Posted: Feb 10, 2008 09:37 Post subject: Developement Software: exploring Cover Designs C(v, k, t)
Last August 07 I began examining cover designs C(v, k, t) or wheels. A quickie generator written in JavaScript proved surprisingly efficient considering the language used and the simplicity of the method. Visual Basic enhanced the system somewhat but still not what I was aiming for.
Many completed wheels were examined from every angle, poked and prodded until my brain hurt. Unfortunately I was not able to isolate any new approach or technique. Every idea had been thought of before, or was a failure.
What did come from re-examining what so many others have already done and attempting to create a better method is a suite of simple functions dedicated to creating better cover designs. They are all contained in a Dynamic Link Library (dll) specifically designed for, but not devoted to, Visual Basic.
The functions within the DLL are:
bitCount: for counting the number of 1 bits in a long data type
combinations: n!/k!(n-k)! [limited to a 32 bit result]
checkCover: counts how many t-sets are covered by a list of k-sets
rankSets: returns the number of unique t-sets within each k-set in a list
bestSet: which k-set most improves the total cover when added to an existing list of k-sets
With these basic functions my test programs create adequate cover designs in a very reasonable amount of time. Each function has been hand written in assembly without any 3rd party optimizers. Since they return a result thousands of times faster than plain Visual Basic, testing alternate theories and methods in this simple to use programming environment does not require hours or days of waiting.
While there are probably better methods employed by other programmers, source code is extremely difficult to locate. That is why each implementation of the functions is truly an original approach. Additionally, to aid in speed, no boundary checks or input validation has been implemented. Use with care, use within specified limits. Please: read the manual!
[ here comes the tricky bit ]
A complete Visual Basic project for creating small enough cover designs utilizing the assembly functions within cover.dll can be downloaded from:
Great job, man! I downloaded and tested your cover processing software. Your package also has the .EXE, so everybody, including non-programmers, can run your project immediately.
I believe the speed is more than adequate. I thought of using your .DLL in PowerBasic Console Compiler. The speed should increase, but there are no forms. The user would input the parameters at the screen prompt, like in my WheelCheck6.EXE:
The WheelCheck.EXE programs generate “lotto wheels” with no bias. All subsets are treated equally. My software attempts to generate ‘totally balanced’ wheels. Of course, the wheels have (many) more combinations than the wheels designed specifically for the minimum size.
I can reduce further the size of “my wheels” by running first the randomized software; e.g. Wheel632.EXE (or Wheel6.EXE in Bright6). I run Wheel632.EXE several times, before I save a partial output. I take that output as…input to Wheel632.EXE. By tedious trial-and-error, I can reduce the wheel size dramatically sometimes. For example, I wanted to reduce the size for what I consider the ideal pool of numbers in lotto 6: 18 numbers. By combining a lot of runs of Wheel.EXE and WheelCheck.EXE, I succeeded to generate lotto 6/18 (4 of 6 guarantee) from 104 combinations down to 45. But the 45-line wheel is far less balanced than the 104-combination 18-wheeler!
I know, the so-called Dimitrov 18-number wheel, ‘4 of 6’, has 42 lines. But that wheel is badly balanced! I saw your program generates a 58-line lotto 6/18-4-of-6 wheel after a number of automatic refinements (a few hundred iterations). Your wheel has a better balance than the Dimitrov’s.
The problem with reducing the wheel size is the balance. I don’t know if it can be done by software entirely. Many of those absolutely-reduced lotto wheels were done manually, long before the personal computers came to life. I remember, in Romania, they had all kinds of ‘reduced lottery systems’ in the 70’s and 80’s.
I think the trick is the division of the pool of numbers in groups. Like you explain for the 12-number case (even numbers in one group, odd numbers in the second group). The famous (49,3,6,163 lines) lotto wheel is actually two-wheels-in-one. There are two separate groups of numbers, which are never combined with one another. The wheel is absolutely imbalanced.
My approach is completely different. I prefer Wheel632.EXE for all the numbers in the game. I know the balance is the best possible. I pursue reduction by applying dynamic filters. I believe the outcome is the best possible, assuring the highest prizes for comparable amounts of combinations.
