No announcement yet.

Looking for Reiterative Solution

  • Filter
  • Time
  • Show
Clear All
new posts

    Hi David. I mentioned Gail Howard because she was (AFAIK) the first
    to suggest that the lottery could be beat through some form or
    strategy. She was mentioned again in earlier discussion after I
    had made reference to her, with a quote where she claims to having
    created many winners. My last comment was to point out that her
    system probably served better in the 1980's when lotteries used far
    fewer balls, and the odds were not as severe.

    I dismissed most of her claims from the get-go. Arguing Evens and
    Odds, or neighbors, or pairs, or triples, or averages, made no
    sence to me. Those were just apparent associations. In my mind
    it was just as likely that 2 was neighbored with 37 or 50, as it
    was to 1 and 3. Thinking that certain numbers would get "hot"
    and go pop! pop! pop! in close succesion seemed improbable and
    unreasonable, but there did seem to be some tendency in that
    regard at certain times, but never very much or very long. Again,
    it is our minds trying to make sence of what we see.

    So I wasn't promoting Gail Howard or her system. But I've noted
    that all competitors seem to make similar claims. If one is
    going to promote Evens and Odds as a gimick for playing the
    lottery, they all seem to want to do the same.

    I did buy her system many years ago, but only because she provided
    details of all the lotteries then going on as part of it. I
    could not find that information idependently - the question of
    how we ever managed to do anything before the Internet is a valid
    one. I wanted to know what lotteries and how they played so that
    I could look at all their histories, rather than be limited to
    just observing one. The USA Today was a boon because it published
    results for lotteries, and you could find it anywhere. I kept
    scrapbooks for several years of lottery results as I built up
    programs and entered in the data by hand to work against them.
    Now I just plug in a couple of URLs that publish the results and
    let my program pull down past drawings. Currently I limit my
    history to about 60 months of data.

    I roughed out one time that of the six balls that are drawn, that
    2 of them, give or take 1, would be what you might call "hot"
    numbers, having occurred once or twice in say, the last twelve
    drawings. Another two balls, plus or minus 1, would have been
    played in say, the last 48 drawings. And 2 balls, plus or minus
    1, would not have been played in recent history. Now if this
    makes sence, then focusing exclusively on "hot" balls is going
    to only deal with one to three of the balls likely to be drawn,
    and you might have a sizeable pool just to deal with them. You
    are also excluding three to five of the balls needed to make up
    the winning pick. So while you might increase your odds of
    getting one to three balls right, you have effectively cut down
    your chances at a bigger prize. One of the sites I consulted
    said pretty much the same thing, but did it from a mathematical

    This guy had done a lot to probe and document various games of
    chance, including lotteries. Here are a couple of other useful
    links to his various web pages, and other sites:

    Old Navy Chief, Systems Engineer, Systems Analyst, now semi-retired


      Hi Donald,

      I didn't think for one minute that you were promoting Gail Howard. I'd never
      heard of her and went to her site out of curiosity.

      There is one test that Robert mentioned and I followed up by mentioning that I'd
      used it myself, namely chi-squared.

      Basically, a system is assumed to be un-biased and then a chi-squared analysis
      is carried out to see if there is some, strong or very strong evidence to doubt
      the assumption. In other words it compares what we have with what we'd get at
      random and if any deviation then if that deviation is sufficient to doubt what
      we have is indeed random?

      If what we have does not put a system's bias into doubt then it is pointless
      using a method which uses historical data because that data is deemed to be
      not sufficiently different to being 'flat'. By 'flat' I mean, in the context of
      lotteries, each and every number has occurred an equal number of times.

      In other words there's no point in using a history method when the system,
      effectively, hasn't got one.

      On the other hand, given doubt then keep very quiet about it and put
      some overtime in at the 'factory'.


