| View previous topic :: View next topic |
| Author |
Message |
IXL Software
Guest
|
 Posted: Wed Apr 20, 2005 3:01 pm Post subject: A Tale Of Two Triples |
 |
|
It was a dark and stormy night. It was the best of times....No....make that
the worst of times. Jesus wept...but tomorrow is another day.
Damn it's tough to get started on that Nobel Prize for Literature. Maybe I
have a better shot at the Nobel Prize for Lottology since my nearest rival
is presently languishing somewhere in the constellation of Taurus...just
under the anus at last report. Here's the next chapter:
In a 649 lottery, the most common minimum prize is awarded to the player
that has matched at least 3 of the 6 main numbers drawn. There are 18,424
possible ways to combine any 3 from 49 numbers to form what I refer to as
"triples". If a player were to employ any one of those triples as 3 banker
or key numbers, this would result in 15,180 lines of 6 numbers that include
all of the remaining 46 numbers. No numbers have been excluded from play and
no filters such as Odd/Even or Sums have been applied. Here are 2 possible
triples:
5-17-31
3-10-25
Is there any reason to believe that one is more likely than the other to
appear in any draw? Of course not! We all know by now that the draw is
totally random and they both have an absolutely equal chance. Over a series
of N trials, they should be drawn an approximately equal number of times.
That's the theory at least. Let's compare that to some real-world results.
As of today, the Canadian 649 lottery has conducted 2,216 draws since June
12, 1982... a period of almost 23 years. In a perfect world that strictly
obeys statistical averages, each possible triple should have appeared
18,424/2216 = 8.3 times...no less than 8...no more than 9. An analysis of
the results so far reveals that 1,709 of the 18,424 possible triples have
yet to make even *1* appearance. In contrast to that, there is one
particular triple that has appeared more than any other with 11 such hits.
So much for that perfect world.
It's impossible to distinguish one from the other by simply looking at them,
so I'll just have to tell you. The three numbers 3-10-25 have *never*
appeared together in any draw, while the 3 numbers 5-17-31 have been drawn
together 11 times so far.
Anybody remember Sherman & Peabody from the Rocky & Bullwinkle show? Let's
jump in the wayback machine and travel back to the morning of June 12,
1982...somewhere in the Great White North. As an experiment, they each
choose any 3 numbers that they will always include in their picks for each
and every draw of the brand new Canadian Lotto 649. As it happens, Sherman
chooses 3-10-25 and Peabody chooses 5-17-31. To this day, no one knows why
(;-)
Fast forward to April of 2005. Many things have changed in a world that is
barely recognizable. In a secret laboratory somewhere near Toronto, Paul
McCoy, once destined to become the first gazillionaire to successfully
market bottled tap-water to the masses, has instead become a notorious evil
genius that against insurmountable obstacles, has managed to program his
computer to rapidly produce answers to questions that no one has asked. This
is largely due to too much time spent listening to the Bonzo Dog Doo-Dah
Band and relentlessly viewing reruns of Monty Python's Flying Circus and the
series of "Carry On" films. (Have to wonder why the bloody limeys around
here are such a grim lot.)
Examine the following data and search for useful clues. As a neutral control
for comparison purposes, I first generated 15,180 totally random lines. All
49 numbers are in use and no filtering of any kind was used. The same lines
were checked against the entire draw history.
Lottery: CA 649
Wheel File: 15180random.txt
Testing 15,180 lines against 2216 draws
***MATCH-6*** for Draw 135 1/5/1985 At Line 3068
Match 0 - 14,670,047 Expected is 14,665,370.000
Match 1 - 13,889,214 Expected is 13,893,510.000
Match 2 - 4,452,320 Expected is 4,453,049.000
Match 3 - 594,076 Expected is 593,739.800 Score is 33,657,930.000
Match 4 - 32,573 Expected is 32,583.280 Score is 33,628,260.000
Match 5 - 635 Expected is 606.201 Score is 35,237,000.000
Match 5+ - 14 Expected is 14.433 Score is 32,628,900.000
Match 6 - 1 Expected is 2.406 Score is 13,983,820
Total Plays - 33,638,880
Total Losses - 33,011,581
Total Wins - 627,299
Expected Total Score Is 168,194,400.000
Actual Total Score Is 149,135,900.000
This Wheel Scored 88.669% Of Random Expectation
Total Draws With At Least 1 Match3 - 2,216
Here's what happened with Sherman's picks:
==========================================
Lottery: CA 649
Wheel File: 3-10-25.txt
Testing 15,180 lines against 2216 draws
Match-5 + Bonus for Draw 1269 3/20/1996 At Line 3985
Match-5 + Bonus for Draw 1269 3/20/1996 At Line 3990
Match-5 + Bonus for Draw 1269 3/20/1996 At Line 4497
Match-5 + Bonus for Draw 1269 3/20/1996 At Line 9701
Match 0 - 14,820,000 Expected is 14,665,370.000
Match 1 - 14,002,300 Expected is 13,893,510.000
Match 2 - 4,285,780 Expected is 4,453,049.000
Match 3 - 508,634 Expected is 593,739.800 Score is 28,817,130.000
Match 4 - 21,922 Expected is 32,583.280 Score is 22,632,200.000
Match 5 - 240 Expected is 606.201 Score is 13,317,920.000
Match 5+ - 4 Expected is 14.433 Score is 9,322,544.000
Match 6 - 0 Expected is 2.406 Score is 0
Total Plays - 33,638,880
Total Losses - 33,108,080
Total Wins - 530,800
Expected Total Score Is 168,194,400.000
Actual Total Score Is 74,089,800.000
This Wheel Scored 44.050% Of Random Expectation
Total Draws With At Least 1 Match3 - 2,216
Here's what happened with Peabody's picks:
=======================================
Lottery: CA 649
Wheel File: 5-17-31.txt
Testing 15,180 lines against 2216 draws
***MATCH-6*** for Draw 229 4/2/1986 At Line 7046
***MATCH-6*** for Draw 247 6/4/1986 At Line 1945
***MATCH-6*** for Draw 568 7/1/1989 At Line 2312
***MATCH-6*** for Draw 676 7/14/1990 At Line 13729
***MATCH-6*** for Draw 840 2/8/1992 At Line 10239
***MATCH-6*** for Draw 982 6/19/1993 At Line 14636
***MATCH-6*** for Draw 1065 4/6/1994 At Line 11674
***MATCH-6*** for Draw 1822 7/7/2001 At Line 14088
***MATCH-6*** for Draw 1950 9/28/2002 At Line 10626
***MATCH-6*** for Draw 2080 12/27/2003 At Line 6673
***MATCH-6*** for Draw 2094 2/14/2004 At Line 390
Match 0 - 14,345,760 Expected is 14,665,370.000
Match 1 - 14,044,160 Expected is 13,893,510.000
Match 2 - 4,497,240 Expected is 4,453,049.000
Match 3 - 695,003 Expected is 593,739.800 Score is 39,376,040.000
Match 4 - 54,995 Expected is 32,583.280 Score is 56,776,660.000
Match 5 - 1,678 Expected is 606.201 Score is 93,114,460.000
Match 5+ - 33 Expected is 14.433 Score is 76,910,990.000
Match 6 - 11 Expected is 2.406 Score is 153,822,000
Total Plays - 33,638,880
Total Losses - 32,887,160
Total Wins - 751,720
Expected Total Score Is 168,194,400.000
Actual Total Score Is 420,000,100.000
This Wheel Scored 249.711% Of Random Expectation
Total Draws With At Least 1 Match3 - 2,216
Can anything useful be deduced from this? Probably nothing truly amazing.
