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# Lexicographic Numbers and a little math

Topic closed. 84 replies. Last post 6 years ago by gpagator.

 Page 1 of 6

United States
Member #59354
March 13, 2008
4083 Posts
Offline
 Posted: April 15, 2011, 10:39 pm - IP Logged

Hello everyone

I am starting a new topic on lexicographic number selection in hopes of gaining some new ideas.

I have been working with lexi's for several years and will be posting links to download software

as this moves along.  I hope to pull in a few pick-3 pick-4 players along the way as I think that

they may have much to say or add to this post.  This might be a way for pick3/4 players to put

there skills to use for the big games and also help big-game players improve their play at the same

time.

In a 5-39 game there are 575757 sets that can be numbered from 1 to 57575 but if you pad this

value with (0's) you can then divide it into two pick-3's.   To start with we would have 000,001 to

575,757 the front-3 with odds of 1 in 575 and The back 3 have odds of 1 in 757.  I have the software

that can make all the conversions and I will be posting this in a few days for anyone interested.  The

good thing about this is that it is possible to miss all the selections and still end up with lower prizes

so to start of with I want to show a few tricks.

LV = Lexicographic Value

Last nights drawing = [01 04 07 11 24]    LV =016012  front 3 = [016]  back-3 = [012]

If a person could hit these both then they could hit a 5 of 5 with one set but that would not be easy to do.

This next information is a little hard to understand so you may need to read it a few times to understand

what I am doing.  Because the back 3 could be any value from 000 to 999 depending on the front-3 digits

I use a little trick to help reduce the field.  The set  10-16-19-35-37 = LV 446999 but above I said that the

back-3 has a range of 000 to 757.  Here is a simple trick to give the back 3 the same conditions as the

front-3.

Example

first add 1 to the greatest value in the matrix in this case it is 39.  39 + 1 = 40  now using 40 subtract the

numbers from the set like this. set = 01-04-07-11-24

40-24 = 16

40-11 = 29

40-7  =  33

40-4  =  36

40-1  =  39

You now have the set 16-29-33-36-39  LV = 541875.  Note, remember the first 3 cannot be greater then 575

You may be asking how can this help. remember above that I said the range for the first three digits were

000 to 575 by using this trick the back-3 have the same odds.  You now have two pick-3 games with odds

of 1 in 575.  In simple you use the converted data to analyze thrn the software reverses the process and gives

you the numbers.  Without this conversion the each digit in the back-6 could be 0 to 9 and with the conversion

the first digit has a range of 0 to 5.  The second digits in the back-3 range is limited by the first digit selection

because the 3 digits combined cannot exceed 575.  So if the first digit in the B-3 is 5 then the second digit must

not be graeter then 7.  If the second B-3 digit = 7 then the third digit cannot be greater then 5.  I have been toying

with this for years to help me set a range for the first and fifth numbers that I use with my digit system.  The way

I use it now is to range the first 2 digits in both the F-3 and B-3 to within a 2 digit span.  This gives me a very small

range for the first and last numbers in my sets.  Many times using this method I can end up with two first numbers

and two fifth numbers thus truning the Pick-5 into a keyed wheel assigning 2 numbers to the 1st and 2 numbers to

the 5th position.  Many times using only the first lexi digit for F-3 and B-3 will determind the first and fifth numbers in

the set.  I am hoping that someone might probe this a little more and see what falls out.  The math behind this has not

been worked out completely and I invite anyone to pitch in.  I posted this in the math forum because I think most of

the replies will be in terms of odds and that is what I am interested in.

RL

United States
Member #59354
March 13, 2008
4083 Posts
Offline
 Posted: April 15, 2011, 10:56 pm - IP Logged

Just wanted to clear something up.  When I refer to the front-3 and back-3 I am really refering to the

front-3 from the original and the front-3 from the reversed lexi.  The last 3 digits for both are never

used so just ignore them.  From this point they will be called Foward lexi = (FL) and Reverse lexi = (RL)

RL

ORLANDO, FLORIDA
United States
Member #4924
June 3, 2004
5970 Posts
Offline
 Posted: April 16, 2011, 10:29 am - IP Logged

Thanks RL, this could be very interesting. Learning something new, sometimes helps.

