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LottoPoster Forums : LOTTO THEORY, CONCEPTS AND METHODS OF PLAY : Pick 3, Pick 4, Pick 5, Pick 6 & Powerball 
Topic: Count of Integers World’s 649 Lotto Games  
Author  Message  
Colin F
Lotto Systems Tester Creator & Analyst To dream the impossible dream ... Joined: September 30 2004 Location: Australia Online Status: Offline Posts: 678 
Topic: Count of Integers World’s 649 Lotto Games Posted: January 18 2005 at 10:41pm 

I recently combined all the World's 649 Lotto's main draw numbers to make a table consisting of some 17,511 Draws. See for yourself how close the tally is for each number to the average of 2144. Regards 

Lotto Draws have no relationship to one another; the integers serve just as identifiers. Any prediction calculation on one history of draws for a same type game is just as irrelevant as another.


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Bertil
Registered Member Joined: April 17 2005 Online Status: Offline Posts: 36 
Posted: April 17 2005 at 1:03pm  
Hi Colin, I just became aware of your table of frequencies for 17511 draws and decided to add my two bits of analysis. There is a std.dev. of 55.44 from the mean 2144.2. Thus the spread covers 4.1 units of s.d., which covers 95%. Bertil 

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Bertil
Registered Member Joined: April 17 2005 Online Status: Offline Posts: 36 
Posted: August 30 2005 at 8:25am  
Hi Colin, Your table of frequencies for the 149 integers seem to yield a high std.dev. of 55.44 if my calculations are correct. There is a formula for predicting the variance for any lotto and it yields 43.37 as std.dev Thus the actual value seems to differ too much from theory. If you know an expert on probability theory you might ask him to predict the theoretical variance for any mean lotto frequency. The formula I was given is V=D*n*(Nn)/(N^2), where D= number of draws and n/N is the lotto matrix. Personally, I think a better formula would be :D*n(N2.5n)/(N2.5)^2 for any pick6 game. Please let me know if you find a formula. Bertil 

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Colin F
Lotto Systems Tester Creator & Analyst To dream the impossible dream ... Joined: September 30 2004 Location: Australia Online Status: Offline Posts: 678 
Posted: August 30 2005 at 10:30am  
Bertil Professor Iliya Bluskov puts his name to a book of Covers/Wheels which purportedly improve a Lotto players chances of winning prizes. People believed him and still do. Then along came Colin who proved him wrong and a few other people too. However, the percentage of Lotto players that look for information beyond that of a few numbers they keep track of on a piece of paper, if that, is extremely small. So we have a situation where the people who do a bit more than the latter know they have been proved wrong but just can't bring themselves to acknowledge it  they probably hope this website and me would fade away and then they can pretend it and me never existed. Bertil the draws are real; the equations are what? If you toss a coin there is less than 1 in a million chance of getting 20 heads in a row  but it can happen. On the 18th of August, 1913 in the famous Monte Carlo casino black was coming up repeatedly. Around the 15 in succession mark the casino was in turmoil  everyone wanted to get on red. So they bet millions on red and lost millions on red because black continued coming up 26 times in succession. The chances of this happening were 1 in 136,823,184. If you were using the results from that week to work out a standard deviation ... Regards


Lotto Draws have no relationship to one another; the integers serve just as identifiers. Any prediction calculation on one history of draws for a same type game is just as irrelevant as another.


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Bertil
Registered Member Joined: April 17 2005 Online Status: Offline Posts: 36 
Posted: August 31 2005 at 7:37am  
Colin, I'm fully aware of short run deviations from ideallity. That is what system players try to take advantage of. But I tested 17511 runs of 6/49 games and found a substantial deviation from a theoretical formula. This makes me wonder if the formula is correct. It is based on a simple binomial model. If possible, please ask an expert. Bertil 