I'll leave that to the reader to decide. Remember...don't argue with
me...argue with the data. I have simply provided that data.
For something really amazing, have a look at this:
http://travelcanada.sympatico.msn.ca/Home/ContentPosting.aspx?contentid=6ee08f6b016e43fba11ddfc33834e644&show=True&number=5&showbyline=False&subtitle=&detect=&abc=abc
I wonder if the main ingredient is still lard. |
|
| Back to top |
|
 |
erce
Guest
|
| Posted: Wed Apr 20, 2005 4:03 pm Post subject: Re: A Tale Of Two Triples |
|
|
IXL Software wrote:
| Quote: | In a 649 lottery, the most common minimum prize is awarded to the
player
that has matched at least 3 of the 6 main numbers drawn. There are
18,424
possible ways to combine any 3 from 49 numbers to form what I refer
to as
"triples". If a player were to employ any one of those triples as 3
banker
or key numbers, this would result in 15,180 lines of 6 numbers that
include
all of the remaining 46 numbers. No numbers have been excluded from
play and
no filters such as Odd/Even or Sums have been applied. Here are 2
possible
triples:
5-17-31
3-10-25
Is there any reason to believe that one is more likely than the other
to
appear in any draw? Of course not!
|
if you believe that why are you here
| Quote: | We all know by now that the draw is
totally random and they both have an absolutely equal chance. Over a
series
of N trials, they should be drawn an approximately equal number of
times.
That's the theory at least. Let's compare that to some real-world
results.
As of today, the Canadian 649 lottery has conducted 2,216 draws since
June
12, 1982... a period of almost 23 years. In a perfect world that
strictly
obeys statistical averages, each possible triple should have appeared
18,424/2216 = 8.3 times...no less than 8...no more than 9.
|
there went any chance of a nobel prize in lottology - care to put
standard
deviations round that 8.3
| Quote: | An analysis of
the results so far reveals that 1,709 of the 18,424 possible triples
have
yet to make even *1* appearance. In contrast to that, there is one
particular triple that has appeared more than any other with 11 such
hits.
So much for that perfect world.
It's impossible to distinguish one from the other by simply looking
at them,
so I'll just have to tell you. The three numbers 3-10-25 have *never*
appeared together in any draw, while the 3 numbers 5-17-31 have been
drawn
together 11 times so far.
|
does that surprise you
erce |
|
| Back to top |
|
|
IXL Software
Guest
|
| Posted: Wed Apr 20, 2005 5:03 pm Post subject: Re: A Tale Of Two Triples |
|
|
"erce" <[email protected]> wrote in message
news:[email protected]...
| Quote: | IXL Software wrote:
In a 649 lottery, the most common minimum prize is awarded to the
player
that has matched at least 3 of the 6 main numbers drawn. There are
18,424
possible ways to combine any 3 from 49 numbers to form what I refer
to as
"triples". If a player were to employ any one of those triples as 3
banker
or key numbers, this would result in 15,180 lines of 6 numbers that
include
all of the remaining 46 numbers. No numbers have been excluded from
play and
no filters such as Odd/Even or Sums have been applied. Here are 2
possible
triples:
5-17-31
3-10-25
Is there any reason to believe that one is more likely than the other
to
appear in any draw? Of course not!
if you believe that why are you here
|
I'm here because I enjoy reading dumbass comments from snipers like you. Why
are *you* here? Certainly not to impress anyone with your knowledge or
entertain anyone with your charming wit.
Lighten up a little Eric. Reading your posts is like living through a scene
in an Ingmar Bergman psycho-drama.
| Quote: | We all know by now that the draw is
totally random and they both have an absolutely equal chance. Over a
series
of N trials, they should be drawn an approximately equal number of
times.
That's the theory at least. Let's compare that to some real-world
results.
As of today, the Canadian 649 lottery has conducted 2,216 draws since
June
12, 1982... a period of almost 23 years. In a perfect world that
strictly
obeys statistical averages, each possible triple should have appeared
18,424/2216 = 8.3 times...no less than 8...no more than 9.
there went any chance of a nobel prize in lottology - care to put
standard
deviations round that 8.3
|
You seem to know everything there is to know. Why don't you do that? Teach
us.
Like that old bumpersticker said, "Ass, gas or grass...nobody rides for
free."
| Quote: | An analysis of
the results so far reveals that 1,709 of the 18,424 possible triples
have
yet to make even *1* appearance. In contrast to that, there is one
particular triple that has appeared more than any other with 11 such
hits.
So much for that perfect world.
It's impossible to distinguish one from the other by simply looking
at them,
so I'll just have to tell you. The three numbers 3-10-25 have *never*
appeared together in any draw, while the 3 numbers 5-17-31 have been
drawn
together 11 times so far.
does that surprise you
|
No more than the fact that insects can fly or birds can sing.
As I clearly indicated, I merely provided the data.
|
|
| Back to top |
|
|
erce
Guest
|
| Posted: Wed Apr 20, 2005 9:03 pm Post subject: Re: A Tale Of Two Triples |
|
|
IXL Software wrote:
| Quote: | "erce" <[email protected]> wrote in message
news:[email protected]...
IXL Software wrote:
In a 649 lottery, the most common minimum prize is awarded to the
player
that has matched at least 3 of the 6 main numbers drawn. There are
18,424
possible ways to combine any 3 from 49 numbers to form what I
refer
to as
"triples". If a player were to employ any one of those triples as
3
banker
or key numbers, this would result in 15,180 lines of 6 numbers
that
include
all of the remaining 46 numbers. No numbers have been excluded
from
play and
no filters such as Odd/Even or Sums have been applied. Here are 2
possible
triples:
5-17-31
3-10-25
Is there any reason to believe that one is more likely than the
other
to
appear in any draw? Of course not!
if you believe that why are you here
I'm here because I enjoy reading dumbass comments from snipers like
you. Why
are *you* here? Certainly not to impress anyone with your knowledge
or
entertain anyone with your charming wit.
Lighten up a little Eric. Reading your posts is like living through a
scene
in an Ingmar Bergman psycho-drama.
We all know by now that the draw is
totally random and they both have an absolutely equal chance. Over
a
series
of N trials, they should be drawn an approximately equal number
of
times.
That's the theory at least. Let's compare that to some real-world
results.