Dallas, Texas
United States
Member #4549
May 2, 2004
1834 Posts
Offline
 Posted: April 16, 2011, 11:25 am - IP Logged

Hello everyone

I am starting a new topic on lexicographic number selection in hopes of gaining some new ideas.

I have been working with lexi's for several years and will be posting links to download software

as this moves along.  I hope to pull in a few pick-3 pick-4 players along the way as I think that

they may have much to say or add to this post.  This might be a way for pick3/4 players to put

there skills to use for the big games and also help big-game players improve their play at the same

time.

In a 5-39 game there are 575757 sets that can be numbered from 1 to 57575 but if you pad this

value with (0's) you can then divide it into two pick-3's.   To start with we would have 000,001 to

575,757 the front-3 with odds of 1 in 575 and The back 3 have odds of 1 in 757.  I have the software

that can make all the conversions and I will be posting this in a few days for anyone interested.  The

good thing about this is that it is possible to miss all the selections and still end up with lower prizes

so to start of with I want to show a few tricks.

LV = Lexicographic Value

Last nights drawing = [01 04 07 11 24]    LV =016012  front 3 = [016]  back-3 = [012]

If a person could hit these both then they could hit a 5 of 5 with one set but that would not be easy to do.

This next information is a little hard to understand so you may need to read it a few times to understand

what I am doing.  Because the back 3 could be any value from 000 to 999 depending on the front-3 digits

I use a little trick to help reduce the field.  The set  10-16-19-35-37 = LV 446999 but above I said that the

back-3 has a range of 000 to 757.  Here is a simple trick to give the back 3 the same conditions as the

front-3.

Example

first add 1 to the greatest value in the matrix in this case it is 39.  39 + 1 = 40  now using 40 subtract the

numbers from the set like this. set = 01-04-07-11-24

40-24 = 16

40-11 = 29

40-7  =  33

40-4  =  36

40-1  =  39

You now have the set 16-29-33-36-39  LV = 541875.  Note, remember the first 3 cannot be greater then 575

You may be asking how can this help. remember above that I said the range for the first three digits were

000 to 575 by using this trick the back-3 have the same odds.  You now have two pick-3 games with odds

of 1 in 575.  In simple you use the converted data to analyze thrn the software reverses the process and gives

you the numbers.  Without this conversion the each digit in the back-6 could be 0 to 9 and with the conversion

the first digit has a range of 0 to 5.  The second digits in the back-3 range is limited by the first digit selection

because the 3 digits combined cannot exceed 575.  So if the first digit in the B-3 is 5 then the second digit must

not be graeter then 7.  If the second B-3 digit = 7 then the third digit cannot be greater then 5.  I have been toying

with this for years to help me set a range for the first and fifth numbers that I use with my digit system.  The way

I use it now is to range the first 2 digits in both the F-3 and B-3 to within a 2 digit span.  This gives me a very small

range for the first and last numbers in my sets.  Many times using this method I can end up with two first numbers

and two fifth numbers thus truning the Pick-5 into a keyed wheel assigning 2 numbers to the 1st and 2 numbers to

the 5th position.  Many times using only the first lexi digit for F-3 and B-3 will determind the first and fifth numbers in

the set.  I am hoping that someone might probe this a little more and see what falls out.  The math behind this has not

been worked out completely and I invite anyone to pitch in.  I posted this in the math forum because I think most of

the replies will be in terms of odds and that is what I am interested in.

RL

RL,

Great idea! Sounds like you are on to something that will help the Pick 3 players relate to the jackpot games. You got my help on it.

The lexicon value for each each number is derived by it's place in the overall 575,757 combinations scheme. So [01 04 07 11 24] is the 016012 combination of the 575,757.

So far so good.

I'm getting confused at the 16-29-33-36-39 LV = 541875. If the back set has 757 possible, then 875 exceeds that. How are we going to compensate?

Dallas, Texas
United States
Member #4549
May 2, 2004
1834 Posts
Offline
 Posted: April 17, 2011, 1:14 am - IP Logged

This is a large Excel file (21.3 Megs) but it will give everyone the opportunity to see the combinations and the lexicon equilvalents in the 5/39 games.

