Thinking Out Of The Box - Part 1
Royce Penny
analysis from my "Thinking Out Of the Box" Series.
The copyright for these articles and the software algorithms
associated with the processes described are the property of
Royce Penny. Use is restricted to personal use only, and
publication without permission is prohibited.
You are also advised to read the disclaimer at the end of
this article.
Thinking Out Of The Box - Part 1
Copyright Royce Penny
--------------------------------
Abstract: Lottery Corporations publish data to show that
the probability of selecting the exact 6 numbers to win the
next lotto 649 draw is 1 in 13,983,816. In this article, I
will describe a very simple proof that the probability of
selecting the jackpot win for a lotto 649 can, with proper
selection of lines, always be limited to at least 1 in
5,245,786. Thus, in each and every draw, you can
successfully eliminate 8,738,030 lines and be correct 100%
of the time.
--------------------------------
For this simple proof, I will construct a 7x7 matrix
containing all of the 49 numbers representing a lotto 649.
This matrix is a "template". What I mean by a template, is
that any number can be substituted with any other of the 49
numbers, provided that all 49 numbers are used to fill the
matrix template.
For this example, I will use the most simple construct. In
future articles, I will look into how you can "design" the
template matrix with patterns that are unique to your
specific lotto draw.
The simple matrix is:
1 2 3 4 5 6 7
8 9 10 11 12 13 14
15 16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35
36 37 38 39 40 41 42
42 44 45 46 47 48 49
The matrix has 7 rows. When the six winning numbers are
drawn, they can only occupy a maximum of 6 of the 7 rows.
Thus, at least one row will always yield 7 numbers that will
*not* appear in the very next draw. These 7 numbers can now
be eliminated. The catch is, that you will be required to
select at least 7 combinations that each *exclude* the seven
numbers from one of each of the 7 rows.
I know that this is also true for the 7 columns. I will
discuss this later as I do not want you to get ahead of me.
I just want you to understand the logic at this time.
When you eliminate 7 numbers from a lotto 649, you are now
playing a lotto 642. In a lotto 642, there are only
C(42,6), or 5,245,786 available lines of six numbers.
The lotto 649 has 13,983,816 lines. So, for all lotto 649's,
you can specifically eliminate at least 8,738,030 lines, or
62.5% of the lines, and still have a 100% guarantee that you
are right 100% of the time. Again, the catch - you must
select 7 lines that contain all 49 numbers from the 7 sets
of 6 rows in the matrix template.
If you understand the maths, you may conclude that
purchasing 7 lines in any draw increases the probability of
a win from 1 in 13.98M to 7 in 13.98M, or 1 in 1,997,688.
Well, trust me, the probability will also always average 1
in 1,997,688 with the 7 lines selected. Draw specific, the
probability will cycle both above and below this number, but
it will always be limited to 1 in 5.25M value.
In conclusion, when you select any 7 lines that contain all
49 numbers, you will have a 100% guarantee the probability
will *always* be limited to 1 in 5,245,786 for *all* future
draws. In many instances, the probability will be much
better than the expected value of 1 in 1,997,688. This is
because the very next draw will never fill all 6 rows of the
matrix for all of the draws. In some cases, the correct
numbers can reside in as little as two of the matrix rows.
In these instances, maximum probability is much greater than
1 in 1,997,688. It is these patterns that I will explore in
the next article.
This pattern analysis is not limited to a lotto 649. By
varying the matrix size, all the various lottery designs can
be accommodated. Later I can describe the 9x6 matrix for
the lotto 654, the 6x7 matrix for the lotto 642, and the 6x6
matrix for the 536 and the 636
Disclaimer:
------------
1. The processes described in this series will not change
the probability of winning a lotto 649. The probability of
a jackpot win for any lotto 649 will always remain at 1 in
13,983,816 when one line is selected.
2. I do not encourage anyone to purchase lottery tickets.
If tickets are purchased, I do not recommend purchasing more
lottery tickets than those which can be considered as
purchased with "normal pocket change" that would have been
spent elsewhere anyway.
--
Royce Penny
Royce Penny's Money Machine
http://www.geocities.com/lottoking.geo
Sean B
Sorry, but, I can't follow what your on about.
I can see that the 6 balls can appear in a
maximum of 6 rows, but, I would have to
cover all 7 rows for the guarantee, which
leaves no advantage.