As of today, the Canadian 649 lottery has conducted 2,216 draws
since
June
12, 1982... a period of almost 23 years. In a perfect world that
strictly
obeys statistical averages, each possible triple should have
appeared
18,424/2216 = 8.3 times...no less than 8...no more than 9.
there went any chance of a nobel prize in lottology - care to put
standard
deviations round that 8.3
You seem to know everything there is to know. Why don't you do that?
Teach
us.
Like that old bumpersticker said, "Ass, gas or grass...nobody rides
for
free."
An analysis of
the results so far reveals that 1,709 of the 18,424 possible
triples
have
yet to make even *1* appearance. In contrast to that, there is one
particular triple that has appeared more than any other with 11
such
hits.
So much for that perfect world.
It's impossible to distinguish one from the other by simply
looking
at them,
so I'll just have to tell you. The three numbers 3-10-25 have
*never*
appeared together in any draw, while the 3 numbers 5-17-31 have
been
drawn
together 11 times so far.
does that surprise you
No more than the fact that insects can fly or birds can sing.
As I clearly indicated, I merely provided the data.
erce
|
18424 triples
20 drawn every draw
18424 * (18404/18424) ^ 2216 not drawn in 2216 draws - approx 1660
thats an underestimate because the 20 triples drawn every draw are not
independent
erce |
|
| Back to top |
|
|
gARY
Guest
|
| Posted: Wed Apr 20, 2005 10:01 pm Post subject: Re: A Tale Of Two Triples |
|
|
erce, why do I like you?
Perhaps it is because I like your idea that "the 20 triples drawn every draw are not independent"!
Past "history triples" (here/rgl) is ONLY promoted by me! And I have NO clue as to why (bias maybe) . However . .
Looking back on my records Paul has had the password for RedCar since - early 06/2003
Paul is on a run? Yeah right!!!
Paul (and Gerry, as it goes) will also jump around any valid comment on his/her ramblings until you subside OR STFU.
Bottom line really!
Good luck,
gARY
"erce" <[email protected]> wrote in message news:[email protected]...
| Quote: | IXL Software wrote:
"erce" <[email protected]> wrote in message
news:[email protected]...
IXL Software wrote:
In a 649 lottery, the most common minimum prize is awarded to the
player
that has matched at least 3 of the 6 main numbers drawn. There are
18,424
possible ways to combine any 3 from 49 numbers to form what I
refer
to as
"triples". If a player were to employ any one of those triples as
3
banker
or key numbers, this would result in 15,180 lines of 6 numbers
that
include
all of the remaining 46 numbers. No numbers have been excluded
from
play and
no filters such as Odd/Even or Sums have been applied. Here are 2
possible
triples:
5-17-31
3-10-25
Is there any reason to believe that one is more likely than the
other
to
appear in any draw? Of course not!
if you believe that why are you here
I'm here because I enjoy reading dumbass comments from snipers like
you. Why
are *you* here? Certainly not to impress anyone with your knowledge
or
entertain anyone with your charming wit.
Lighten up a little Eric. Reading your posts is like living through a
scene
in an Ingmar Bergman psycho-drama.
We all know by now that the draw is
totally random and they both have an absolutely equal chance. Over
a
series
of N trials, they should be drawn an approximately equal number
of
times.
That's the theory at least. Let's compare that to some real-world
results.
As of today, the Canadian 649 lottery has conducted 2,216 draws
since
June
12, 1982... a period of almost 23 years. In a perfect world that
strictly
obeys statistical averages, each possible triple should have
appeared
18,424/2216 = 8.3 times...no less than 8...no more than 9.
there went any chance of a nobel prize in lottology - care to put
standard
deviations round that 8.3
You seem to know everything there is to know. Why don't you do that?
Teach
us.
Like that old bumpersticker said, "Ass, gas or grass...nobody rides
for
free."
An analysis of
the results so far reveals that 1,709 of the 18,424 possible
triples
have
yet to make even *1* appearance. In contrast to that, there is one
particular triple that has appeared more than any other with 11
such
hits.
So much for that perfect world.
It's impossible to distinguish one from the other by simply
looking
at them,
so I'll just have to tell you. The three numbers 3-10-25 have
*never*
appeared together in any draw, while the 3 numbers 5-17-31 have
been
drawn
together 11 times so far.
does that surprise you
No more than the fact that insects can fly or birds can sing.
As I clearly indicated, I merely provided the data.
erce
18424 triples
20 drawn every draw
18424 * (18404/18424) ^ 2216 not drawn in 2216 draws - approx 1660
thats an underestimate because the 20 triples drawn every draw are not
independent
erce
|
|
|
| Back to top |
|
|
Robert Perkis
Guest
|
| Posted: Thu Apr 21, 2005 6:01 am Post subject: Re: A Tale Of Two Triples |
|
|
IXL Software wrote:
| Quote: |
It was a dark and stormy night. It was the best of times....No....make that
the worst of times. Jesus wept...but tomorrow is another day.
Damn it's tough to get started on that Nobel Prize for Literature. Maybe I
have a better shot at the Nobel Prize for Lottology since my nearest rival
is presently languishing somewhere in the constellation of Taurus...just
under the anus at last report. Here's the next chapter:
In a 649 lottery, the most common minimum prize is awarded to the player
that has matched at least 3 of the 6 main numbers drawn. There are 18,424
possible ways to combine any 3 from 49 numbers to form what I refer to as
"triples". If a player were to employ any one of those triples as 3 banker
or key numbers, this would result in 15,180 lines of 6 numbers that include
all of the remaining 46 numbers. No numbers have been excluded from play and
no filters such as Odd/Even or Sums have been applied. Here are 2 possible
triples:
5-17-31
3-10-25
Is there any reason to believe that one is more likely than the other to
appear in any draw? Of course not! We all know by now that the draw is
totally random and they both have an absolutely equal chance. Over a series
of N trials, they should be drawn an approximately equal number of times.
That's the theory at least. Let's compare that to some real-world results.
As of today, the Canadian 649 lottery has conducted 2,216 draws since June
12, 1982... a period of almost 23 years. In a perfect world that strictly
obeys statistical averages, each possible triple should have appeared
18,424/2216 = 8.3 times...no less than 8...no more than 9. An analysis of
the results so far reveals that 1,709 of the 18,424 possible triples have
yet to make even *1* appearance. In contrast to that, there is one
particular triple that has appeared more than any other with 11 such hits.
So much for that perfect world.
It's impossible to distinguish one from the other by simply looking at them,
so I'll just have to tell you. The three numbers 3-10-25 have *never*
appeared together in any draw, while the 3 numbers 5-17-31 have been drawn
together 11 times so far.
