Parpaluck
2009-12-31 16:39:28 UTC
Wheeling Mathematics by Ion Saliu
Hello, again, RGL-ers, respectful and respected colleagues of mine!
Have a wonderful New Year 2010!
I announced a while ago about my book on theory of probability. I
would like to share with you now a lotto wheel. I know how much you
love the lotto wheels (that is, a majority of RGLers).
One chapter of my book is dedicated to the proto-mathematics of
lottery. You’ve already heard of attempts of mathematical treatises of
so-called “lotto designs” or ‘covering designs”. My viewpoint is also
clearly expressed at my website:
http://saliu.com/gambling-lottery-lotto/lottery-math.htm
(“Introduction to Lottery Mathematics: Probabilities, Appearance,
Repeat, Affinity or Number Affiliation, Wheels, Systems, Strategies”).
I prove that there are no mathematical formulae or theorems to improve
the coverings or lotto designs. There is only one method, more like
trial-and-error. I call that method “randomization”.
Many here remember we had at least two serious debates related to
lotto wheeling. I refer only to the debates I participated with my own
lotto wheels. Of course, there is no wheeling debate without Robert
Perkis, I called, at that time, Wheely! He is now known as Kotkoduck.
How about Koverker, the author of CoverMaster? And, hey, no lotto
wheeling debate is valid without the participation of Kokostirk (aka
Joey Roberts).
I make available another lotto wheel now — still for 49 numbers with
the ‘3 of 6’ minimum guarantee. My software only generates “balanced
lotto wheels”: All numbers are treated equally. By contrast, the world-
record lotto wheel in 163 combinations is two groups of numbers in
one. That’s the “design” the lottery protomathematicians analyze in
their university papers.
My lotto wheeling software is named WheelCheck6.EXE. It is part of a
large integrated lotto software package known as Bright6.exe. All my
software is free to use but the download requires paid membership (a
nominal fee). Easy to see th terms and easy to apply for membership
(most RGLers already are members):
http://saliu.com/membership.html
WheelCheck6.EXE also checks for missing lines in a lotto wheel. The
program generates larger lotto wheels in order to strike mathematical
balance (equal treatment of all numbers). The '3 of 6 from 49' lotto
design generated by the WheelCheck6 program consists of 514 lines. The
numbers are fairly equitably distributed, but there is a bias towards
the first 3 numbers. The bias is caused by the fact that the
lexicographical lotto generation starts with #1. If we did the
generation in descending number (starting at #49), then the bias would
favor #s 49, 48 and 47.
I was able to reduce this lotto system down to 412 combinations. The
minimal guarantee was preserved, while the balance was improved. The
procedure is painstaking, however. First, I generated all 13983816
combinations in lexicographical order. It is a huge file (it can be
also downloaded from my site)! Next, I ran another great piece of
software I created: Shuffle.EXE. Among other functions, the program
shuffles a text file. That is, the lines of a file are distributed in
a random manner. (The randomized 13983816 combinations can be also
downloaded at my software site).
I will post the 412-line lotto wheel in the very next post.
Here is the deal. Everyone can try here to improve the wheel. The
individual numbers are very closely distributed: from 11.2% to 13.8%
frequency-wise. Every lotto number is paired with the rest of the
numbers. The frequencies are less balanced: from 2 times to 9 times.
One section where the wheel can be improved.
Total triplets for 49 numbers: 18424. A number of 10184 triples are
not generated (frequency = 0). Another place for improvement.
The improvement can be achieved via randomizing. You don’t need to
generate the 13983816-line file and then shuffle it. I uploaded both
files to the members-only area of my site:
http://saliu.com/code/CombosLotto.649 (“All lotto 6-49 combosnations”
= 340 MB)
http://saliu.com/code/SIM-6 (“All lotto 6-49 combinations: Shuffled to
SIM-6” = 326 MB).
But it is required to shuffle several times CombosLotto.649. You
should never overwrite that file. I recommend you preserve also every
randomized file. For example: Random649.1, Random649.2, Random649.3,
etc. I can be useful also for generating other types of coverings,
like ‘4 of 6’.
The randomization itself only takes minutes. The real lengthy process
is generating the wheel. You use WheelIn6.exe, also part of
Bright6.exe (option ‘F = Wheels from Files’). You enter the name of
randomized file as input (e.g. SIM-6 or Random649.1). It took me
around 4 hours on my pretty well-equipped and fast PC to generate the
412-line wheel.
The tightest wheel published here will be the winner. The winner will
get ALL my software (EXE files) on a CD, plus an autographed copy of
my book on probability theory.
Take advantage of the opportunity! Best of luck to all!