United States
Member #59354
March 13, 2008
4083 Posts
Offline
 Posted: April 17, 2011, 5:46 am - IP Logged

Just wanted to let everyone know that I got pulled away on another project and it will be a

couple days before I can get back to this.  As Arnold would say, "I'll be back"

RL

United States
Member #105312
January 29, 2011
435 Posts
Offline
 Posted: April 17, 2011, 9:53 am - IP Logged

Just wanted to let everyone know that I got pulled away on another project and it will be a

couple days before I can get back to this.  As Arnold would say, "I'll be back"

RL

Doug MacArthur said that the night he snuck out of Corregidor in a PT boat, March 12, 1942, and left his troops to surrender to the Japanese and be entertained by the Bataan Death March.  When the got back they'd all gone somewhere else.

Don't wait too long is the moral of that.

Good luck.

Dallas, Texas
United States
Member #4549
May 2, 2004
1834 Posts
Offline
 Posted: April 17, 2011, 1:21 pm - IP Logged

RL,

Stay safe! Keep in touch.

United States
Member #59354
March 13, 2008
4083 Posts
Offline
 Posted: April 20, 2011, 3:31 am - IP Logged

Still a couple more days before I can get back to this.  I was able to get some of the software done so

keep checking back

RL

United States
Member #59354
March 13, 2008
4083 Posts
Offline
 Posted: April 22, 2011, 3:44 am - IP Logged

Hello

Below is a link to the first program, just run the setup and it's ready to go.  This program is a stand alone

program and does not change any settings on your computer. It just installs the program and creates a

shortcut to run it.  Just copy and paste the link below and it will take you to the download.  This program

is a lexi-calculator and will be used later in this post to help explain the how I use lexigraphic values to

select my first and fifth numbers in a set.  Windows vista / 7 users may get a security warning when dealing

with EXE files but the program is harmless.  There is a Pic  named LEX1.png that shows a few of the options and

settings it will be in the main folder with the program.

http://www.box.net/shared/7d5sf6jmpx

RL

United States
Member #59354
March 13, 2008
4083 Posts
Offline
 Posted: April 22, 2011, 8:49 pm - IP Logged

Below is a list for a 5-39 game showing the Lexigraphic value the set and the mirror set.
The mirror of a set is calculated by adding 1 to the highest number in the matrix and then
subtracting each of the 5 numbers from this value.

Lexi    Normal SET          Mirror set

000001  01 02 03 04 05  --  39 38 37 36 35
000002  01 02 03 04 06  --  39 38 37 36 34
000003  01 02 03 04 07  --  39 38 37 36 33
000004  01 02 03 04 08  --  39 38 37 36 32
000005  01 02 03 04 09  --  39 38 37 36 31
000006  01 02 03 04 10  --  39 38 37 36 30
000007  01 02 03 04 11  --  39 38 37 36 29
000008  01 02 03 04 12  --  39 38 37 36 28
000009  01 02 03 04 13  --  39 38 37 36 27
000010  01 02 03 04 14  --  39 38 37 36 26
000011  01 02 03 04 15  --  39 38 37 36 25
000012  01 02 03 04 16  --  39 38 37 36 24
000013  01 02 03 04 17  --  39 38 37 36 23
000014  01 02 03 04 18  --  39 38 37 36 22
000015  01 02 03 04 19  --  39 38 37 36 21
000016  01 02 03 04 20  --  39 38 37 36 20
000017  01 02 03 04 21  --  39 38 37 36 19
000018  01 02 03 04 22  --  39 38 37 36 18
000019  01 02 03 04 23  --  39 38 37 36 17
000020  01 02 03 04 24  --  39 38 37 36 16

Mirror Example set = 01 15 22 27 38

39 = numbers in matrix so 39 + 1 = 40

40 -01 = 39
40 -15 = 25
40 -22 = 18
40 -27 = 13
40 -38 = 02

mirror set = 39 25 18 13 02.  Now reverse the order and you have 02 13 18 25 39. The term
reverse-lexi or RL is the lexigraphic value of this mirror set which would be 123489.