Anybody remember Sherman & Peabody from the Rocky & Bullwinkle show? Let's
jump in the wayback machine and travel back to the morning of June 12,
1982...somewhere in the Great White North. As an experiment, they each
choose any 3 numbers that they will always include in their picks for each
and every draw of the brand new Canadian Lotto 649. As it happens, Sherman
chooses 3-10-25 and Peabody chooses 5-17-31. To this day, no one knows why
(;-)
Fast forward to April of 2005. Many things have changed in a world that is
barely recognizable. In a secret laboratory somewhere near Toronto, Paul
McCoy, once destined to become the first gazillionaire to successfully
market bottled tap-water to the masses, has instead become a notorious evil
genius that against insurmountable obstacles, has managed to program his
computer to rapidly produce answers to questions that no one has asked. This
is largely due to too much time spent listening to the Bonzo Dog Doo-Dah
Band and relentlessly viewing reruns of Monty Python's Flying Circus and the
series of "Carry On" films. (Have to wonder why the bloody limeys around
here are such a grim lot.)
Examine the following data and search for useful clues. As a neutral control
for comparison purposes, I first generated 15,180 totally random lines. All
49 numbers are in use and no filtering of any kind was used. The same lines
were checked against the entire draw history.
Lottery: CA 649
Wheel File: 15180random.txt
Testing 15,180 lines against 2216 draws
***MATCH-6*** for Draw 135 1/5/1985 At Line 3068
Match 0 - 14,670,047 Expected is 14,665,370.000
Match 1 - 13,889,214 Expected is 13,893,510.000
Match 2 - 4,452,320 Expected is 4,453,049.000
Match 3 - 594,076 Expected is 593,739.800 Score is 33,657,930.000
Match 4 - 32,573 Expected is 32,583.280 Score is 33,628,260.000
Match 5 - 635 Expected is 606.201 Score is 35,237,000.000
Match 5+ - 14 Expected is 14.433 Score is 32,628,900.000
Match 6 - 1 Expected is 2.406 Score is 13,983,820
Total Plays - 33,638,880
Total Losses - 33,011,581
Total Wins - 627,299
Expected Total Score Is 168,194,400.000
Actual Total Score Is 149,135,900.000
This Wheel Scored 88.669% Of Random Expectation
Total Draws With At Least 1 Match3 - 2,216
Here's what happened with Sherman's picks:
==========================================
Lottery: CA 649
Wheel File: 3-10-25.txt
Testing 15,180 lines against 2216 draws
Match-5 + Bonus for Draw 1269 3/20/1996 At Line 3985
Match-5 + Bonus for Draw 1269 3/20/1996 At Line 3990
Match-5 + Bonus for Draw 1269 3/20/1996 At Line 4497
Match-5 + Bonus for Draw 1269 3/20/1996 At Line 9701
Match 0 - 14,820,000 Expected is 14,665,370.000
Match 1 - 14,002,300 Expected is 13,893,510.000
Match 2 - 4,285,780 Expected is 4,453,049.000
Match 3 - 508,634 Expected is 593,739.800 Score is 28,817,130.000
Match 4 - 21,922 Expected is 32,583.280 Score is 22,632,200.000
Match 5 - 240 Expected is 606.201 Score is 13,317,920.000
Match 5+ - 4 Expected is 14.433 Score is 9,322,544.000
Match 6 - 0 Expected is 2.406 Score is 0
Total Plays - 33,638,880
Total Losses - 33,108,080
Total Wins - 530,800
Expected Total Score Is 168,194,400.000
Actual Total Score Is 74,089,800.000
This Wheel Scored 44.050% Of Random Expectation
Total Draws With At Least 1 Match3 - 2,216
Here's what happened with Peabody's picks:
=======================================
Lottery: CA 649
Wheel File: 5-17-31.txt
Testing 15,180 lines against 2216 draws
***MATCH-6*** for Draw 229 4/2/1986 At Line 7046
***MATCH-6*** for Draw 247 6/4/1986 At Line 1945
***MATCH-6*** for Draw 568 7/1/1989 At Line 2312
***MATCH-6*** for Draw 676 7/14/1990 At Line 13729
***MATCH-6*** for Draw 840 2/8/1992 At Line 10239
***MATCH-6*** for Draw 982 6/19/1993 At Line 14636
***MATCH-6*** for Draw 1065 4/6/1994 At Line 11674
***MATCH-6*** for Draw 1822 7/7/2001 At Line 14088
***MATCH-6*** for Draw 1950 9/28/2002 At Line 10626
***MATCH-6*** for Draw 2080 12/27/2003 At Line 6673
***MATCH-6*** for Draw 2094 2/14/2004 At Line 390
Match 0 - 14,345,760 Expected is 14,665,370.000
Match 1 - 14,044,160 Expected is 13,893,510.000
Match 2 - 4,497,240 Expected is 4,453,049.000
Match 3 - 695,003 Expected is 593,739.800 Score is 39,376,040.000
Match 4 - 54,995 Expected is 32,583.280 Score is 56,776,660.000
Match 5 - 1,678 Expected is 606.201 Score is 93,114,460.000
Match 5+ - 33 Expected is 14.433 Score is 76,910,990.000
Match 6 - 11 Expected is 2.406 Score is 153,822,000
Total Plays - 33,638,880
Total Losses - 32,887,160
Total Wins - 751,720
Expected Total Score Is 168,194,400.000
Actual Total Score Is 420,000,100.000
This Wheel Scored 249.711% Of Random Expectation
Total Draws With At Least 1 Match3 - 2,216
Can anything useful be deduced from this? Probably nothing truly amazing.
I'll leave that to the reader to decide. Remember...don't argue with
me...argue with the data. I have simply provided that data.
|
I'm surprised you can take the knights that say nik nik nik . . .
As for the lottery. If the triple hits are nicely spaced
within the current ballset and does well in it's pairs,
why not start playing it with in a minimum number of lines
with all the other numbers in properly balanced lines. The
worst possible result would be three 4# wins when it comes
in. The top ten triples played this way might be an
interesting pool play. One could also wait out most of
the previous gap between hits before playing.
Robert Perkis / http://www.lotto-logix.com |
|
| Back to top |
|
|
erce
Guest
|
| Posted: Thu Apr 21, 2005 12:01 pm Post subject: Re: A Tale Of Two Triples |
|
|
gARY wrote:
| Quote: | erce, why do I like you?
Perhaps it is because I like your idea that "the 20 triples drawn
every draw are not independent"!
Past "history triples" (here/rgl) is ONLY promoted by me! And I have
NO clue as to why (bias maybe) . However . .
Looking back on my records Paul has had the password for RedCar since
- early 06/2003
Paul is on a run? Yeah right!!!
Paul (and Gerry, as it goes) will also jump around any valid comment
on his/her ramblings until you subside OR STFU.
Bottom line really!
Good luck,
gARY
|
i made the same mistake as 'i excel' and made an assumption about
something i dont know about
if the most drawn triplet were 7 14 21 then the other triplets
involving 7 and 14 would also outperform on average so the distribution
would be lumpier than a standard binomial
one of the lumps would be of triplets never drawn
given an infinitely long time the distribution should approach the
binomial and the lumpiness disappear
would any math-heads care to comment
erce |
|
| Back to top |
|
|
Gerry
Guest
|
| Posted: Thu Apr 21, 2005 1:01 pm Post subject: Re: A Tale Of Two Triples |
|
|
"erce" <[email protected]> wrote in message
news:[email protected]...
| Quote: | gARY wrote:
erce, why do I like you?
