Combination '1,2,3,4,5,6': Probability and Reality
Ion Saliu
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:
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 most the same.
May Its Almighty grant us in our testy day the righteous proportion of
being at most unlikely the same and at least likely different. For our
strength is in our inequities."
Copyright © 2002 Ion Saliu. All rights reserved worldwide.
Of interest: Winning lottery strategies:
http://www.saliu.com/LottoWin.htm
Of interest: Fundamental Formula of Gambling (FFG):
http://www.saliu.com/Saliu2.htm
Of interest: Mathematical Foundation of Fundamental Formula of
Gambling (FFG): http://www.saliu.com/formula.htm
Of interest: Free Lottery Software Excel Spreadsheets Strategies:
http://www.saliu.com/Newsgroups.htm
Of interest: The essentials of filters in lottery software:
http://www.saliu.com/bbs/messages/42.html
Of interest: Pick-3 lottery strategy:
http://www.saliu.com/bbs/messages/928.html
Of interest: "My kingdom for a good tutorial!":
http://www.saliu.com/bbs/messages/818.html
Of interest: ODDSCALC.EXE – Calculate the odds of lotto games:
http://www.saliu.com/bbs/messages/549.html
Of interest: Winning reports for the wonder grid: GridCheck632.EXE
(freeware!): http://www.saliu.com/bbs/messages/9.html
Duncan Smith
"Ion Saliu" <isa...@onebox.com> wrote in message
news:f2567897.0207...@posting.google.com...
> . Reposted from "The World Message Board" http://www.saliu.com/bbs/
[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
> disproving is 'data analysis'.
Unfortnately not Ion. Statistical analysis is not about 'proof', it's about
evaluating evidence.
[snip]
> 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'.
No it isn't. How about ball frequencies (regardless of 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.
And it never came up in the sixth position.? Wow!
I
> can do some sophisticated analysis using a tool such as Microsoft
> Excel.
Hahahahahahaha. That is so wrong on several levels.
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.
Oh dear.
[snip]
Duncan
Nigel Hurneyman
>
> • Reposted from "The World Message Board" http://www.saliu.com/bbs/
>
> 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.
>
There's a very important third. On average, 10,000 people pick
1,2,3,4,5,6 for every UK Lotto draw, so if that combination did come up
the jackpot would be pathetic.
> 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'.
I'm repeating a previous posting here, but my in correlation analysis of
every ball vis a vis every other ball in the UK Lotto, 50% of the
highest ranked correlations were between numbers with a difference of 8,
ie where one ball starts on top of the other. The corollary to this is
that you are reducing your chances slightly by choosing 1,2,3,4,5,6 in
the UK Lottery because none of the ball numbers differ by 8. Of course,
now I've published this fact, if anyone notifies Camelot they may reduce
the amount of waffle in the program and let the balls churn round for
longer. (As an aside, much as I hated Anthea Turner, at least she could
read an autocue and smile convincingly, unlike poor petrified Gigi.)
<snip>
Evil Nigel
mark macmillan
Duncan Smith
"mark macmillan " <employment-...@sympatico.ca> wrote in message
news:QxY99.26891$_75.2...@news20.bellglobal.com...
> hi
Yes, Ion posted some gibberish. So?
Duncan
Terry Szczur
Every one in here, if your going to listen to anybody in here, and
the person isn't Szur-Can, Ion is the person who is willing and can
actually help you understand the lottery better.
Odds are 1 in 13,983,816 But by using past draws as a form of
checking to see how the lottery hits. Instead of building a system
based on repeated nubers... play the repeated patterns. The numbers
change from hot to cold and hot again but we don't know when the time,
the switch is. Kind of like trying to play the stock market. Buy now
or wait a bit longer is it due or not?
If you analyze the past patterns you see that the patterns remain
constant...But the numbers with in the patterns will change. We can
play the patterns that seem to keep repeating and leave out the ones
that don't ever win...in ours or any 6/49 in the world. Why play the 6
consecutive rule
1,2,3,4,5,6, -> -> up to -> 44,45,46,47,48,49 By 1
1,3,5,7,9,11, -> -> up to -> 39,41,43,45,47,49 By 2
1,4,7,10,13,16 -> -> up to -> 34,37,40,43,46,49 By 3
Continue with this till you have taken it to X4 ,X5 ,X6 and so on.
You can say the same thing over and over again "each combo has the
same odds" all you want blah blah blah...I beleive in what my Eyes
show me, Reality,What really happens! Check it out for yourself in
your lottery and see if you remove that pattern, would you have ever
lost a Jackpot? Check in any lottery and see if you would have missed
one. Not just the 6/49 lottery's but check any lottery like 6/45 6/39
6/42 6/51 6/54 and so on. We have found that by removing those
patterns that are least likely to be drawn, and consentrating on what
seems to be most likely to be drawn , we have found our best return on
investment for playing a 6/49 lottery is by playing around 315,000
sequences of the most likely patterns to be drawn. WWW.SZUR-CAN.COM
hifi55
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.
isa...@onebox.com (Ion Saliu) wrote in message news:<f2567897.0207...@posting.google.com>...
hifi
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 news:<6fa1e6bc.02082...@posting.google.com>...
Ion Saliu
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…
Ion Saliu
hifi5...@yahoo.com (hifi) wrote in message news:<b53070b6.02083...@posting.google.com>...
Terry
> 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':
> leading to:
> {Sqr(5) ą 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
>
I'll have a pint of whatever it is you've been drinking :O)
Terry
> > > > . Reposted from "The World Message Board" http://www.saliu.com/bbs/
> > > > Copyright Š 2002 Ion Saliu. All rights reserved worldwide.
> > > >
> > > >
> > > > Of interest: Winning lottery strategies:
> > > > http://www.saliu.com/LottoWin.htm
> > > >
> > > > Of interest: Fundamental Formula of Gambling (FFG):
> > > > http://www.saliu.com/Saliu2.htm
> > > >
> > > > Of interest: Mathematical Foundation of Fundamental Formula of
> > > > Gambling (FFG): http://www.saliu.com/formula.htm
> > > >
> > > > Of interest: Free Lottery Software Excel Spreadsheets Strategies:
> > > > http://www.saliu.com/Newsgroups.htm
> > > >
> > > > Of interest: The essentials of filters in lottery software:
> > > > http://www.saliu.com/bbs/messages/42.html
> > > >
> > > > Of interest: Pick-3 lottery strategy:
> > > > http://www.saliu.com/bbs/messages/928.html
> > > >
> > > > Of interest: "My kingdom for a good tutorial!":
> > > > http://www.saliu.com/bbs/messages/818.html
> > > >
> > > > Of interest: ODDSCALC.EXE - Calculate the odds of lotto games:
Christoph Hager
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