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Colin F
Lotto Systems Tester Creator & Analyst To dream the impossible dream ... Joined: September 30 2004 Location: Australia Online Status: Offline Posts: 678 
Posted: November 10 2009 at 8:24pm  
Here is a table of AllWorld649 Lotto draws increased to 20,682 in 6 columns as requested by Bertil or Stig Holmquist in another forum and as well, similarly all the combinations of 6 integers enumerated lexicographically. The columns P1 to P6 each sum to the number of combinations, respectively 20,682 and 13,983,816. Stig Holmquist has been obsessed with applying Standard Deviation measurements to Lotto combinations since the late 90's. The problem is he ascribes magnitude to the identifiers which is the stuff of numerology. Whatever calculation you do in Lotto analysis must be applicable if the balls are identified in some other way than numbers eg pictures of animals or hieroglyphic symbols.
The All World table Line Total column has an average of 2532.49, a Variance of 2621.80 and Standard Deviation (Average of the Sum of the Squared Differences to Average) of 51.20. Does this provide anything worthwhile in producing a set of numbers to play Lotto? None that I can see.
For the AllCombs table the Line Total column sum is
1,712,304 x 49 = 83,902,896 = 13,983,816 x 6. This table is given just for reference and in no way resembles a table that would be produced for the same number of combinations by Random Selections. Why? Because from the second selection you could have a repeat and this very event occurred recently in Bulgaria. The irrelevance of applying Standard Deviation measurements based on attributing magnitude to the identifiers is made abundantly clear in this table with 0 deviation in the relevant line Total column but still irrelevant deviations in the P1 to P6 columns. You may notice that Column 1 is the inverse of Column 6 and the sequence is given by the combinations of 5 from a pool increasing from 5 to 49.
by Numerical Order Position Lexicographic Enumeration
Stig or Bertil thought something wonderful was obtained by a formula that gave the Standard Deviations for the 6 columns for all the 13,983,816 combinations. Well, let's do a comparison between various sets and see if it comes up with anything other than what is expected after random selections displayed in order drawn are presented in numerical order.
Most of the tables referred to are too long to show here except firstly a little 8/6/8/5/9 Offset 6/49 gem from my collection with no repeat Threes and close to maximum optimization. Secondly, from December 24, 2004 a 49 line set with equal representation of 6 for each integer, maximized repeat consecutive subsets and poor coverage of only 36.64% compared to an optimum of around 69.88%. This set is isomorphic with each integer having the same occurrence after randomization but as shown all over the place with Standard Deviation based on attributing magnitude to the integers.
Just bear in mind that the Standard Deviation for the sequence 1, 2, 3 ... 47, 48, 49 is 14.29 when erroneously attributed magnitude in a Lotto context ie the identifier 49 is 49 times bigger than the identifier 1 in some way. If we take out either 11 or 39 and do the Standard Deviation on 48 integers we still have 14.29!
Fairbrother 6/49 Matrix Offset 8/6/8/5/9
Equal Representation set 49 lines each integer occurrence 6
Comparison Standard Deviations per column for various Lotto 6/49 sets
Summary and conclusions
When a Pool 49 Pick 6 Lotto games's draws are presented in 6 columns as drawn as by the South African Lotto operators then over a reasonable number of draws it is expected that each column will have a near equal distribution of the integers.
Usually draw results are presented in Numerical Order rather than order drawn and if an add on game applies such as the Australian Lotto Strike where the order drawn of the first four random selections is guessed then the results are given separately.
Statistics on integers in the history of draws for a Lotto game are usually given as absence (recency) or occurrence (frequency). Attributing magnitude to the integers is unnecessary and is usually the stuff of numerologists.
If magnitude is attributed then from the sequence 1, 2, 3, 4 .... 47, 48, 49 a Standard Deviation is derived of 14.288690166. A calculation of the Standard Deviation per column on a sample 874 draws presented in drawn order from the South African 6/49 Lotto game gives close to the 14.29 for each column. If the draws are now converted to numerical order and a calculation done on the Standard Deviation per column then the results obtained may also be obtained using the following conversion factors: 
Col 1 and 6: 0.4017
Col 2 and 5: 0.5185
Col 3 and 4: 0.5675
The usefulness of this presupposes a desire to want to know a Standard Deviation measurement per column for the draws when presented in Numeric order. From my long experience in dealing with Lotto numbers and how pseudo analysts work the only use I see for this is an added "tool" for those that predict the numbers. Tests already exist based on occurrence of the integers that adequately measure the fairness of the Random Selections.
I think it comes down to understanding what the rows and columns represent. A Lotto draw recorded in a row usually has an identifying number and date. From the draw you can record a hit in the appropriate 6 columns from 49 and then get some meaningful data by counting the hits in each column. Aggregating Lotto draws by column when presented in numerical order leads to nowhere meaningful. You can't get back to how the integers were drawn as for each draw there are 720 possibilities.
Colin Fairbrother


Lotto Draws have no relationship to one another; the integers serve just as identifiers. Any prediction calculation on one history of draws for a same type game is just as irrelevant as another.


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Colin F
Lotto Systems Tester Creator & Analyst To dream the impossible dream ... Joined: September 30 2004 Location: Australia Online Status: Offline Posts: 678 
Posted: November 22 2009 at 1:13am  
Stig Holmquist aka Bertil proposed that the Standard Deviation of the columns when presented in numerical order may be useful in determining the randomness of a Lotto game's draws.
In alt.math.recreational November 9,2009 he wrote, "Colin was on a fishing expedition hoping to disprove my data. You might as well have told him to wait until Hell freezes over before you can come up with any data to disprove mine. I know there is a formula for predicting the means and s.d., but I can't find it. Some time ago it was used to predict the values for the 5/55 Powerball game."
The South African 6/49 Lotto game presents the draws with the integers shown as drawn. Placing the integers in numerical order for 874 draws the following Standard Deviations are obtained for the columns: 
Col 1 5.82
Col 2 7.19
Col 3 7.91
Col 4 8.17
Col 5 7.56
Col 6 5.62
South African 6/49 Lotto 874 draws
The Standard Deviation for the Line Totals is 10.37
If we now massage the data such that identifier 11 has no occurrence then the following Standard Deviations are obtained for the column totals which are not much different to those with identifier 11 having an occurrence of 113: 
Col 1 6.03
Col 2 7.66
Col 3 8.07
Col 4 8.23
Col 5 7.57
Col 6 5.62
Lotto 6/49 example 874 draws with nooccurrence identifier 11.
However, for the normal occurrence calculation irrespective of the column there are three sore thumb indications of something being wrong 
firstly the line total is 0 for identifier 11 and 199 for identifier 1 whereas the others are around the average 107 mark. Thirdly, the Standard Deviation for the line totals has more than doubled to 23.13.
I guess we can now take this as proof that hell can freeze over!
Colin Fairbrother


Lotto Draws have no relationship to one another; the integers serve just as identifiers. Any prediction calculation on one history of draws for a same type game is just as irrelevant as another.


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