How many entries are you suggesting?
Each line of 7 needs 6 entries to cover
it as do the columns, as do all the other
permutations of columns and rows.
Cheers,
Sean B
Royce Penny
>
> Hi Royce,
>
> Sorry, but, I can't follow what your on about.
> I can see that the 6 balls can appear in a
> maximum of 6 rows, but, I would have to
> cover all 7 rows for the guarantee, which
> leaves no advantage.
>
> How many entries are you suggesting?
> Each line of 7 needs 6 entries to cover
> it as do the columns, as do all the other
> permutations of columns and rows.
>
> Cheers,
>
> Sean B
>
Sean - Just read it again...because you only need 7 lines of
6 numbers with at least one number from each of the C(7,6)
rows.
Dick Adams
I've read it twice. I see the logic, but not the process. Here's last
Saturday's Maryland Lotto numbers (11-15-16-33-44-49). Please show me
the process.
Dick -- The Wizard of Odds and sometimes Taxes too.
Royce Penny
Hi Dick - Actually, what you are asking falls in line with
my Part 3 article. This set of 6 numbers does fall into one
of the 7 sets of 42, but it is contained in 4 of the 6
lines. In Part 3, I will discuss this in full detail when I
get into further reducing the numbers and the 100% guarantee
- so be patient. Part 1 is only the simple proof. I have
to present what you ask in part 3, because part 2 deals
with a further reduction while still holding the guarantee
at 100%.
Thomas Grüneberg
I'm working on the same thing ! and I'm sure there must be a way to beat
the C49,6,3,6=161 and to minimize the tickets to an area < 100
!!!!!!!!!!!!!!!!!
Brgds Thomas
Royce Penny schrieb:
Robert Perkis
Is the 7x7 matrix for a Pick-7 game or must each
line of 7 numbers be full wheeled for a total of
7 combinations per line or 49 combinations down
and/or 49 combinations across? Criss Cross too?
Or is it not really a 7x7 matrix, but a 6x8 or two
to cover the 49 numbers?
I can see how a 6x6 matrix would make six across or
six down and 6+6 criss cross. The 42 number matrix
of 6x7 would be 7 lines of 6 no questions there and
heck 6x8 would be 8 lines of 6 with two automatically
out of the picture.
Robert Perkis
Dick Adams
>> I've read it twice. I see the logic, but not the process. Here's last
>> Saturday's Maryland Lotto numbers (11-15-16-33-44-49). Please show me
>> the process.
> Hi Dick - Actually, what you are asking falls in line with
> my Part 3 article. This set of 6 numbers does fall into one
> of the 7 sets of 42, but it is contained in 4 of the 6
> lines. In Part 3, I will discuss this in full detail when I
> get into further reducing the numbers and the 100% guarantee
> - so be patient. Part 1 is only the simple proof. I have
> to present what you ask in part 3, because part 2 deals
> with a further reduction while still holding the guarantee
> at 100%.
The suspense is killing me.
Robert Perkis
Sorry about replying to my own post, but I think I got it.
The 7x7 matrix eliminates one line, but we don't know which
one it will be. We also know none of those numbers can hit,
so we can take each line from one direction at a time and
take out those numbers from the lines in the other direction,
thus making those 7 number line 6 number combinations and we
would have to do this 49 times so we would end up with 49
lines, still don't see where this is going.
Robert Perkis
Richard McTavish
I cut these 3 sections, because I don't quite follow them :
If possible, can you re-explain each statement ?
1)
The catch is, that you will be required to
select at least 7 combinations that each *exclude* the seven
numbers from one of each of the 7 rows.
2)
Again, the catch - you must
select 7 lines that contain all 49 numbers from the 7 sets
of 6 rows in the matrix template.
3)
In conclusion, when you select any 7 lines that contain all
49 numbers,
Joe Galenko
I don't understand. What is the point of this? The only things that seem
relevant in the whole thing are the discliaimers at the end. Since you
can't eliminate any of the rows until after the numbers have been drawn,
what is the point? If we're choosing things afte the fact then I can
eliminate 13,983,815 of the 13,983,816 possibilities every single time.
Also, the dislcaimer at the end seems to contradict the following sentence
from the abstract.
> In this article, I
> will describe a very simple proof that the probability of
> selecting the jackpot win for a lotto 649 can, with proper
> selection of lines, always be limited to at least 1 in
> 5,245,786.
