:
The calculation of total lotto clusters involves the factorial (e.g. 49!). Today's computers can only generate random lotto clusters. Generating lexicographic clusters would take many, many years. My program Shuffle.exe can also generate lotto clusters. The software also shuffles all lotto numbers and randomly arranges them in one vector (line). The 49-number vector, for example, can be broken into 7 lines of 7 numbers each. Thus, a 49-number vector was converted to a 7-by-7 matrix.
My free combinatorial software PermuteCombine.EXE might be the only program today capable of generating every possible Sudoku grid. Actually, the Arrangements function in PermuteCombine.EXE is capable of such a daunting task (provided that a capable computer is available).
If you want to play with Sudoku why so often? Wouldn't be a whole loto more rewarding to play with the all-lotto-number clusters? You can even eliminate 6-number combinations that came out in the past: The probability for their repeating is negligible in a lifetime. Meanwhile, playing (with) the all-lotto-number clusters offer a far-better-than-negligible chance to win big money.
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