123486  02 13 18 25 36  --  38 27 22 15 04
123487  02 13 18 25 37  --  38 27 22 15 03
123488  02 13 18 25 38  --  38 27 22 15 02
123489  02 13 18 25 39  --  38 27 22 15 01 <-------
123490  02 13 18 26 27  --  38 27 22 14 13
123491  02 13 18 26 28  --  38 27 22 14 12
123492  02 13 18 26 29  --  38 27 22 14 11

Notice in the top list of sets how that the first number is 01 in every set while the fifth
number changes in each set.  Now lets say that you think that the lexi value for the next
draw will be between 210000 and 247999. Now if you look at the first numbers of the sets
between this range you will find 210000 = set 04 06 28 30 35 and lexi 247999 = 04 21 31 34 39.
From this information you can see that all the sets between this range start with the number 04.
so if you could range the foward lexi and be correct then the first number in the next draw will
be 04.

209998  04 06 28 30 33  --  36 34 12 10 07
209999  04 06 28 30 34  --  36 34 12 10 06
210000  04 06 28 30 35  --  36 34 12 10 05  <--- starting set
210001  04 06 28 30 36  --  36 34 12 10 04
210002  04 06 28 30 37  --  36 34 12 10 03
""  ""  ""  ""  ""  ""  ""   ""  ""  ""  "
247997  04 21 31 34 37  --  36 19 09 06 03
247998  04 21 31 34 38  --  36 19 09 06 02
247999  04 21 31 34 39  --  36 19 09 06 01  <--- ending point
248000  04 21 31 35 36  --  36 19 09 05 04
248001  04 21 31 35 37  --  36 19 09 05 03

____________________________________________________________________

However if you look at all the 5th numbers of the sets between 210000 and 247999 then you will
find every number from 10 to 39. This is where the mirror and RL values come into play. Notice
that when you mirror the sets then the highest number in the set acts as the first number does
in the normal set, meaning that all the fifth numbers are now in order and the lowest number in
each set changes with each set. Now you can set a range for the mirror. Lets say that for the
reverse lexi we think that the next draw
next draw we think the RL will between 125000 to 195999.

124998  02 14 15 20 22  --  38 26 25 20 18
124999  02 14 15 20 23  --  38 26 25 20 17
125000  02 14 15 20 24  --  38 26 25 20 16  <--- starting set
125001  02 14 15 20 25  --  38 26 25 20 15
125002  02 14 15 20 26  --  38 26 25 20 14
""  ""  ""  ""  ""  ""  ""   ""  ""  ""  "
195997  03 22 25 32 36  --  37 18 15 08 04
195998  03 22 25 32 37  --  37 18 15 08 03
195999  03 22 25 32 38  --  37 18 15 08 02  <--- ending set
196000  03 22 25 32 39  --  37 18 15 08 01
196001  03 22 25 33 34  --  37 18 15 07 06

Looking at the mirror sets we find that the first numbers will be 37 or 38.  So if one chooses
the FL and RL values correctly then the next draws first number will be 04 and the last number
will be 37 or 38.
The software I provided a link to allows the user to set a low and hi range for both the FL and RL
and then it does all the calculations and produces the first and last number/numbers for the
range you have selected. This could be done by hand if you had a list of all the sets for your
matrix but these would be very large files and it could get confusing at times making all the
conversions needed.

For years in my spare time I have been working on this to find a similar method to resolve the
third number from a lexi-like value and consider this the lottery holy-grail. Many SP players
often range numbers by position and this is just another method that could be used. Because of
the way the numbers are sorted by this method the reverse lexi range will be the same as the
foward lexi range. Since this method only requires the first 3 digits of the lexigraphic value
then the fild of choices is limited to these 3 digits.  A 5-36 game would range from 000 to 376
and Powerball is 000 to 500.  The software adds 0's to the end of the low value and 9's to the
end of the hi value.  This ensures that all sets will be covered in the range.  So in a 5-39
game if FL low is set to 015 and FL hi is set to 125 then the range covered will be 015000 to
125999.

The reason for doing this is to give the user a sort of keyed wheel where you can say which number
or numbers are for the first position and which number/numbers for the fifth. If one can correctly
select the range for these values then you will have both the first and fifth numbers within a very
small group.

The program has a set generator that will build all the sets between the low/hi ranges. Depending on
the ranges set this will often be to many to play but if your range selections are correct and produce
one number for both the first and fifth then every set will have a 2 of 5 match. If you could find
a keyed number wheel that would allow you to input the numbers goten from this program and then
allowed all the rest of the numbers to hit as the other three then a three of five could be gotten
within very few sets.