Manfred
to eliminate 7 numbers from 49 and to generate the rest
of the lines we can also use a simple program.
The following QBASIC programm uses a filter and
generates all 5,245,786 combinations for 6 of 49 without
the chooseable 7 numbers .
This program could easily be modified in that way:
If you expect that the 6 winning numbers will come within certain 15
numbers
from a pool of 49 numbers, then the filter lines and the input lines
have
to be extended to 34 variables, so that 49 - 15 = 34 numbers are
filtered out and we have a complete 6 of 15 cover from 6 of 49.
For testing the program you should start it with a small pool of
numbers
at the first input request,
e.g. 15 numbers, because with 49 numbers it needs nearly one hour
for screen output.
For Sean B : Without the line numbers I don't see an advantage for
understanding the program, but if most want it without line numbers,
I will omit them.
Manfred
REM this QBASIC program from Manfred identifies and counts
REM all 5,245,786 entries for 6 of 49 from which 7 numbers
REM and all combinations with this numbers are eliminated
REM There is no copyright. Using this program is on the own risk of
the user
CLS : REM clear screen
PRINT " Please input now the number of the pool size": PRINT
PoolSize: INPUT ; "Example: for 6 of 49 type 49. For 6 of 54 type
54"; yy
IF yy < 13 THEN PRINT " entry no valid": GOTO
PoolSize
PRINT
InputA1: INPUT ; "Please type the first suppressed number and press
Entry"; a1
PRINT
InputB1: INPUT ; "Please type the second suppressed number and press
Entry "; b1
IF b1 = a1 THEN PRINT " double number entry, try
again": GOTO InputB1
PRINT
InputC1: INPUT ; "Please type the third suppressed number and press
Entry "; c1
IF c1 = a1 OR c1 = b1 THEN PRINT " double number entry,
try again": GOTO InputC1
PRINT
InputD1: INPUT ; "Please type the fourth suppressed number and press
Entry"; d1
IF d1 = a1 OR d1 = b1 OR d1 = c1 THEN PRINT " double
number entry, try again": GOTO InputD1
PRINT
InputE1: INPUT ; "Please type the fifth suppressed number and press
Entry"; e1
IF e1 = a1 OR e1 = b1 OR e1 = c1 OR e1 = d1 THEN PRINT
" double number entry, try again": GOTO InputE1
PRINT
InputF1: INPUT ; "Please type the sixth suppressed number and press
Entry"; f1
IF f1 = a1 OR f1 = b1 OR f1 = c1 OR f1 = d1 OR f1 = e1
THEN PRINT "double number entry, try again": GOTO InputF1
PRINT
InputG1: INPUT ; "Please type the seventh suppressed number and press
Entry"; g1
IF g1 = a1 OR g1 = b1 OR g1 = c1 OR g1 = d1 OR g1 = e1 OR
g1 = f1 THEN PRINT "double number entry, try again": GOTO InputG1
PRINT : PRINT "Please Wait"
x# = 0: REM x# = counter for the output lines
FOR a = 1 TO yy - 5
FOR b = a + 1 TO yy - 4
FOR c = b + 1 TO yy - 3
FOR d = c + 1 TO yy - 2
FOR e = d + 1 TO yy - 1
FOR f = e + 1 TO yy
REM following lines filter all combinations out which contain one or
more of the suppressed numbers
IF (a = a1 OR a = b1 OR a = c1 OR a = d1 OR a = e1 OR a = f1 OR
a = g1) THEN GOTO Continue
IF (b = a1 OR b = b1 OR b = c1 OR b = d1 OR b = e1 OR b = f1 OR
b = g1) THEN GOTO Continue
IF (c = a1 OR c = b1 OR c = c1 OR c = d1 OR c = e1 OR c = f1 OR
c = g1) THEN GOTO Continue
IF (d = a1 OR d = b1 OR d = c1 OR d = d1 OR d = e1 OR d = f1 OR
d = g1) THEN GOTO Continue
IF (e = a1 OR e = b1 OR e = c1 OR e = d1 OR e = e1 OR e = f1 OR
e = g1) THEN GOTO Continue
IF (f = a1 OR f = b1 OR f = c1 OR f = d1 OR f = e1 OR f = f1 OR
f = g1) THEN GOTO Continue
x# = x# + 1
REM for i=1 to 10000: next i: REM remove the first REM for slow screen
output
PRINT x#, a; b; c; d; e; f
REM lprint x#,a; b; c; d; e; f
Continue: NEXT f, e, d, c, b, a
PRINT : PRINT " finished"
PRINT : PRINT "This are"; x#; "lines from 6 of"; yy;
"without the numbers"; a1; b1; c1; d1; e1; f1; g1
How to use the program with QBASIC:
Store the programm code with the Editor e.g. with the name
XYZ. The file has then the name XYZ.txt .