Perhaps it is because I like your idea that "the 20 triples drawn
every draw are not independent"!
Past "history triples" (here/rgl) is ONLY promoted by me! And I have
NO clue as to why (bias maybe) . However . .
Looking back on my records Paul has had the password for RedCar since
- early 06/2003
Paul is on a run? Yeah right!!!
Paul (and Gerry, as it goes) will also jump around any valid comment
on his/her ramblings until you subside OR STFU.
Bottom line really!
Good luck,
gARY
i made the same mistake as 'i excel' and made an assumption about
something i dont know about
if the most drawn triplet were 7 14 21 then the other triplets
involving 7 and 14 would also outperform on average so the distribution
would be lumpier than a standard binomial
one of the lumps would be of triplets never drawn
given an infinitely long time the distribution should approach the
binomial and the lumpiness disappear
would any math-heads care to comment
erce
|
Lotto 101
I'm not a math head but just a propeller head. Some people here think
I'm a dick head. |
|
| Back to top |
|
|
Gerry
Guest
|
| Posted: Thu Apr 21, 2005 1:01 pm Post subject: Re: A Tale Of Two Triples |
|
|
"Robert Perkis" <[email protected]> wrote in message
news:[email protected]...
| Quote: |
IXL Software wrote:
It was a dark and stormy night. It was the best of times....No....make
that
the worst of times. Jesus wept...but tomorrow is another day.
Damn it's tough to get started on that Nobel Prize for Literature. Maybe
I
have a better shot at the Nobel Prize for Lottology since my nearest
rival
is presently languishing somewhere in the constellation of Taurus...just
under the anus at last report. Here's the next chapter:
In a 649 lottery, the most common minimum prize is awarded to the player
that has matched at least 3 of the 6 main numbers drawn. There are
18,424
possible ways to combine any 3 from 49 numbers to form what I refer to
as
"triples". If a player were to employ any one of those triples as 3
banker
or key numbers, this would result in 15,180 lines of 6 numbers that
include
all of the remaining 46 numbers. No numbers have been excluded from play
and
no filters such as Odd/Even or Sums have been applied. Here are 2
possible
triples:
5-17-31
3-10-25
Is there any reason to believe that one is more likely than the other to
appear in any draw? Of course not! We all know by now that the draw is
totally random and they both have an absolutely equal chance. Over a
series
of N trials, they should be drawn an approximately equal number of
times.
That's the theory at least. Let's compare that to some real-world
results.
As of today, the Canadian 649 lottery has conducted 2,216 draws since
June
12, 1982... a period of almost 23 years. In a perfect world that
strictly
obeys statistical averages, each possible triple should have appeared
18,424/2216 = 8.3 times...no less than 8...no more than 9. An analysis
of
the results so far reveals that 1,709 of the 18,424 possible triples
have
yet to make even *1* appearance. In contrast to that, there is one
particular triple that has appeared more than any other with 11 such
hits.
So much for that perfect world.
It's impossible to distinguish one from the other by simply looking at
them,
so I'll just have to tell you. The three numbers 3-10-25 have *never*
appeared together in any draw, while the 3 numbers 5-17-31 have been
drawn
together 11 times so far.
Anybody remember Sherman & Peabody from the Rocky & Bullwinkle show?
Let's
jump in the wayback machine and travel back to the morning of June 12,
1982...somewhere in the Great White North. As an experiment, they each
choose any 3 numbers that they will always include in their picks for
each
and every draw of the brand new Canadian Lotto 649. As it happens,
Sherman
chooses 3-10-25 and Peabody chooses 5-17-31. To this day, no one knows
why
(;-)
Fast forward to April of 2005. Many things have changed in a world that
is
barely recognizable. In a secret laboratory somewhere near Toronto, Paul
McCoy, once destined to become the first gazillionaire to successfully
market bottled tap-water to the masses, has instead become a notorious
evil
genius that against insurmountable obstacles, has managed to program his
computer to rapidly produce answers to questions that no one has asked.
This
is largely due to too much time spent listening to the Bonzo Dog Doo-Dah
Band and relentlessly viewing reruns of Monty Python's Flying Circus and
the
series of "Carry On" films. (Have to wonder why the bloody limeys around
here are such a grim lot.)
Examine the following data and search for useful clues. As a neutral
control
for comparison purposes, I first generated 15,180 totally random lines.
All
49 numbers are in use and no filtering of any kind was used. The same
lines
were checked against the entire draw history.
Lottery: CA 649
Wheel File: 15180random.txt
Testing 15,180 lines against 2216 draws
***MATCH-6*** for Draw 135 1/5/1985 At Line 3068
Match 0 - 14,670,047 Expected is 14,665,370.000
Match 1 - 13,889,214 Expected is 13,893,510.000
Match 2 - 4,452,320 Expected is 4,453,049.000
Match 3 - 594,076 Expected is 593,739.800 Score is 33,657,930.000
Match 4 - 32,573 Expected is 32,583.280 Score is 33,628,260.000
Match 5 - 635 Expected is 606.201 Score is 35,237,000.000
Match 5+ - 14 Expected is 14.433 Score is 32,628,900.000
Match 6 - 1 Expected is 2.406 Score is 13,983,820
Total Plays - 33,638,880
Total Losses - 33,011,581
Total Wins - 627,299
Expected Total Score Is 168,194,400.000
Actual Total Score Is 149,135,900.000
This Wheel Scored 88.669% Of Random Expectation
Total Draws With At Least 1 Match3 - 2,216
Here's what happened with Sherman's picks:
==========================================
Lottery: CA 649
Wheel File: 3-10-25.txt
Testing 15,180 lines against 2216 draws
Match-5 + Bonus for Draw 1269 3/20/1996 At Line 3985
Match-5 + Bonus for Draw 1269 3/20/1996 At Line 3990
Match-5 + Bonus for Draw 1269 3/20/1996 At Line 4497
Match-5 + Bonus for Draw 1269 3/20/1996 At Line 9701
Match 0 - 14,820,000 Expected is 14,665,370.000
Match 1 - 14,002,300 Expected is 13,893,510.000
Match 2 - 4,285,780 Expected is 4,453,049.000
Match 3 - 508,634 Expected is 593,739.800 Score is 28,817,130.000
Match 4 - 21,922 Expected is 32,583.280 Score is 22,632,200.000
Match 5 - 240 Expected is 606.201 Score is 13,317,920.000
Match 5+ - 4 Expected is 14.433 Score is 9,322,544.000
Match 6 - 0 Expected is 2.406 Score is 0
Total Plays - 33,638,880
Total Losses - 33,108,080
Total Wins - 530,800
Expected Total Score Is 168,194,400.000
Actual Total Score Is 74,089,800.000
This Wheel Scored 44.050% Of Random Expectation
Total Draws With At Least 1 Match3 - 2,216
Here's what happened with Peabody's picks:
=======================================
Lottery: CA 649
Wheel File: 5-17-31.txt
Testing 15,180 lines against 2216 draws
***MATCH-6*** for Draw 229 4/2/1986 At Line 7046
***MATCH-6*** for Draw 247 6/4/1986 At Line 1945
***MATCH-6*** for Draw 568 7/1/1989 At Line 2312
***MATCH-6*** for Draw 676 7/14/1990 At Line 13729
***MATCH-6*** for Draw 840 2/8/1992 At Line 10239
***MATCH-6*** for Draw 982 6/19/1993 At Line 14636
***MATCH-6*** for Draw 1065 4/6/1994 At Line 11674
***MATCH-6*** for Draw 1822 7/7/2001 At Line 14088
***MATCH-6*** for Draw 1950 9/28/2002 At Line 10626
***MATCH-6*** for Draw 2080 12/27/2003 At Line 6673
***MATCH-6*** for Draw 2094 2/14/2004 At Line 390
Match 0 - 14,345,760 Expected is 14,665,370.000
Match 1 - 14,044,160 Expected is 13,893,510.000
Match 2 - 4,497,240 Expected is 4,453,049.000
Match 3 - 695,003 Expected is 593,739.800 Score is 39,376,040.000
Match 4 - 54,995 Expected is 32,583.280 Score is 56,776,660.000
Match 5 - 1,678 Expected is 606.201 Score is 93,114,460.000
Match 5+ - 33 Expected is 14.433 Score is 76,910,990.000
Match 6 - 11 Expected is 2.406 Score is 153,822,000
Total Plays - 33,638,880
Total Losses - 32,887,160
Total Wins - 751,720
Expected Total Score Is 168,194,400.000
Actual Total Score Is 420,000,100.000
This Wheel Scored 249.711% Of Random Expectation
Total Draws With At Least 1 Match3 - 2,216
Can anything useful be deduced from this? Probably nothing truly
amazing.