There is quite a lot more to be said about using this in many different ways. I also think that
since we are working with only a 3 digit value that the pick-3 players might be able to add some
good suggestions or help in working out the ranges. A pick-3/4 version of this might also be
possible.

Please feel free to jump in and say whatever turns your knob. I would like to hear any suggestions.
the math behind this and the odds are also welcome. This is a work in progress.

PS if you see something that does not add up then please comment because I may have made a mistake.
will allow me to reply once and may answer others questions at the same time.

RL

Dallas, Texas
United States
Member #4549
May 2, 2004
1834 Posts
Offline
 Posted: April 23, 2011, 2:12 am - IP Logged

Great post RL! Good stuff. I'll have to read it carefully and keep up with everything.

Here's the link to the boxnet file right?  Click the blue to get it.

Nice chart explaining the program too! Thanks!

United States
Member #59354
March 13, 2008
4083 Posts
Offline
 Posted: April 23, 2011, 3:14 am - IP Logged

Gary

RL

United States
Member #105312
January 29, 2011
435 Posts
Offline
 Posted: April 23, 2011, 8:42 am - IP Logged

Below is a list for a 5-39 game showing the Lexigraphic value the set and the mirror set.
The mirror of a set is calculated by adding 1 to the highest number in the matrix and then
subtracting each of the 5 numbers from this value.

Lexi    Normal SET          Mirror set

000001  01 02 03 04 05  --  39 38 37 36 35
000002  01 02 03 04 06  --  39 38 37 36 34
000003  01 02 03 04 07  --  39 38 37 36 33
000004  01 02 03 04 08  --  39 38 37 36 32
000005  01 02 03 04 09  --  39 38 37 36 31
000006  01 02 03 04 10  --  39 38 37 36 30
000007  01 02 03 04 11  --  39 38 37 36 29
000008  01 02 03 04 12  --  39 38 37 36 28
000009  01 02 03 04 13  --  39 38 37 36 27
000010  01 02 03 04 14  --  39 38 37 36 26
000011  01 02 03 04 15  --  39 38 37 36 25
000012  01 02 03 04 16  --  39 38 37 36 24
000013  01 02 03 04 17  --  39 38 37 36 23
000014  01 02 03 04 18  --  39 38 37 36 22
000015  01 02 03 04 19  --  39 38 37 36 21
000016  01 02 03 04 20  --  39 38 37 36 20
000017  01 02 03 04 21  --  39 38 37 36 19
000018  01 02 03 04 22  --  39 38 37 36 18
000019  01 02 03 04 23  --  39 38 37 36 17
000020  01 02 03 04 24  --  39 38 37 36 16

Mirror Example set = 01 15 22 27 38

39 = numbers in matrix so 39 + 1 = 40

40 -01 = 39
40 -15 = 25
40 -22 = 18
40 -27 = 13
40 -38 = 02

mirror set = 39 25 18 13 02.  Now reverse the order and you have 02 13 18 25 39. The term
reverse-lexi or RL is the lexigraphic value of this mirror set which would be 123489.

123486  02 13 18 25 36  --  38 27 22 15 04
123487  02 13 18 25 37  --  38 27 22 15 03
123488  02 13 18 25 38  --  38 27 22 15 02
123489  02 13 18 25 39  --  38 27 22 15 01 <-------
123490  02 13 18 26 27  --  38 27 22 14 13
123491  02 13 18 26 28  --  38 27 22 14 12
123492  02 13 18 26 29  --  38 27 22 14 11

Notice in the top list of sets how that the first number is 01 in every set while the fifth
number changes in each set.  Now lets say that you think that the lexi value for the next
draw will be between 210000 and 247999. Now if you look at the first numbers of the sets
between this range you will find 210000 = set 04 06 28 30 35 and lexi 247999 = 04 21 31 34 39.
From this information you can see that all the sets between this range start with the number 04.
so if you could range the foward lexi and be correct then the first number in the next draw will
be 04.