Change the file extension .txt with the explorer to .bas then you'll
have the
file XYZ.bas, which is executable with QBASIC. Start it in QBASIC.
Qbasic.exe is delivered with all Windows programs and runs under DOS
mode.
If Qbasic.exe and Qbasic.hlp is not on your hard disk, then copy them
from
the Windows CD to your hard disk.
Royce Penny <lottokin...@hotmail.com> wrote in message news:<3C08FC27...@hotmail.com>...
Royce Penny
Manfred wrote:
>
> Hi Royce,
>
> to eliminate 7 numbers from 49 and to generate the rest
> of the lines we can also use a simple program.
> The following QBASIC programm uses a filter and
> generates all 5,245,786 combinations for 6 of 49 without
> the chooseable 7 numbers .
>
-------------
Sorry Manfred, I do not get your point...I only want to
select 7 lines with the win guarantee, not all the lines.
Royce Penny
--------------------
Robert - You are close. You do not need the 49 lines
though. See the Part 2 post...
Manfred
if we filter out(remove) 7 numbers from 49, or remove a line
of a 7 x 7 matrix, then there remain
7 lines with 6 numbers or 6 lines with 7 numbers or 6 colons with 7
numbers,
if we put them into a matrix and that are 42 numbers! My program then
simply uses this 42 numbers.
Manfred
Hi all,
sorry if with cut and paste the program didn't work because the posted
version inserts line feeds on the wrong positions.
Therefore I have added now line numbers, so that everybody
easily can edit the programm in the editor.
Each line of the program has to start with a line
number, starting with 100 and step size 10.
The following QBASIC programm uses a filter and
generates all 5,245,786 combinations for 6 of 49 without
the chooseable 7 numbers .
This program could easily be modified in that way:
If you expect that the 6 winning numbers will come within certain 15
numbers
from a pool of 49 numbers, then the filter lines and the input lines
have
to be extended to 34 variables, so that 49 - 15 = 34 numbers are
filtered out and we have a complete 6 of 15 cover from 6 of 49.
For testing the program you should start it with a small pool of
numbers
at the first input request,
e.g. 15 numbers, because with 49 numbers it needs nearly one hour
for screen output.
Manfred
100 REM this QBASIC program from Manfred identifies and counts
110 REM all 5,245,786 entries for 6 of 49 from which 7 numbers
120 REM and all combinations with this numbers are eliminated
130 REM There is no copyright. Using this program is on the own risk
of the user
140 CLS : REM clear screen
150 PRINT " Please input now the number of the pool size": PRINT
160 INPUT ; "Example: for 6 of 49 type 49. For 6 of 54 type 54"; yy
170 IF yy < 13 THEN PRINT " entry no valid": GOTO 160
180 PRINT
190 INPUT ; "Please type the first suppressed number and press Entry";
a1
200 PRINT
210 INPUT ; "Please type the second suppressed number and press Entry
"; b1
220 IF b1 = a1 THEN PRINT " double number entry, try
again": GOTO 210
230 PRINT
240 INPUT ; "Please type the third suppressed number and press Entry
"; c1
250 IF c1 = a1 OR c1 = b1 THEN PRINT " double number
entry, try again": GOTO 240
260 PRINT
270 INPUT ; "Please type the fourth suppressed number and press
Entry"; d1
280 IF d1 = a1 OR d1 = b1 OR d1 = c1 THEN PRINT " double
number entry, try again": GOTO 270
290 PRINT
300 INPUT ; "Please type the fifth suppressed number and press Entry";
e1
310 IF e1 = a1 OR e1 = b1 OR e1 = c1 OR e1 = d1 THEN
PRINT " double number entry, try again": GOTO 300
320 PRINT