I'll leave that to the reader to decide. Remember...don't argue with
me...argue with the data. I have simply provided that data.
I'm surprised you can take the knights that say nik nik nik . . .
As for the lottery. If the triple hits are nicely spaced
within the current ballset and does well in it's pairs,
why not start playing it with in a minimum number of lines
with all the other numbers in properly balanced lines. The
worst possible result would be three 4# wins when it comes
in. The top ten triples played this way might be an
interesting pool play. One could also wait out most of
the previous gap between hits before playing.
Robert Perkis / http://www.lotto-logix.com
|
Did you know if you play 10 triples you can guarantee a 3 match with 10
lines
when one of them occurs ?
Here's how 10 triples reduce using all 49 numbers:
3x3 = 30 lines
5x3 = 50
10x3 = 90...8% chance for a 5
1x4 = 145...13% chance for a 5
1x5 = ~ 2,800
1x6 = ~146,000
Big wheels keep on rollin' |
|
| Back to top |
|
|
IXL Software
Guest
|
| Posted: Thu Apr 21, 2005 7:03 pm Post subject: Re: A Tale Of Two Triples |
|
|
"gARY" <[email protected]> wrote in message
news:[email protected]...
| Quote: | erce, why do I like you?
Perhaps it is because I like your idea that "the 20 triples drawn every
draw are not independent"!
Past "history triples" (here/rgl) is ONLY promoted by me! And I have NO
clue as to why (bias maybe) . However . .
Looking back on my records Paul has had the password for RedCar since -
early 06/2003
Paul is on a run? Yeah right!!!
Paul (and Gerry, as it goes) will also jump around any valid comment on
his/her ramblings until you subside OR STFU.
Bottom line really!
Good luck,
gARY
|
Everything always has to be about *you* doesn't it?
Since I lack a reliable translator for whatever your mother tongue is, this
suspiciously reads like an insinuation that the analysis of triples is
exclusively your private preserve because of your ridiculous "RedCar"
theory. That's a pretty big stretch...even for a dolt such as yourself.
Just as I have no doubt that you have spilled more beer than I have ever
drank, I am confident in the fact that I have forgotten more about lottery
theory than you'll ever fkn know.
The only thing I am interested in hearing from your direction is the sound
of the door slamming from the other side. Now kindly piss off and leave me
alone. |
|
| Back to top |
|
|
IXL Software
Guest
|
| Posted: Thu Apr 21, 2005 7:03 pm Post subject: Re: A Tale Of Two Triples |
|
|
"Robert Perkis" <[email protected]> wrote in message
news:[email protected]...
| Quote: |
IXL Software wrote:
It was a dark and stormy night. It was the best of times....No....make
that
the worst of times. Jesus wept...but tomorrow is another day.
Damn it's tough to get started on that Nobel Prize for Literature. Maybe
I
have a better shot at the Nobel Prize for Lottology since my nearest
rival
is presently languishing somewhere in the constellation of Taurus...just
under the anus at last report. Here's the next chapter:
In a 649 lottery, the most common minimum prize is awarded to the player
that has matched at least 3 of the 6 main numbers drawn. There are 18,424
possible ways to combine any 3 from 49 numbers to form what I refer to as
"triples". If a player were to employ any one of those triples as 3
banker
or key numbers, this would result in 15,180 lines of 6 numbers that
include
all of the remaining 46 numbers. No numbers have been excluded from play
and
no filters such as Odd/Even or Sums have been applied. Here are 2
possible
triples:
5-17-31
3-10-25
Is there any reason to believe that one is more likely than the other to
appear in any draw? Of course not! We all know by now that the draw is
totally random and they both have an absolutely equal chance. Over a
series
of N trials, they should be drawn an approximately equal number of
times.
That's the theory at least. Let's compare that to some real-world
results.
As of today, the Canadian 649 lottery has conducted 2,216 draws since
June
12, 1982... a period of almost 23 years. In a perfect world that strictly
obeys statistical averages, each possible triple should have appeared
18,424/2216 = 8.3 times...no less than 8...no more than 9. An analysis of
the results so far reveals that 1,709 of the 18,424 possible triples have
yet to make even *1* appearance. In contrast to that, there is one
particular triple that has appeared more than any other with 11 such
hits.
So much for that perfect world.
It's impossible to distinguish one from the other by simply looking at
them,
so I'll just have to tell you. The three numbers 3-10-25 have *never*
appeared together in any draw, while the 3 numbers 5-17-31 have been
drawn
together 11 times so far.
Anybody remember Sherman & Peabody from the Rocky & Bullwinkle show?
Let's
jump in the wayback machine and travel back to the morning of June 12,
1982...somewhere in the Great White North. As an experiment, they each
choose any 3 numbers that they will always include in their picks for
each
and every draw of the brand new Canadian Lotto 649. As it happens,
Sherman
chooses 3-10-25 and Peabody chooses 5-17-31. To this day, no one knows
why
(;-)
Fast forward to April of 2005. Many things have changed in a world that
is
barely recognizable. In a secret laboratory somewhere near Toronto, Paul
McCoy, once destined to become the first gazillionaire to successfully
market bottled tap-water to the masses, has instead become a notorious
evil
genius that against insurmountable obstacles, has managed to program his
computer to rapidly produce answers to questions that no one has asked.
