Lotto combination 1-2-3-4-5-6: Probability versus statistics, standard deviation

Reposted from the Lotto, Lottery Message Board.

The definitive presentation is here: Lotto Combination 1,2,3,4,5,6: Probability, Frequency, Odds, Statistics.

[snip]

> It can turn into a very complicated debate. I will make it as simple
> as possible.

Very wise.

The simplest way and the clearest method of proving or

[snip]

It strikes me that the number '6' in the 6th position is

I

Open the data file as 'Text only'. The spreadsheet application

[snip]

Duncan

Ion Saliu wrote in message <>...
> • Reposted from "The World Message Board" Lotto Forums, Lottery Message Board

> We can hear two divisive opinions:
> 1: "Combination 1-2-3-4-5-6 has the same chance of being drawn as any
> other lotto combination. I play it religiously!"
> 2: "Combination 1-2-3-4-5-6 should not be played. It represents a
> weird arrangement of numbers. Only fools can waste their money and
> play such a combination!"
> It is the kind of issue that pits brother-of-opposites against
> brother-of-opposites and enemy against foe.
> Incidentally, the combination 1-2-3-4-5-6 is played by thousands of
> lotto players worldwide in any given drawing.

> We was also opinionated in this regard. Let us start with the
> fundamental concept of 'probability'. If the lotto 6/49 has a total of
> 13,983,816 lotto combinations and only one is drawn as the winner, the
> probability is undeniably '1 / 13,983,816'. It is also expressed as '
> 1 in 13,983,816'; or, as odds: '13,983,816 to 1' (even as '13,983,815
> to 1'). The relations are mathematically valid. But the probability is
> rather an abstract concept. We can infuse more life into probability
> if we look at the probability as:
> expected successes in one trial.
> This explains more clearly the requirement that the probability cannot
> be larger than 1. No event can have more than one success in one
> trial! Very logical!
> Successes and trials are real elements, not abstract concepts. All
> real-life random events are characterized by successes and trials.
> Real-life random events do not deal with simply one success in one
> trial. Life is a whole lot more complex than that.
> I presented on one of my web pages (More Gambling Analysis: Odds,
> House Edge, Fraud the reality of lottery combinations. In the pick-3
> game, every combination has the same probability: 1/1000. Yet, some
> combinations have come out ten or more times, while another
> combination waited for over 6000 draws to see the daylight! (Real
> case: combination 2,1,4 in Pennsylvania lottery.)

> The discrepancy is much wider in lotto-6 games. The higher the odds
> (or the lower the probability) , the wider the frequency gap. I said
> previously that we was never ever to see equal frequencies in lotto
> games. Test it for billions of draws! I know, we was not built by
> beloved Mother Nature to live that long. But we can use computers to
> generate that many gazillions of combinations. Never ever will we see
> equal frequencies of combinations!
> But what's wrong with a combination like '1-2-3-4-5-6'? Why shouldn't
> it come out even more frequently than combinations considered to be
> "more random"? For example, 3,17,28,29,34,47 is considered by many
> 'more likely to be drawn' because appears to be 'more random'. I think
> 'more random' has come to life as a result of statistical analysis of
> lottery draws.

> It can turn into a very complicated debate. I will make it as simple
> as possible. The simplest way and the clearest method of proving or
> disproving is 'data analysis'. They say 'a picture is worth a thousand
> words'. Also, 'real data is worth millions of words'. I will add to
> analysis 6 more numbers. That way, we can analyze real draws that
> occurred in our lifetime. Many lotto players also play combinations
> like 7,8,9,10,11,12. I saw with my own eyes a Jamaican player (farm
> worker in the US) always starting his play card this way:
> 1,2,3,4,5,6
> 7,8,9,10,11,12
> I will do the analysis for 12 numbers: 1,2,3,4,5,6,7,8,9,10,11,12. The
> combination '1,2,3,4,5,6' is in there.
> I will use a 642-draw data file in UK lotto 6/49 game. Look at the
> combination '1,2,3,4,5,6'. The clearest way to look at it is 'position
> by position'. It strikes me that the number '6' in the 6th position is
> way too low. I compare it with all the data in the UK-6 draw file. I
> can do some sophisticated analysis using a tool such as Microsoft
> Excel. Open the data file as 'Text only'. The spreadsheet application
> is intelligent enough to open it in the correct format (642 rows by 6
> columns). Select column A. Select 'Data analysis' in the 'Tools' menu
> (an add-in), then 'Descriptive statistics' for the range A1:A642. The
> minimum value in the 1st position of UK-6 is 1; the maximum value is
> 30; the median is 6, the mode (the most frequent number) is 1. For
> column F (the 6th position), the results are:
> - minimum value = 19
> - maximum value = 49
> - median = 45
> - mode (the most frequent number) = 45.
> A number such as '6' in the 6th position appears to be way out of
> range. So, what?, some may ask legitimately. Let's do an analysis, I
> would answer. I would generate all 924 combinations for the numbers 1
> through 12. Then I will generate combinations for the 3 most frequent
> numbers in lotto UK-6 position by position.
> I created a file with the most frequent numbers by position. The most
> frequent numbers are situated around the median of the respective
> position. The exception is position 1, where the first number is the
> most frequent. The median can be calculated by the Fundamental Formula
> of Gambling (FFG). Or, we can use the Excel median values for each
> column. The UK-6 draws history generated the following positional
> ranges:

> 1 2 3
> 13 14 15
> 22 23 24
> 29 31 32
> 37 38 39
> 45 48 49

> The 6 positional ranges generate, in this case, 729 combinations, from
> '1 13 22 29 37 45' to '3 15 24 32 39 49'. This is an easier situation,
> so the combinations can be generated manually. I use software to
> generate combinations based on positional ranges; thus, no errors are
> possible.
> Notice that the result files: WHEEL12.66 and POSIT6.3 are not equal in
> size. The numbers 1 through 12 generated 924 combinations. The
> positional ranges file generated 729 combinations. We might expect
> that the 1-12 file would hit 924/729 = 1.27 times more winners.
> I used my freeware WINNERS.EXE to check for 3, 4, 5, 6 winners against
> the UK draws file UK-6 (642 draws). The reports follow:

>                    LOTTO-6 Winning Number Checking
>                    Files: POSIT6.3 ( 729 ) against > UK-6 ( 642 )
>                    Date: 07-31-2002

> ---------------------------------------------------------------------------­--
>    Line    Combinations                          6       5       4    
>   3
>    no.       Checked                            Hits    Hits    Hits  
>  Hits
> ---------------------------------------------------------------------------­--
>       1    1 13 22 29 37 45         in draw #                        
>   52
>       1    1 13 22 29 37 45         in draw #                        
>   59
>       1    1 13 22 29 37 45         in draw #                        
>   61
>       1    1 13 22 29 37 45         in draw #                        
>   163
> ........
> ........
>     729    3 15 24 32 39 49         in draw #                        
>   268
>     729    3 15 24 32 39 49         in draw #                        
>   294
>     729    3 15 24 32 39 49         in draw #                        
>   318
>     729    3 15 24 32 39 49         in draw #                        
>   328
>     729    3 15 24 32 39 49         in draw #                        
>   379
> ---------------------------------------------------------------------------­--
>          Total Hits:                             0       21      606  
>   9219
> ---------------------------------------------------------------------------­--

>                    LOTTO-6 Winning Number Checking
>                    Files: WHEEL12.66 ( 924 ) against > UK-6 ( 642 )
>                    Date: 07-31-2002

> ---------------------------------------------------------------------------­--
>    Line    Combinations                          6       5       4    
>   3
>    no.       Checked                            Hits    Hits    Hits  
>  Hits
> ---------------------------------------------------------------------------­--
>       1    1  2  3  4  5  6         in draw #                        
>   32
>       1    1  2  3  4  5  6         in draw #                        
>   35
>       1    1  2  3  4  5  6         in draw #                        
>   60
>       1    1  2  3  4  5  6         in draw #                        
>   207
> ............
> ............
>     924    7  8  9 10 11 12         in draw #                        
>   546
>     924    7  8  9 10 11 12         in draw #                        
>   547
>     924    7  8  9 10 11 12         in draw #                        
>   556
>     924    7  8  9 10 11 12         in draw #                        
>   565
>     924    7  8  9 10 11 12         in draw #                        
>   575
> ---------------------------------------------------------------------------­--
>          Total Hits:                             0       7       497  
>   10458
> ---------------------------------------------------------------------------­--

> The positional ranges registered the following hits:
> - 6 winners: 0
> - 5 winners: 21
> - 4 winners: 606
> - 3 winners: 9219

> The WHEEL12.66 file (numbers 1 through 12) registered the following
> hits:
> - 6 winners: 0
> - 5 winners: 7
> - 4 winners: 497
> - 3 winners: 10458

> WHEEL12.66 fared clearly worse! Yet, it had 1.27 times more
> combinations! The WHEEL12.66 file (numbers 1 through 12) should have
> registered the following hits:
> - 6 winners: 0
> - 5 winners: 27
> - 4 winners: 770
> - 3 winners: 11708
> to maintain size parity.

> We can also notice that the higher the prize, the worse '1-12' fares.
> The performance gap widens from low prizes to jackpot.

> The probabilities are equal, but the combinations are not equal. As
> George Orwell put it: "Some animals are more equal than others."