330 INPUT ; "Please type the sixth suppressed number and press Entry";
f1
340 IF f1 = a1 OR f1 = b1 OR f1 = c1 OR f1 = d1 OR f1 = e1
THEN PRINT "double number entry, try again": GOTO 330
350 PRINT
360 INPUT ; "Please type the seventh suppressed number and press
Entry"; g1
370 IF g1 = a1 OR g1 = b1 OR g1 = c1 OR g1 = d1 OR g1 = e1
OR g1 = f1 THEN PRINT "double number entry, try again": GOTO 370
380 PRINT : PRINT "Please Wait"
390 x# = 0: REM x# = counter for the output lines
400 FOR a = 1 TO yy - 5
410 FOR b = a + 1 TO yy - 4
420 FOR c = b + 1 TO yy - 3
430 FOR d = c + 1 TO yy - 2
440 FOR e = d + 1 TO yy - 1
450 FOR f = e + 1 TO yy
460 REM following lines filter all combinations out which contain one
or more of the suppressed numbers
470 IF (a = a1 OR a = b1 OR a = c1 OR a = d1 OR a = e1 OR a = f1
OR a = g1) THEN GOTO 570
480 IF (b = a1 OR b = b1 OR b = c1 OR b = d1 OR b = e1 OR b = f1
OR b = g1) THEN GOTO 570
490 IF (c = a1 OR c = b1 OR c = c1 OR c = d1 OR c = e1 OR c = f1
OR c = g1) THEN GOTO 570
500 IF (d = a1 OR d = b1 OR d = c1 OR d = d1 OR d = e1 OR d = f1
OR d = g1) THEN GOTO 570
510 IF (e = a1 OR e = b1 OR e = c1 OR e = d1 OR e = e1 OR e = f1
OR e = g1) THEN GOTO 570
520 IF (f = a1 OR f = b1 OR f = c1 OR f = d1 OR f = e1 OR f = f1
OR f = g1) THEN GOTO 570
530 x# = x# + 1
540 REM for i=1 to 10000: next i: REM remove the first REM for slow
screen output
550 PRINT x#, a; b; c; d; e; f
560 REM lprint x#,a; b; c; d; e; f
570 NEXT f, e, d, c, b, a
580 PRINT : PRINT " finished"
590 PRINT : PRINT "This are"; x#; "lines from 6 of";
yy; "without the numbers"; a1; b1; c1; d1; e1; f1; g1
How to use the program with QBASIC:
Store the programm code with the Editor e.g. with the name
XYZ. The file has then the name XYZ.txt .
First remove all wrong line feeds, so that each line starts with a
number from
100 to 590 with a step size of 10 and save it again on your hard disk.
Change the file extension .txt with the explorer to .bas then you'll
have the
file XYZ.bas, which is executable with QBASIC. Start it in QBASIC.
Qbasic.exe is delivered with all Windows programs and runs under DOS
mode.
If Qbasic.exe and Qbasic.hlp is not on your hard disk, then copy them
from
the Windows CD to your hard disk.
Royce Penny <lottokin...@hotmail.com> wrote in message news:<3C0F8A7B...@hotmail.com>...
Manfred
I answered too quick because I was just changing my program
with line numbers.
I did missunderstand your idea, but it is too early to
discuss about it as long as we don't know your lesson 2
and 3.
Manfred
Royce Penny <lottokin...@hotmail.com> wrote in message news:<3C08FC27...@hotmail.com>...
Royce Penny
--------------------
Martin Sewell wrote:
>
> On Sat, 01 Dec 2001 08:49:59 -0700, Royce Penny
> <lottokin...@hotmail.com> wrote:
>
> >This is the first my the series of articles on pattern
> >analysis from my "Thinking Out Of the Box" Series.
> >
> ><SNIP>
>
> Can we hope that it is also the last?
>
> Martin
Dick Adams
> I don't understand. What is the point of this? The only things that seem
> relevant in the whole thing are the discliaimers at the end. Since you
> can't eliminate any of the rows until after the numbers have been drawn,
> what is the point? If we're choosing things afte the fact then I can
> eliminate 13,983,815 of the 13,983,816 possibilities every single time.
> ....
Joe,
I sincerely fail to understand how an academic good enough to be on the
Faculty of the University of the Promised Land at Chapel Hill does not
comprehend the thrill of mental masturbation while in search of a
contingent bonanza!!