Your programming approach is probably the most interesting, by using assembly and binary. I am sure you keep working on improving the reduction of combinations. You shouldn’t make your source code public until you patent it. This is a serious topic in mathematics, besides the interest of lotto players. My problem with patenting is mainly time related. Yes, it is also expensive. But it is very much time consuming. I still have to patent my software at one point. When I started to generate lotto combinations (1988), it was largely unknown how to do it in software. My PermuteCombine.EXE still has absolutely unique algorithms. Also in 1988, my software was able to generate balanced lotto wheels, pretty much like WheelCheck6.EXE.
Thanks for allowing us to use your project freely.
Perhaps the library functions could increase the speed of processing for a compiled PB console. I know that any improvement on the Visual Basic side would have to come from removing more VB code. But as stated, VB is oh so easy for testing. I had hoped to create a better generator in VB then convert it to raw asm. However, it’s simply ‘just ok’.
C(18,6,4)=42 was used as a target for most testing. Left long enough the current program can get down to 55 which is where you said your best first attempts reached before alternate refinement. Why it cannot randomly reduce further is probably due to the quantity of total combinations and because the logic does not allow for easy removal of certain sets; it tends to hang onto some when removal would allow better reduction.
I wonder how your shuffle program works. When I examined some small wheels as bits on a grid I could see that swapping any two sets would not change anything. This also applied to columns. Swapping any two columns of bit did not change the covering but did randomize the numbers in the set.
Copyright/Patent is a good thing except when the item produces worse results than others or is another version of existing models. Then, as you’ve mentioned before, protecting that copyright can be a full time occupation. I’ve called this Open Source Cover but that it misleading. Only the methodology is visible at a glance. What is packed into the .dll could be copyrighted but I’ll not bother because without comments I am confident that even someone who solely works with assembly would have some trouble understanding what was going on. I know I get lost sometimes even though each line has a comment. And there are many methods to identify the true author of software which does not prevent usage or resale; rather it proves who wrote it.
Many hours were wasted with coffee and cigarettes under a summer moon trying to ‘see’ how someone could hand assemble an extremely small cover design. My imagination is not that good and I am too reliant on a computer to tell me the answer.
So now I have some real work to do for there are bills to pay. But I am willing to consider additions to the library if anyone should so wish. Free to use yes. Call it an advert as I’d rather be programming than repairing electronics or cleaning dust and malware from computers.
Dim D(2,2) as Long, I as Integer, N as Single
N=0
For I=0 to 2
D(I,0)=N
Next I
Interesting software Dion. I specially like your long/array approach for speed! Bit fields are very powerful when it comes to comparisons!
Some time ago I thought about doing something similar but unfortunately I never got around to do it! My day job is really time consuming!! Have you thought about using other optimization algorithms for the cover improvements? If you have a function to rank lines and you are already using binary strings then a Genetic Algorithm might be interesting... _________________ Just ME here....
Shuffling ain’t no big deal. I think I posted some code here before, when ThornC posted his Python code for lotto frequency groups. I don’ even remember how I came up with my code. It might consist of a combination of randomizing subroutines. But the algorithm very much resembles shuffling a deck of cards.
Here is one of my randomizing algorithms in PowerBasic Console Compiler…
Code:
DIM N AS LONG ‘Total elements in the set to be shuffled
DIM X() AS LONG ‘Create an array with all the elements from 1 to N
FOR I = 1 TO N
X(I) = I
NEXT I
FOR I = 1 TO N - 1
SWAP X(I), X(INT(RND * (N - I + 1) + I))
NEXT I
The new X(N) is pretty well shuffled after just one iteration.
Visual Basic dropped the SWAP statement, so you’ll have to use the old method with a TEMP variable.
You surely can rewrite a shuffling function in assembly. Your assembly skills are still valuable today…good for you. I realized I could not afford to spend time learning assembly. I chose speed of development over speed of execution. I was quite content with QuickBasic and Turbo Basic soon after the compilers were released. I reached a point of real excitement when I realized I could do wonders with the two cheap compilers. I didn’t bother even with C. I still have a bunch of books on assembly and C programming. I still have the MASM 16-bit compiler (Microsoft’s).
If you said you wanted to do things for free, ThornC is the guy to think of cooperating with. He posted a lot of Python code in these forums. He is not a Basic guy, though.