> "For only Almighty Number is exactly the same, and at least the same,
> and at

I read you don't respond to emails. I would like your generator of
positional combs. I'll send you one of my lottery programs and the source code
(several statistical functions). Please check your email.
Thanks.

Brother and Beautiful Sister:

Beauty is the only thing Almighty Number allows to be worshipped. For that reason, Almighty Number created Phi or the ‘golden proportion':
X^2 +X –1 = 0
leading to:
{Sqr(5) ± 1} / 2 = 1.618033989… or Phi = 0.618033989…

The ‘perfect line river' is a beauty of a mind game! There is absolutely no evidence of a river flowing in perfectly straight line. (We know what ‘straight line ‘ means for all intents and purposes. The Universe is curved, of course. The classical geometry is a particular sub-system of a larger geometry, where all lines are curved. Then a straight line represents a segment of a circle with the radius equal to infinite.)

How about the probability of a mountain in the shape of a perfect pyramid? How about the probability of a tree in the shape of a perfect cylinder, in a perfectly vertical position? There is absolutely no evidence of such shapes on our planet.  But I don't think the probability of one of such shapes is zero. I think such probability is equal to the probability of any other shape. The Universe is infinite; the matter takes an infinite number of shapes. Therefore, the probability of an individual shape is close to zero, but never equal to zero. Who knows, maybe somewhere in this Universe, there is a mountain in the shape of a perfect pyramid! If not in the present, maybe in the infinite future. The Universe is the result of absolutely free interaction of forces. Randomness is the supreme form of free interaction. We may call Almighty Number Randomness the Almighty. Randomness creates all those shapes of matter. Randomness also creates all those lottery combinations where ‘1,2,3,4,5,6' is noticeably missing! The same individual probability, but apparently, Randomness Almighty prefers certain shapes or combinations thereof…

The definitive presentation is here: Probability of perfect shapes in nature: Rivers, mountains, trees..

Ion Saliu

hifi552@yahoo.com (hifi) wrote in message <>...
> Ion,
> A cutie in this office is crazy about everything you write. She wrote
> a poem to you, would post it if your bbs were open. She has a question
> for you-
> What is the probability of a river flowing in straight line all the
> way ?
> Perfect line, no deviation. Is it possible?
> HF

> hif@netzero.com (hifi55) wrote in message <>...
> > Great site, neat (free) software!
> > You did an outstanding analysis of a controversial problem.
> > I tested 3 more lottos. I checked 84 combs for 9 numbers instead of
> > 1-12. I compared the results with 84 random combs of Excel positional
> > numbers. The difference is much worse for 1-9 sometimes. If the draw
> > history is older the gap is also much worse for 1-9.

> > I read you don't respond to emails. I would like your generator of
> > positional combs. I'll send you one of my programs and the source code
> > (several statistical functions). Please check your email.
> > Thanks.

Terry

> > . Reposted from "The World Message Board" Lotto Forums, Lottery Message Board

> > > > We can hear two divisive opinions:
> > > > 1: "Combination 1-2-3-4-5-6 has the same chance of being drawn as
any
> > > > other lotto combination. I play it religiously!"
> > > > 2: "Combination 1-2-3-4-5-6 should not be played. It represents a
> > > > weird arrangement of numbers. Only fools can waste their money and
> > > > play such a combination!"
> > > > It is the kind of issue that pits brother-of-opposites against
> > > > brother-of-opposites and enemy against foe.
> > > > Incidentally, the combination 1-2-3-4-5-6 is played by thousands of
> > > > lotto players worldwide in any given drawing.

> > > > We was also opinionated in this regard. Let us start with the
> > > > fundamental concept of 'probability'. If the lotto 6/49 has a total
of
> > > > 13,983,816 combinations and only one is drawn as the winner, the
> > > > probability is undeniably '1 / 13,983,816'. It is also expressed as
'
> > > > 1 in 13,983,816'; or, as odds: '13,983,816 to 1' (even as
'13,983,815
> > > > to 1'). The relations are mathematically valid. But the probability
is
> > > > rather an abstract concept. We can infuse more life into probability
> > > > if we look at the probability as:
> > > > expected successes in one trial.
> > > > This explains more clearly the requirement that the probability
cannot
> > > > be larger than 1. No event can have more than one success in one
> > > > trial! Very logical!
> > > > Successes and trials are real elements, not abstract concepts. All
> > > > real-life random events are characterized by successes and trials.
> > > > Real-life random events do not deal with simply one success in one
> > > > trial. Life is a whole lot more complex than that.
> > > > I presented on one of my web pages (More Gambling Analysis: Odds,
> > > > House Edge, Fraud the reality of lottery combinations. In the pick-3
> > > > game, every combination has the same probability: 1/1000. Yet, some
> > > > combinations have come out ten or more times, while another
> > > > combination waited for over 6000 draws to see the daylight! (Real
> > > > case: combination 2,1,4 in Pennsylvania lottery.)