Dick "My blood runs Carolina Blue" Adams
aka The Wizard of Odds and sometimes Taxes too.
Sean B
>The simple matrix is:
>
> 1 2 3 4 5 6 7
>
> 8 9 10 11 12 13 14
>
>15 16 17 18 19 20 21
>
>22 23 24 25 26 27 28
>
>29 30 31 32 33 34 35
>
>36 37 38 39 40 41 42
>
>42 44 45 46 47 48 49
>
>The matrix has 7 rows. When the six winning numbers are
>drawn, they can only occupy a maximum of 6 of the 7 rows.
>Thus, at least one row will always yield 7 numbers that will
>*not* appear in the very next draw. These 7 numbers can now
>be eliminated. The catch is, that you will be required to
>select at least 7 combinations that each *exclude* the seven
>numbers from one of each of the 7 rows.
>
>I know that this is also true for the 7 columns. I will
>discuss this later as I do not want you to get ahead of me.
>I just want you to understand the logic at this time.
>
>When you eliminate 7 numbers from a lotto 649, you are now
>playing a lotto 642. In a lotto 642, there are only
>C(42,6), or 5,245,786 available lines of six numbers.
Royce, You would have to cover......
All 7 possibilities of the line you eliminate.
(no problem with that)
7 possibilities of the other 6 lines =
7 possibilities of 42 numbers =
7 x 5,245,786 say 36M lines.
Because all the 49 numbers appear at some time
during the 7 possibilities of 42 numbers only
14M lines are possible after you eliminate
all the duplicates...... so no advantage, sorry ;-(
Right about the 100% guarantee though ;-)
Think about it another way.... to guarantee 100%
your entry has to include every one of 14M possible
lines.
Keep trying,
Sean B
steve.649
"Sean B" <se...@XXXsbacc3.fsnet.co.uk> wrote in message
news:rd661u0v57ndgvml9...@4ax.com...
> Royce Penny <lottokin...@hotmail.com> wrote:
Comments embedded further down.
==================================
> Because all the 49 numbers appear at some time
> during the 7 possibilities of 42 numbers only
> 14M lines are possible after you eliminate
> all the duplicates...... so no advantage, sorry ;-(
>
==================================
I may be wrong here Sean but if I have understood
Royce's theory correctly only 42 numbers appear
NOT 49 numbers as you stated because 7 numbers
were eliminated right from the start.
Quoting Royce -
"The catch is, that you will be required to
select at least 7 combinations that each *exclude* the seven
numbers from one of each of the 7 rows."
Thus - once the duplicates are stripped you have
5,245,786 lines which is what he is saying.
So I think Royce is right.
Steve Highfield.
Royce Penny
>
(...snip for brevity...)
> Think about it another way.... to guarantee 100%
> your entry has to include every one of 14M possible
> lines.
>
> Keep trying,
>
> Sean B
--------------------
Sean - thanks for the response. But again, you are only
looking at one line of the cover. Each individual line
always as the the 1:13983816 probability of a win. It is
the collective lines of the cover that provide the
guarantee...
Lets simplify things a little and analyze a lotto 2/9.
In this lotto, there are 9 numbers, and two are drawn.
In a lotto 2/9 the chance of selecting the correct two
numbers are 1 in C(9,2), or 1 in 36.
I will represent the nine numbers in a 3x3 matrix as
follows:
1 2 3
4 5 6
7 8 9
Since only two numbers are drawn, they can only occupy a
*maximum* of two columns *and* two rows of the matrix.
Sometimes less, but *never* more.
There are nine possible outcomes when I delete one column
and one row from this matrix template.
These outcomes are:
1 2 4 5
1 2 7 8
1 3 4 6
1 3 7 9
2 3 5 6
2 3 8 9
4 5 7 8
4 6 7 9
5 6 8 9
In every *very_next_draw*, the two winning numbers are
*always* located in it least one of these 9 sets of 4
numbers. Each of these 9 lines carries a 1:C(4,2), or 1:6
chance of selecting the correct set of two numbers. So if
you select one set of two numbers from each of the nine
lines, the probability of selecting the winning two numbers
*remains* at a maximum of 1:6 in every very_next_draw. This
is a 100% guaranteed cover that the probability will never
*exceed* 1:6 in nine lines.