209998  04 06 28 30 33  --  36 34 12 10 07
209999  04 06 28 30 34  --  36 34 12 10 06
210000  04 06 28 30 35  --  36 34 12 10 05  <--- starting set
210001  04 06 28 30 36  --  36 34 12 10 04
210002  04 06 28 30 37  --  36 34 12 10 03
""  ""  ""  ""  ""  ""  ""   ""  ""  ""  "
247997  04 21 31 34 37  --  36 19 09 06 03
247998  04 21 31 34 38  --  36 19 09 06 02
247999  04 21 31 34 39  --  36 19 09 06 01  <--- ending point
248000  04 21 31 35 36  --  36 19 09 05 04
248001  04 21 31 35 37  --  36 19 09 05 03

____________________________________________________________________

However if you look at all the 5th numbers of the sets between 210000 and 247999 then you will
find every number from 10 to 39. This is where the mirror and RL values come into play. Notice
that when you mirror the sets then the highest number in the set acts as the first number does
in the normal set, meaning that all the fifth numbers are now in order and the lowest number in
each set changes with each set. Now you can set a range for the mirror. Lets say that for the
reverse lexi we think that the next draw
next draw we think the RL will between 125000 to 195999.

124998  02 14 15 20 22  --  38 26 25 20 18
124999  02 14 15 20 23  --  38 26 25 20 17
125000  02 14 15 20 24  --  38 26 25 20 16  <--- starting set
125001  02 14 15 20 25  --  38 26 25 20 15
125002  02 14 15 20 26  --  38 26 25 20 14
""  ""  ""  ""  ""  ""  ""   ""  ""  ""  "
195997  03 22 25 32 36  --  37 18 15 08 04
195998  03 22 25 32 37  --  37 18 15 08 03
195999  03 22 25 32 38  --  37 18 15 08 02  <--- ending set
196000  03 22 25 32 39  --  37 18 15 08 01
196001  03 22 25 33 34  --  37 18 15 07 06

Looking at the mirror sets we find that the first numbers will be 37 or 38.  So if one chooses
the FL and RL values correctly then the next draws first number will be 04 and the last number
will be 37 or 38.
The software I provided a link to allows the user to set a low and hi range for both the FL and RL
and then it does all the calculations and produces the first and last number/numbers for the
range you have selected. This could be done by hand if you had a list of all the sets for your
matrix but these would be very large files and it could get confusing at times making all the
conversions needed.

For years in my spare time I have been working on this to find a similar method to resolve the
third number from a lexi-like value and consider this the lottery holy-grail. Many SP players
often range numbers by position and this is just another method that could be used. Because of
the way the numbers are sorted by this method the reverse lexi range will be the same as the
foward lexi range. Since this method only requires the first 3 digits of the lexigraphic value
then the fild of choices is limited to these 3 digits.  A 5-36 game would range from 000 to 376
and Powerball is 000 to 500.  The software adds 0's to the end of the low value and 9's to the
end of the hi value.  This ensures that all sets will be covered in the range.  So in a 5-39
game if FL low is set to 015 and FL hi is set to 125 then the range covered will be 015000 to
125999.

The reason for doing this is to give the user a sort of keyed wheel where you can say which number
or numbers are for the first position and which number/numbers for the fifth. If one can correctly
select the range for these values then you will have both the first and fifth numbers within a very
small group.

The program has a set generator that will build all the sets between the low/hi ranges. Depending on
the ranges set this will often be to many to play but if your range selections are correct and produce
one number for both the first and fifth then every set will have a 2 of 5 match. If you could find
a keyed number wheel that would allow you to input the numbers goten from this program and then
allowed all the rest of the numbers to hit as the other three then a three of five could be gotten
within very few sets.

There is quite a lot more to be said about using this in many different ways. I also think that
since we are working with only a 3 digit value that the pick-3 players might be able to add some
good suggestions or help in working out the ranges. A pick-3/4 version of this might also be
possible.

Please feel free to jump in and say whatever turns your knob. I would like to hear any suggestions.
the math behind this and the odds are also welcome. This is a work in progress.

PS if you see something that does not add up then please comment because I may have made a mistake.
will allow me to reply once and may answer others questions at the same time.

RL

Thanks RL.  You are a treasure chest of helpful information and a saint for sharing your work.

United States
Member #105312
January 29, 2011
435 Posts
Offline
 Posted: April 23, 2011, 8:57 am - IP Logged

This is a large Excel file (21.3 Megs) but it will give everyone the opportunity to see the combinations and the lexicon equilvalents in the 5/39 games.