> > > > The discrepancy is much wider in lotto-6 games. The higher the odds
> > > > (or the lower the probability) , the wider the frequency gap. I said
> > > > previously that we was never ever to see equal frequencies in lotto
> > > > games. Test it for billions of draws! I know, we was not built by
> > > > beloved Mother Nature to live that long. But we can use computers to
> > > > generate that many gazillions of combinations. Never ever will we
see
> > > > equal frequencies of combinations!
> > > > But what's wrong with a combination like '1-2-3-4-5-6'? Why
shouldn't
> > > > it come out even more frequently than combinations considered to be
> > > > "more random"? For example, 3,17,28,29,34,47 is considered by many
> > > > 'more likely to be drawn' because appears to be 'more random'. I
think
> > > > 'more random' has come to life as a result of statistical analysis
of
> > > > lottery draws.

> > > > It can turn into a very complicated debate. I will make it as simple
> > > > as possible. The simplest way and the clearest method of proving or
> > > > disproving is 'data analysis'. They say 'a picture is worth a
thousand
> > > > words'. Also, 'real data is worth millions of words'. I will add to
> > > > analysis 6 more numbers. That way, we can analyze real draws that
> > > > occurred in our lifetime. Many lotto players also play combinations
> > > > like 7,8,9,10,11,12. I saw with my own eyes a Jamaican player (farm
> > > > worker in the US) always starting his play card this way:
> > > > 1,2,3,4,5,6
> > > > 7,8,9,10,11,12
> > > > I will do the analysis for 12 numbers: 1,2,3,4,5,6,7,8,9,10,11,12.
The
> > > > combination '1,2,3,4,5,6' is in there.
> > > > I will use a 642-draw data file in UK lotto 6/49 game. Look at the
> > > > combination '1,2,3,4,5,6'. The clearest way to look at it is
'position
> > > > by position'. It strikes me that the number '6' in the 6th position
is
> > > > way too low. I compare it with all the data in the UK-6 draw file. I
> > > > can do some sophisticated analysis using a tool such as Microsoft
> > > > Excel. Open the data file as 'Text only'. The spreadsheet
application
> > > > is intelligent enough to open it in the correct format (642 rows by
6
> > > > columns). Select column A. Select 'Data analysis' in the 'Tools'
menu
> > > > (an add-in), then 'Descriptive statistics' for the range A1:A642.
The
> > > > minimum value in the 1st position of UK-6 is 1; the maximum value is
> > > > 30; the median is 6, the mode (the most frequent number) is 1. For
> > > > column F (the 6th position), the results are:
> > > > - minimum value = 19
> > > > - maximum value = 49
> > > > - median = 45
> > > > - mode (the most frequent number) = 45.
> > > > A number such as '6' in the 6th position appears to be way out of
> > > > range. So, what?, some may ask legitimately. Let's do an analysis, I
> > > > would answer. I would generate all 924 combinations for the numbers
1
> > > > through 12. Then I will generate combinations for the 3 most
frequent
> > > > numbers in UK-6 position by position.
> > > > I created a file with the most frequent numbers by position. The
most
> > > > frequent numbers are situated around the median of the respective
> > > > position. The exception is position 1, where the first number is the
> > > > most frequent. The median can be calculated by the Fundamental
Formula
> > > > of Gambling (FFG). Or, we can use the Excel median values for each
> > > > column. The UK-6 draws history generated the following positional
> > > > ranges:

> > > > 1 2 3
> > > > 13 14 15
> > > > 22 23 24
> > > > 29 31 32
> > > > 37 38 39
> > > > 45 48 49

> > > > The 6 positional ranges generate, in this case, 729 combinations,
from
> > > > '1 13 22 29 37 45' to '3 15 24 32 39 49'. This is an easier
situation,
> > > > so the combinations can be generated manually. I use software to
> > > > generate combinations based on positional ranges; thus, no errors
are
> > > > possible.
> > > > Notice that the result files: WHEEL12.66 and POSIT6.3 are not equal
in
> > > > size. The numbers 1 through 12 generated 924 combinations. The
> > > > positional ranges file generated 729 combinations. We might expect
> > > > that the 1-12 file would hit 924/729 = 1.27 times more winners.
> > > > I used my freeware WINNERS.EXE to check for 3, 4, 5, 6 winners
against
> > > > the UK draws file UK-6 (642 draws). The reports follow:

Hi

On 04/10/1999 on German Lotto the numbers 2,3,4,5,6, 26 have been
drawn (not in this order). It is a 6 from 49 System. Of course the
stakes where quite low :)

Christoph