This
is largely due to too much time spent listening to the Bonzo Dog Doo-Dah
Band and relentlessly viewing reruns of Monty Python's Flying Circus and
the
series of "Carry On" films. (Have to wonder why the bloody limeys around
here are such a grim lot.)
Examine the following data and search for useful clues. As a neutral
control
for comparison purposes, I first generated 15,180 totally random lines.
All
49 numbers are in use and no filtering of any kind was used. The same
lines
were checked against the entire draw history.
Lottery: CA 649
Wheel File: 15180random.txt
Testing 15,180 lines against 2216 draws
***MATCH-6*** for Draw 135 1/5/1985 At Line 3068
Match 0 - 14,670,047 Expected is 14,665,370.000
Match 1 - 13,889,214 Expected is 13,893,510.000
Match 2 - 4,452,320 Expected is 4,453,049.000
Match 3 - 594,076 Expected is 593,739.800 Score is 33,657,930.000
Match 4 - 32,573 Expected is 32,583.280 Score is 33,628,260.000
Match 5 - 635 Expected is 606.201 Score is 35,237,000.000
Match 5+ - 14 Expected is 14.433 Score is 32,628,900.000
Match 6 - 1 Expected is 2.406 Score is 13,983,820
Total Plays - 33,638,880
Total Losses - 33,011,581
Total Wins - 627,299
Expected Total Score Is 168,194,400.000
Actual Total Score Is 149,135,900.000
This Wheel Scored 88.669% Of Random Expectation
Total Draws With At Least 1 Match3 - 2,216
Here's what happened with Sherman's picks:
==========================================
Lottery: CA 649
Wheel File: 3-10-25.txt
Testing 15,180 lines against 2216 draws
Match-5 + Bonus for Draw 1269 3/20/1996 At Line 3985
Match-5 + Bonus for Draw 1269 3/20/1996 At Line 3990
Match-5 + Bonus for Draw 1269 3/20/1996 At Line 4497
Match-5 + Bonus for Draw 1269 3/20/1996 At Line 9701
Match 0 - 14,820,000 Expected is 14,665,370.000
Match 1 - 14,002,300 Expected is 13,893,510.000
Match 2 - 4,285,780 Expected is 4,453,049.000
Match 3 - 508,634 Expected is 593,739.800 Score is 28,817,130.000
Match 4 - 21,922 Expected is 32,583.280 Score is 22,632,200.000
Match 5 - 240 Expected is 606.201 Score is 13,317,920.000
Match 5+ - 4 Expected is 14.433 Score is 9,322,544.000
Match 6 - 0 Expected is 2.406 Score is 0
Total Plays - 33,638,880
Total Losses - 33,108,080
Total Wins - 530,800
Expected Total Score Is 168,194,400.000
Actual Total Score Is 74,089,800.000
This Wheel Scored 44.050% Of Random Expectation
Total Draws With At Least 1 Match3 - 2,216
Here's what happened with Peabody's picks:
=======================================
Lottery: CA 649
Wheel File: 5-17-31.txt
Testing 15,180 lines against 2216 draws
***MATCH-6*** for Draw 229 4/2/1986 At Line 7046
***MATCH-6*** for Draw 247 6/4/1986 At Line 1945
***MATCH-6*** for Draw 568 7/1/1989 At Line 2312
***MATCH-6*** for Draw 676 7/14/1990 At Line 13729
***MATCH-6*** for Draw 840 2/8/1992 At Line 10239
***MATCH-6*** for Draw 982 6/19/1993 At Line 14636
***MATCH-6*** for Draw 1065 4/6/1994 At Line 11674
***MATCH-6*** for Draw 1822 7/7/2001 At Line 14088
***MATCH-6*** for Draw 1950 9/28/2002 At Line 10626
***MATCH-6*** for Draw 2080 12/27/2003 At Line 6673
***MATCH-6*** for Draw 2094 2/14/2004 At Line 390
Match 0 - 14,345,760 Expected is 14,665,370.000
Match 1 - 14,044,160 Expected is 13,893,510.000
Match 2 - 4,497,240 Expected is 4,453,049.000
Match 3 - 695,003 Expected is 593,739.800 Score is 39,376,040.000
Match 4 - 54,995 Expected is 32,583.280 Score is 56,776,660.000
Match 5 - 1,678 Expected is 606.201 Score is 93,114,460.000
Match 5+ - 33 Expected is 14.433 Score is 76,910,990.000
Match 6 - 11 Expected is 2.406 Score is 153,822,000
Total Plays - 33,638,880
Total Losses - 32,887,160
Total Wins - 751,720
Expected Total Score Is 168,194,400.000
Actual Total Score Is 420,000,100.000
This Wheel Scored 249.711% Of Random Expectation
Total Draws With At Least 1 Match3 - 2,216
Can anything useful be deduced from this? Probably nothing truly amazing.
I'll leave that to the reader to decide. Remember...don't argue with
me...argue with the data. I have simply provided that data.
I'm surprised you can take the knights that say nik nik nik . . .
|
I'm a lumberjack and that's OK (;-)
| Quote: | As for the lottery. If the triple hits are nicely spaced
within the current ballset and does well in it's pairs,
why not start playing it with in a minimum number of lines
with all the other numbers in properly balanced lines. The
worst possible result would be three 4# wins when it comes
in. The top ten triples played this way might be an
interesting pool play. One could also wait out most of
the previous gap between hits before playing.
Robert Perkis / http://www.lotto-logix.com |
|
|
| Back to top |
|
|
IXL Software
Guest
|
| Posted: Thu Apr 21, 2005 7:03 pm Post subject: Re: A Tale Of Two Triples |
|
|
"erce" <[email protected]> wrote in message
news:[email protected]...
| Quote: | IXL Software wrote:
"erce" <[email protected]> wrote in message
news:[email protected]...
IXL Software wrote:
In a 649 lottery, the most common minimum prize is awarded to the
player
that has matched at least 3 of the 6 main numbers drawn. There are
18,424
possible ways to combine any 3 from 49 numbers to form what I
refer
to as
"triples". If a player were to employ any one of those triples as
3
banker
or key numbers, this would result in 15,180 lines of 6 numbers
that
include
all of the remaining 46 numbers. No numbers have been excluded
from
play and
no filters such as Odd/Even or Sums have been applied. Here are 2
possible
triples:
5-17-31
3-10-25
Is there any reason to believe that one is more likely than the
other
to
appear in any draw? Of course not!
if you believe that why are you here
I'm here because I enjoy reading dumbass comments from snipers like
you. Why
are *you* here? Certainly not to impress anyone with your knowledge
or
entertain anyone with your charming wit.
Lighten up a little Eric. Reading your posts is like living through a
scene
in an Ingmar Bergman psycho-drama.
We all know by now that the draw is
totally random and they both have an absolutely equal chance. Over
a
series
of N trials, they should be drawn an approximately equal number
of
times.
That's the theory at least. Let's compare that to some real-world
results.