Ion Saliu,
The True-and-Only Parpaluck
Hello, again, RGL-ers, respectful and respected colleagues of mine!
Have a wonderful New Year 2010!
I announced a while ago about my book on theory of probability. I
would like to share with you now a lotto wheel. I know how much you
love the lotto wheels (that is, a majority of RGLers).
One chapter of my book is dedicated to the proto-mathematics of
lottery. You’ve already heard of attempts of mathematical treatises of
so-called “lotto designs” or ‘covering designs”. My viewpoint is also
clearly expressed at my website:
http://saliu.com/gambling-lottery-lotto/lottery-math.htm
(“Introduction to Lottery Mathematics: Probabilities, Appearance,
Repeat, Affinity or Number Affiliation, Wheels, Systems, Strategies”).
I prove that there are no mathematical formulae or theorems to improve
the coverings or lotto designs. There is only one method, more like
trial-and-error. I call that method “randomization”.
Many here remember we had at least two serious debates related to
lotto wheeling. I refer only to the debates I participated with my own
lotto wheels. Of course, there is no wheeling debate without Robert
Perkis, I called, at that time, Wheely! He is now known as Kotkoduck.
How about Koverker, the author of CoverMaster? And, hey, no lotto
wheeling debate is valid without the participation of Kokostirk (aka
Joey Roberts).
I make available another lotto wheel now — still for 49 numbers with
the ‘3 of 6’ minimum guarantee. My software only generates “balanced
lotto wheels”: All numbers are treated equally. By contrast, the world-
record lotto wheel in 163 combinations is two groups of numbers in
one. That’s the “design” the lottery protomathematicians analyze in
their university papers.
My lotto wheeling software is named WheelCheck6.EXE. It is part of a
large integrated lotto software package known as Bright6.exe. All my
software is free to use but the download requires paid membership (a
nominal fee). Easy to see th terms and easy to apply for membership
(most RGLers already are members):
http://saliu.com/membership.html
WheelCheck6.EXE also checks for missing lines in a lotto wheel. The
program generates larger lotto wheels in order to strike mathematical
balance (equal treatment of all numbers). The '3 of 6 from 49' lotto
design generated by the WheelCheck6 program consists of 514 lines. The
numbers are fairly equitably distributed, but there is a bias towards
the first 3 numbers. The bias is caused by the fact that the
lexicographical lotto generation starts with #1. If we did the
generation in descending number (starting at #49), then the bias would
favor #s 49, 48 and 47.
I was able to reduce this lotto system down to 412 combinations. The
minimal guarantee was preserved, while the balance was improved. The
procedure is painstaking, however. First, I generated all 13983816
combinations in lexicographical order. It is a huge file (it can be
also downloaded from my site)! Next, I ran another great piece of
software I created: Shuffle.EXE. Among other functions, the program
shuffles a text file. That is, the lines of a file are distributed in
a random manner. (The randomized 13983816 combinations can be also
downloaded at my software site).
I will post the 412-line lotto wheel in the very next post.
Here is the deal. Everyone can try here to improve the wheel. The
individual numbers are very closely distributed: from 11.2% to 13.8%
frequency-wise. Every lotto number is paired with the rest of the
numbers. The frequencies are less balanced: from 2 times to 9 times.
One section where the wheel can be improved.
Total triplets for 49 numbers: 18424. A number of 10184 triples are
not generated (frequency = 0). Another place for improvement.
The improvement can be achieved via randomizing. You don’t need to
generate the 13983816-line file and then shuffle it. I uploaded both
files to the members-only area of my site:
http://saliu.com/code/CombosLotto.649 (“All lotto 6-49 combosnations”
= 340 MB)
http://saliu.com/code/SIM-6 (“All lotto 6-49 combinations: Shuffled to
SIM-6” = 326 MB).
But it is required to shuffle several times CombosLotto.649. You
should never overwrite that file. I recommend you preserve also every
randomized file. For example: Random649.1, Random649.2, Random649.3,
etc. I can be useful also for generating other types of coverings,
like ‘4 of 6’.
The randomization itself only takes minutes. The real lengthy process
is generating the wheel. You use WheelIn6.exe, also part of
Bright6.exe (option ‘F = Wheels from Files’). You enter the name of
randomized file as input (e.g. SIM-6 or Random649.1). It took me
around 4 hours on my pretty well-equipped and fast PC to generate the
412-line wheel.
The tightest wheel published here will be the winner. The winner will
get ALL my software (EXE files) on a CD, plus an autographed copy of
my book on probability theory.
Take advantage of the opportunity! Best of luck to all!
Ion Saliu,
The True-and-Only Parpaluck