I can cover all nine lines with the following seven sets of
two numbers (possibly less, I did not optimize this):
1 2
2 3
3 4
4 5
3 7
6 7
8 9
Thus, this cover design provides a guaranteed 1:6
2_if_2_in_9 number cover in 7 lines. By selecting this
cover design, I now have a 1:6 guarantee in 7 lines for
every very_next_draw. My probability of a win will always
be better than 1:6 in the long term, but the point is that
it will *never* ever be less than 1:6. This guarantee that
only is attained only when you purchase this cover. If I
select 7 random sets of two numbers, I will never have any
*guarantee*. This is what a covering design is all about.
When I select one line, my guarantee is always 1:36. I need
to select the 7 line cover to get the 1:6 guarantee. Since
these 7 lines are a template, I can always substitute any
number for any of the 9 numbers in the template and still
keep this 1:6 guarantee.
It is really that simple. The lotto 649 cover I presented,
is just an extension of this cover using the 7x7 matrix.
What I presented was only the proof. What I did not
present, was the additional results of my research which I
have passed on to others who have much more knowledge of the
maths than I do.
One example - I have been researching the results of
"forcing" the matrix. You may want to try this. If your
lotto has a bonus number, try loading it with lines that
have already occurred in your draw history and analyze the
patterns in the results.
I find these results to be of great interest, others may
not. To avoid any conflict on this point, and for the
purposes of this newsgroup, my public response is that this
type of forcing has absolutely no value greater than random
chance in determining the results of the very_next_draw. :-)
Royce Penny
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Dick, Good to see you are adding humor to all this.
Regarding the "mental masterbation", methinks it is leading
to massive hemorrhaging, and not orgasmic height. Do you
think this will ever "come_to_head", so to speak?
Also, your excellent post has earned you one more credit
towards your free copy of my "sorry_it_is_not_for_sale"
roulette system.
Mike Long
pairs it is at least 6/36 (can't quite see why it is not just 7/36). And I
cannot see why 7 random (but different) pairs do not give the same result.
And unless it is one of the roll-overs (winning prize more than 36), hasn't
the expected winnings reduced?
Also, aren't some of the terms inverted. When you say "probability of
selecting the winning two numbers
*remains* at a maximum of 1:6 in every very_next_draw" don't you mean
minimum (ditto with exceed).
I think that I am missing something here, but isn't the summary that if you
purchase n distinct tickets, your probability of winning the jackpot has
gone up by a factor of n.
Mike
--
"Royce Penny" <lottokin...@hotmail.com> wrote in message
news:3C14401C...@hotmail.com...
Sean B
Hi Steve,
If we are talking about Jackpot wins with all
6 being correct. There are 14M combs. possible
and just no way of covering 100% without
entering all 14M combinations.
The formula 100 x (14M/14M) = 100%
is cast in stone.
>Quoting Royce -
> "The catch is, that you will be required to
>select at least 7 combinations that each *exclude* the seven
>numbers from one of each of the 7 rows."
>
Shouldn't it also be done by the 7th son at the 7th hour
on the 7th day of the 7th month ;-)
>Thus - once the duplicates are stripped you have
>5,245,786 lines which is what he is saying.
>So I think Royce is right.
>
Well if you and Royce say so I'm willing to experiment,
I've bought 7 700ml cans of Newkie Brown and 14 700ml
glasses. Tonight I'm going to try and fill all the glasses
to the brim with the 7 cans....... If I fail at least I'll go to
bed Happy.... knowing that I eventually found a more
sensible solution ;-)
Cheers,
Sean
Sean B
have to chew over it for a day or so.
Sean B
Royce Penny
"Probability" should say "1/p", or "max" should change to
"min".
Again, as mentioned in previous posts, the chance in this
case "in_the_long_term" will always be 7:36, not 6:36. Only
because this is a cover design, the guarantee is that 6:36
will be attained in *each* very_next_draw, as versus a
random selection which has *no* guarantee.
All cover designs when applied to lottos will eventually
meet random expectation. You must pay a slight penalty to
purchase the guarantee initially, but the random genome is
very kind in paying it back to you over time. (This is not
the case in, say, "covered" calls and puts in the options
market, where the results are *not* random events.)
Hope this helps.
--
Royce Penny
Royce Penny's Money Machine
http://www.geocities.com/lottoking.geo
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