I, too, worked in a computer store as a service techie. I believed then and I believe now that programming is the way out and onto fame and riches!
C(18,6,4)=42 was used as a target for most testing.
I am a bit lost here (maybe because of the time of the night I am looking at this...)
Isn't C(18,6,4,6)>18 ? The formula in this place make me think so... but maybe I got the numbers wrong in my calculation or this is one of those cases where the minimum bounds are impossible to reach..... _________________ Just ME here....
This is different from the original but equivalent in its cover. No matter the number of times two bitwise columns are swapped, the result is the same total cover of 100%.
That’s what I called shuffling sets rather than shuffling 1,2,3,4,5,6,7,8,9,10,12 into random order.
I have read a little of Genetic Algorithms but simply fail to grasp the theory in its entirety without some form of programming as example. Communication via programming is easier for me than deciphering a new mathematical equation featuring unfamiliar symbols.
I’ve recently read a lengthy document featuring examples of about 6 different approaches to Cover Designs. Most I could not see myself investigating as the learning curve is too steep for the time I have available.
C(18,6,4)=42 was a shorthand method of stating that I was attempting to reach the lower bounds of a known wheel significant for being unusually small. When I have more time and motivational drives hit again, I will be taking a much closer look at the page detailing ‘Theoretical Minimum Bound of Coverings.” Thank you for brining that to my attention.
Super Crocodilule Of Lottery Mathematical Endeavors:
Quote:
The general lowest bound L(n,k,t,m)=b
...
This equation comes from a Kari J. Nurmela and Patric R. J. Ostergard technical paper.
That technical paper that I read was meant to be…a treatise in lottery mathematics! In fact, it is an analysis of a lotto 6/49 wheel. It is not even a wheel: A complete set of numbers. The famous world-record breaking wheel in 163 combinations consists of two groups of separate numbers. The lotto numbers in the first set are never combined with any of the numbers of the second set. It is more like two lotto wheels played at the same time.
The equation they talk about in the resource referred to by Cristi ThornC is actually the hypergeometric distribution probability (HGDP). HGDP calculates all possible lotto odds. Only in one case — the jackpot or ‘6 of 6’ — the probability is equivalent to the ‘odds’. Odds is really an odd term! For the other cases — from ‘0 of 6’ to ‘5 of 6’ — we are not talking really about probability. We do not have discrete cases of ‘4 of 6’ for example. All lotto-6 combinations consist of exactly 6 (winning) numbers each.
The probability is calculated as ‘number of Favorable cases over Total possible cases, F/T. HGDP calculates the odds not as F/T, but as ‘exactly one success in N trials’. They say the odds of winning ‘3 of 6 from 49 lotto numbers’ is something like ‘1 in 56’. It means, the player can expect one success if playing 56 lotto draws (with one ticket). We cannot put together 56 lotto 6/49 combinations that guarantee one ‘3 of 6’ ticket. Of course, only in the ‘6 of 6’ case we can put together those approx. 14 million combos that guarantee the lotto 6/49 jackpot!
I thought I had discovered the secret to generate lotto wheels according to the HGDP exactly! I had a few lotto wheeling books in the 1980’s and 1990’s. The 10-number lotto-6 wheels with the ‘4 of 6’ guarantee had 5 lines. My software was generating random lotto combinations, including wheels, since the 1980’s. My software was generating 10-number lotto-6 wheels with the ‘4 of 6’ guarantee in 5 lines. At one time, the program froze after 3 lines! I wrote down the wheel. I generated a few more wheels in 3 lines. I needed to write software to check the wheels for 100% assurance.
I was astonished when I saw all my 10-number lotto-6 wheels with the ‘4 of 6’ guarantee in 3 lines assuring 100% the minimum guarantee! Three combinations represent the odds calculated as exactly (‘1 in two-something). I had reasons to believe that it was the case for all wheeling situations!
An early version of PowerBasic added fuel to the fire! Every lotto wheel I generated in lexicographical order followed the HGDP odds exactly! Alas! My lexicpgraphical software had some bugs. PowerBasic had the bad habit of not resetting the compilation after an error. I learnt sadly that I had to reboot my PC and rerun my software! Only the 10-number lotto-6 wheel followed the HGDP odds exactly, and only for the ‘4 of 6’ guarantee!