As of today, the Canadian 649 lottery has conducted 2,216 draws
since
June
12, 1982... a period of almost 23 years. In a perfect world that
strictly
obeys statistical averages, each possible triple should have
appeared
18,424/2216 = 8.3 times...no less than 8...no more than 9.
there went any chance of a nobel prize in lottology - care to put
standard
deviations round that 8.3
You seem to know everything there is to know. Why don't you do that?
Teach
us.
Like that old bumpersticker said, "Ass, gas or grass...nobody rides
for
free."
An analysis of
the results so far reveals that 1,709 of the 18,424 possible
triples
have
yet to make even *1* appearance. In contrast to that, there is one
particular triple that has appeared more than any other with 11
such
hits.
So much for that perfect world.
It's impossible to distinguish one from the other by simply
looking
at them,
so I'll just have to tell you. The three numbers 3-10-25 have
*never*
appeared together in any draw, while the 3 numbers 5-17-31 have
been
drawn
together 11 times so far.
does that surprise you
No more than the fact that insects can fly or birds can sing.
As I clearly indicated, I merely provided the data.
erce
18424 triples
20 drawn every draw
18424 * (18404/18424) ^ 2216 not drawn in 2216 draws - approx 1660
thats an underestimate because the 20 triples drawn every draw are not
independent
|
Could you explicitly clarify what you mean by "not independent"? I'm not
entirely sure of your meaning in this context.
You are quite correct in that each line of 6 drawn numbers contains 20
triples. More on that later.
Your formula above should be correctly expressed as 18424 *
((18404/18424) ^ 2216) to equal ~1660. I take this to be the theoretical
statistical expectation of the number of triples that will NOT be drawn
after 2216 trials. The real-world data for the Canadian 649 is 1709 at this
point. The logical converse of this would be 18424-1660=16764 that *should*
have
been drawn. The actual figure is 16715. Oddly enough we're off by 49.
Coincidence? I don't know.
Where's my old buddy Duncan? He's pretty good at cipherin'. Oh Duncan...come
out, come out wherever you are...please.
Assuming that your formula is correct, we can extrapolate some values far
into the future:
In order to get the value as close as possible to 1 (meaning there would
*still* be 1 triple that hasn't appeared), it would require 9,042 draws. At
a constant rate of 2 draws per week, we won't reach that target for another
65.5 years. My youngest grandson will be considerably older in 2071 than I
am now. I haven't got time to wait for the curve to flatten out...none of us
do. We have to deal with the conditions *as they currently exist*.
At 652,220 draws, we would still have a value >0, which Excel tells me is
4.1017850483e-304. This is obviously an extremely small value. By
comparison, Planck's Constant, one of the smallest measurable values in the
physical universe, is an almost inconceivably gigantic 6.626068e-34.
Only when we reach 652,221 draws does this value go to 0 (at least by
Excel's
precision). At a constant rate of 2 draws per week, I reckon we won't reach
that
milestone until sometime in 8238 AD. Put another way, if the Sumerians had
started a lottery draw circa 4228 BC, they would only now be that far along.
I know that these figures border on the silly. Maybe I should be working for
the Ministry Of Silly Walks. I just like to put an interesting perspective
on things like this.
Here's another formula: (20/18424)*2216 equals ~2.4. The same result can be
found with (20*2216)/18424.
This is what I should have used in my original post instead of
18424/2216=8.3 and I hereby correct myself.
Notice that this is obviously greater than 1...meaning that every triple has
had a statistically equal chance to have appeared at least twice in 2216
draws. So why the discrepancy and how do we reconcile the 2 contradictory
formulas that appear to be equally valid? I really want to know if anyone
cares to take a stab at it.
Paul |
|
| Back to top |
|
|
IXL Software
Guest
|
| Posted: Thu Apr 21, 2005 7:03 pm Post subject: Re: A Tale Of Two Triples |
|
|
"erce" <[email protected]> wrote in message
news:[email protected]...
| Quote: | gARY wrote:
erce, why do I like you?
Perhaps it is because I like your idea that "the 20 triples drawn
every draw are not independent"!
Past "history triples" (here/rgl) is ONLY promoted by me! And I have
NO clue as to why (bias maybe) . However . .
Looking back on my records Paul has had the password for RedCar since
- early 06/2003
Paul is on a run? Yeah right!!!
Paul (and Gerry, as it goes) will also jump around any valid comment
on his/her ramblings until you subside OR STFU.
Bottom line really!
Good luck,
gARY
i made the same mistake as 'i excel' and made an assumption about
something i dont know about
if the most drawn triplet were 7 14 21 then the other triplets
involving 7 and 14 would also outperform on average so the distribution
would be lumpier than a standard binomial
one of the lumps would be of triplets never drawn
given an infinitely long time the distribution should approach the
binomial and the lumpiness disappear
would any math-heads care to comment
erce
|
What you say is not without merit. Unfortunately, we mere mortals don't have
an "infinitely long time". |
|
| Back to top |
|
|
Gerry
Guest
|
| Posted: Thu Apr 21, 2005 8:03 pm Post subject: Re: A Tale Of Two Triples |
|
|
"IXL Software" <[email protected]> wrote in message
news:[email protected]...
| Quote: | I'm a lumberjack and that's OK (
|
Ha!
I'm a dumbass Texas farmboy always steppin' in doo-doo or gettin' it
thrown at me but it's OK ;-)
There's a lot of doo-doo gets thrown around here... |
|
| Back to top |
|
|
gARY
Guest
|
| Posted: Thu Apr 21, 2005 9:03 pm Post subject: Re: A Tale Of Two Triples |
|
|
"erce"
| Quote: | gARY wrote:
erce, why do I like you?
Perhaps it is because I like your idea that "the 20 triples drawn
every draw are not independent"!
Past "history triples" (here/rgl) is ONLY promoted by me! And I have
NO clue as to why (bias maybe) . However . .
Looking back on my records Paul has had the password for RedCar since
- early 06/2003
Paul is on a run? Yeah right!!!
Paul (and Gerry, as it goes) will also jump around any valid comment
on his/her ramblings until you subside OR STFU.
Bottom line really!
Good luck,
gARY
i made the same mistake as 'i excel' and made an assumption about
something i dont know about
if the most drawn triplet were 7 14 21 then the other triplets
involving 7 and 14 would also outperform on average so the distribution
would be lumpier than a standard binomial
one of the lumps would be of triplets never drawn
|
Combine them (undrawn trios) in strings of 16+ numbers and then see the lumps, humps and spikes.
That is where Paul is so far removed as you would NEVER find 16numbers using the whole UK history.
But at least Paul is trying to understand I spose!
Good luck,
gARY
| Quote: | given an infinitely long time the distribution should approach the
binomial and the lumpiness disappear
would any math-heads care to comment
erce
|
|
|
| Back to top |
|
|
|
|
You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum
You cannot vote in polls in this forum
|
Powered by phpBB 2.0.11 © 2001, 2002 phpBB Group
|
FAQ
Search
Memberlist
Usergroups
Register
Profile
Log in to check your private messages
Log in