There is no formula and no algorithm to calculate the minimum minimorum of a lotto wheel size for various odds. As I said, the only exception is the jackpot case. The 10-number case is an incredible coincidence!
Still, my LexicoWheels.EXE software takes a very original approach to lotto wheeling. LexicoWheels.EXE generates lotto wheels based on lexicographical indexes. The program does all the calculations automatically. Each lotto wheel guarantee (e.g. '4 of 6') has a specific step and a specific start index. A wheel does not have the 100% guarantee for each and every drawing. But it goes like: 0 winners one drawing, then 2 winners next drawing. Or something like 10 winners in 10 drawings. It gets very close to the odds for a large number of trials.
I had a test in newsgroups. An earlier lexico-wheel I generated for a member hit a couple of jackpots in Florida, beating random play by an order of magnitude. Poor Kokostirk lost his speech that day! He still speaks in tongues…as we speak!
It is with relief that I read your words and know I am not crazy or missing some point. For the nth time I browsed web page after page to see minimum bounds for various C(v, k, t) higher than what can easily be generated. Now I understand why. Often it is beneficial to research the answers to questions just as much as it is important to locate the answer. Thorncs’ link was not truly examined; I’ve saved the document for later. However, similar information found everywhere else confused me. With your explanation I’ve found understanding.
Like you, I created scrap programs and piles of paper with scribbled calculations, charts, hypothetical lists and assorted ‘chicken scratches’ all with aim of deducing the lowest bounds. Perhaps I’ll resurrect that line of research now that I have a few tools which enable VB to function better.
One of the first tests I performed with the dll functions happened to be a 10,6,4 with 3 lines. Like you, I thought, “Damn!” but as it turns out, calculated lower bounds can be surprisingly wrong.
Another item searched for during my last info-hunt was a copy of the Dimitrov 18,6,4=42 wheel. I’d heard his name but did not realize the influence he had had on Cover Designs theory and methodology. I am going to have to take the sources word for it as everywhere you go, you need to pay for the information. How can people justify selling access to other people’s information? Do you have a copy of this particular wheel or any other highly prized wheel? Of most interest is a very unbalanced one. I’ve got a few ideas about manipulating the numbers without losing 100% covering in an attempt to balance a lop-sided wheel.
Gotta post this stuff before the winter storm hits my area (and my cold symptoms). The thing I hate most — an ice storm — is also in the forecast for early tomorrow, just before driving to work…
I may not respond to your requests positively from your standpoint. There are copyright issues in play.
That famous world-record breaking wheel C(49,6,4)=163 lines belongs to (principally) a guy from former Yugoslavia: Rade Belic. He and another Eastern-European fellow own the copyright to that lotto wheel. But they placed the wheel in the public domain. You can download and use it freely. You need to google for all the info, including links to the download.
The 42-line wheel(18,6,4)=42 lines (hope I complied with the complicated format) by Dimitrov appears to be strictly copyrighted. I own a copy from an old newsletter from Gail Howard. I don’t remember exactly how I got that copy of the newsletter that shows several lotto wheels, all Dimitrovs. I did NOT find the wheels of much interest. The wheels they showed to me were badly imbalanced. Easy to check with the frequency or statistical analysis routines in my Util.EXE or MDIEditor And Lotto WE. If a lotto 6/49 wheel has 163 lines, analyze all 163 lotto-6 combinations.
I listed (advertising was not the main goal) two lotto wheels (18,6,4). I have always recommended the Cover (18,6,4)=51 lines as the best lotto wheel ever to consider. The wheel is very well balanced. Its size also makes it efficient from a cost-to-prize ratio viewpoint. I created that lotto wheel several years back in the newsgroups (when I was a whole lot more active; other guys of worthwhile intentions were also very active). One of the main cooperators was the creator of that piece of worthy software named CoverMaster.
The 51-line lotto ‘(18,6,4)=51 lines’ wheel is the tightest-and-most-balanced wheel ever created. The wheel(18,6,4) created by Dimitrov has, indeed, 9 fewer lines. But the Dimitrov wheel is badly imbalanced. They created such smallest-size lotto wheels by GROUPING the numbers. Numbers were divided in groups. This number group was favored to combine with numbers from that group. But if you knew that this 10-number group had to be wheeled (combined) with that 8-number group — why do you need to wheel two groups, anyway? Just play a 10-number wheel — and also an 8-number wheel! Play the two groups in the same draw! It is cheaper and far more efficient!
When I said I reduced my lotto wheel ‘(18,6,4)=45 lines’, I also mentioned that the balance was lost. Check and see the frequency of individual number and also the ‘most’ and ‘least’ pairings.
The lotto wheel ‘(18,6,4)=45 lines’ and the lotto wheel ‘(18,6,4)=51 lines’ are in my SYSTEM6.EXE lotto wheel packages.
I stopped lotto wheeling analysis for all intents and purposes. Of course, you will continue research with all head-on force, if you find gnoseological interest. Nothing can stop Homo sapiens on the path of knowledge. Lions, tigers, cobras, viruses…you name it…no beast could stop the little-guy-beast on its run-for-dear-life-leading to knowledge…
I couldn’t make it to work today. It was my cold, not the weather. As I said, it is easier to forecast the lottery, than the weather. The set of elements is limited in gambling, than weather-wise. In gambling (or lottery) missing is very acceptable. The player accepts the idea of losing a number of trials by playing a reduced set of elements. The bottom line is to make a profit: Win exceeds Cost. In weather forecasting, there is no recuperation sometimes. For example, the weather guy did not forecast a tornado. The person who was killed by the tornado has no way to recoup the loss!
So, I drank a lot of hot medication that fights the cold. I might be a little grumpy now because of that. ‘Cuz I am really disappointed by Big Brother Google lately. Speaking of lotto wheels. I just did a google on the two keywords. My web site is not listed even in the top 100 results!!! Is it listed in the top 1000??? No false modesty — but I can’t believe it! A while ago, a google on lotto wheels listed two pages at saliu.com as #1 and #2 in the search result list! What a hell of a change!
But just look at the top 100 list for lotto wheels. There is a whole lot of crapp from top to bottom! It’s not only that my web site is missing. I remember other worthy websites that were listed high on lotto wheels searching. The same is valid regarding searches on ‘lotto software’ or ‘lottery systems’, ‘gambling’ stuff, theory, software… What the hell happened to the Google. algorithms? Lately, they list very high the lowest kind of garbage! It is valid for many other fields. For example, I was unable to use Google for paid membership software. I asked for help in some forums. I did a whole lot of searching and researching before I came across a really useful resource (aMember, in my case). That resource is of high value to many people, because the resource is worthy in itself and by itself. The searK engines are totally ignorant of the intrinsic value, in this particular case (and probably most cases).
Going back to the lotto wheels concept. I am not biased in favor of saliu.com. But let’s look honestly at just one piece of lotto wheeling software: LottoWheeler.EXE. I don’t think one can find a bit of a counter-argument here: LottoWheeler.EXE is the best lotto wheeling software. What else handles with so much ease the action of wheeling lotto numbers, including for Powerball, Mega Millions, Euromillions? Add to that piece of software the entire theory of lottery wheeling presented at saliu.com, plus the entire list of software.
What happened then? Google went from considering saliu.com the best lotto wheels site to considering it as an irrelevant site. Google had a few years back another such severe lapse. I think they called it the Florida Update. Google intentionally removed the best web sites from the top list of search results, especially in the case of popular keywords. Google’s idea was simple greed: If a popular search is high, the high-ranked websites must be willing to pay for Google advertising. If I know that my website is not listed high on lotto wheels, which seems to be a popular search, then I must pay for Google advertising! We all know by now that people have the tendency to choose the ads (the so-called ‘sponsored links’) over the results of searching. I’ve done it many times! Especially now, when the natural results of the search represent pure junk. The ads seem to represent superior resources in most cases!
My advertising campaign would be a very expensive adventure. My website deals with a large number of topics. Not to mention that some Googles (employees) are resentful guys. I received invitations from Google to advertise (Goggle AdWords). I tried once for ‘lotto, lottery, gambling software’. It started…but it never started! The resentful guys informed me that they stopped my AdWords campaign because Google no longer accepts gambling advertising! But they still ask me to come back and advertise! I tried again once — the same result. Gambling advertising not acceptable by Google!!!
It might be also the result of complaining. Google applied lately a campaign of listening to complaining. Problem is, they don’t realize that complaining is the result of hatred for the most part. How come Google didn’t realize that the overwhelming majority of the complaints are by hateful guys complaining against their competitors??? I have never complained against anything or anybody — competitor or not. Meanwhile, google might listen to the complaints against my site filed by the likes of Kokostirk, Kulai, Kotkoduck, Karaklonchah, Kotskarr…
Whatever it is…it is bad news for Google in the first place. Honesty made them number one. Dishonesty will not keep anybody as number one, in any field. Microsoft knows it better than anybody else. They feel in serious danger because of their dishonesty dealing with the competition. They are aware that their search engine is totally irrelevant. Microsoft wants now badly to buy Yahoo. They offer over 40 billion US dollars to buy the Yahoo search engine. Yahoo resists, honestly I think. Yahoo realizes how important the Internet search is. A good business step — and Yahoo might be in the position to buy Microsoft$! By the way, the Microsoft search engine absolutely bans in their search any resource containing the text string ‘saliu’. China and Iran do the same thing: Saliu is taboo! Probably the Vatican, too! Probably Dubbyia’s White Hou’, too!
So many so-called giants have risen and fallen on the computer planet! I only mention here real pioneers: Word Star, Lotus, WordPerfect, Ashton-Tate (dBase III)… Dishonesty played the major role in the deadly falls…
‘To thine own self be true’ — Google used to rank my website very high on that search. Honestly, it should have not. I only wrote a few sentences on the Shakespearean concept inspired by Socrates (Know thyself). Appears that Google lost track of that important adagio: To thine own self be true.
It appears that Ion Saliu and what he writes are of major interest to Google. They follow me faithfully wherever I go. Say, there is a forum of very low interest google-wise. But as soon as I post there, Google indexes the page immediately. Do a search on Ion Saliu and that new resource is ranked pretty high. I put many spots on the map as a result of my posting there.
I did an experiment. I made this message board for registered members only. It happened between March of 2007 and January of 2008. Goggle bots were also banned from indexing this very message board. The bots cannot register — only humans can register!
Before the registration was required, I would see a large number of googlebots as visitors. During the registration-required period, the number of trying googlebots dropped dramatically. Now, when everybody and everything may freely access this message board, the numbers of googlebots is high again. It is at least three, at any given time of the day when I access my message board. There are displays like this one:
Quote:
In total there are 6 users online :: 1 Registered, 1 Hidden and 4 Guests
The majority of the guests are:
Code:
66.249.70.42
Host resolves to:
42.70.249.66.in-addr.arpa domain name pointer crawl-66-249-70-42.googlebot.com.
Whois record:
[Querying whois.arin.net]
[whois.arin.net]
OrgName: Google Inc.
OrgID: GOGL
Address: 1600 Amphitheatre Parkway
City: Mountain View
StateProv: CA
PostalCode: 94043
Country: US
I can imagine the attention was appreciated in the beginning, as with a movie star and the first encounter of paparazzi. Now I can imagine you’ve become blasé and accept someone is watching continually. Hope you don’t get paranoid.
I wonder if you’ve been targeted from a generic list or have had dedicated ‘bots’ cycle through all your sites. Or, more likely, it’s not of conscious human construction but rather you are the target of a logical analysis of search input queries building a fuzzy logic probably beneficial results or which most people have clicked on in the past.
I’ve got a few aliases which I use for various areas of interest. Each one can generate a modest amount of google results. Enough to give me that warm fuzzy feeling of being someone, of having left an impression.
Google should watch what they are doing. They are getting pretty invasive. Adverts in everything. Not as bad as MSN which I’ve permanently blocked from spamming me from rad.msn.
Ion, you’ve put yourself in a position where everything you say is of interest to someone. I’ve gone the other way, where hours of work and thousands of words ultimately lead to a singular item of interest.
Saw some frozen waterfalls on the news in your area last night. Understand what you were saying about being clod and snowed in the other day.
Posted: Mar 17, 2009 20:47 Post subject: cover.dll
hi i have been looking at your program and trying to see the code but i cannot access the cover.dll file
i am using VB2005 a .net version
do you have a code listing of the dll file that i can down load?
or what do i need to be able to take a look inside it and see the code?
i am new to this type of coding so need a littel mor help.
thanks steve
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