      I haven't got any of my old code to hand, written on an Atari ST , and needed
      a sextuplet generator to test some of Howard's claims. Instead of a brute force
      method which could see RND used many more times than six per set I wrote a little
      Sub to emulate the lottery machine. That is, select a number from [1,49], then
      from [1,48] and so on. The [1,49] is, of course, fixed and the subsets [1,48],
      and so on, are 'merged' by skipping numbers in the [1,49] already chosen. With
      this method RND is only used six times.

      If you'd like a copy to play around with, let me know and I'll post it here.

      I'll have a look at your links later.

      David Roberts

      [This message has been edited by David Roberts (edited January 14, 2005).]


        Thanks, I would appreciate that. I had a bit of college math,
        and a short course in statistics several decades ago. My strong
        suit was the computer and systems training I got in the Navy, and
        I worked up from machine language to various programming languages.
        As a Systems Engineer, I had myrad hardware and software
        responsibilities, and as a Systems Analyst, I had more to do with
        collecting performance data and devising methods of finding the
        rule, then applying the rules to spotting the troublesome exceptions.
        I got real good at manipulating data that was intended to be read by
        human eyes and reducing it to a form that machines could handle.

        So It's not like I didn't earn my titles or deserve my pay. But It
        just takes me longer to get a handle on the math involved. I don't
        read advanced math notation very well, since little of it surfaced
        in my courses. If mathematics is the universal language, then for
        the most part I have been rendered deaf and dumb.

        But I can write code. And if I can understand the notation, I
        can correlate it to coding processes. I guess I'm part of a
        small group that feels that coding is a better (and more
        practical) way of speaking the universal language.

        So yes, I would be pleased to see what else you have to say on
        the subject.

        As to a random process for picking a series of lottery numbers,
        this technique works well:

        Assume a drawing of 53 balls, of which six will be needed:
        DIM balls(1 TO 53) AS BYTE
        FOR a=1 TO 53
          balls(a)=a              'set up the balls first
        RANDOMIZE                 'randomize the random seed using timer
        FOR a=1 to 53             'ensure every ball is targeted
          b=RND(1,53)             'point to any other ball position 
          SWAP balls(a),balls(b)  'swap every ball at least once
        DIM picks(1 TO 6) AS BYTE 'these will be our current picks
        for a=1 to 6               'there will be six balls
           b=RND(a,53)             'the random pick comes from unpicked balls
           SWAP balls(a),balls(b)  'this is now at least two sorts on balls
           picks(a)=balls(a)       'we move the selected ball into Picks()
        It's essentially the same method I use for suffling and dealing
        cards, but in this case I worked from the bottom instead of the
        top. Note you do not have to set up the balls again before you
        start the next drawing - The selected balls are still in the
        balls array, and will be resorted and picked from, right along
        with the rest. You just begin at the label called next_game.
        This method causes more sorts on top of prior sorts, making the
        outcome more difficult to predict - unless you can account for
        all the changes each sort produces.

        I've heard that story before, about a lottery being based on a
        pseuod-random process, and I've also heard that some genius of
        a programmer has broken the random process used to pick the
        cards dealt in one of the online poker games. I don't believe
        either one.

        First, while lottery officials are possibly stupid enough to trust
        the randomness of PRNG in a computer, no competent programmer
        should be that ignorant.

        Second, the amount of times that the drawing has to occur in
        order to build history before it starts over has got to be a real
        long time, and what lottery has that much history?

        Third, the order of the balls as they come up in the drawing is
        rarely reported - instead, we see the picks displayed in a
        numerical sequence. That would be disruptive to efforts to
        recognize the sequence of those numbers in the random sequence.

        Fourth, we would have to assume that the random sequencer was
        never interrupted, never reseeded, and never used for anything
        else. Now how probable is it that one computer sits there with
        power on, doing nothing but sitting there waiting for the next
        lotto drawing? It could not even be used for any type of game
        or additional drawings, unless each instance of an PRNG was
        fully independent of all other instances. Even the lottery
        program could not be terminated and restarted for this condition
        to hold true.

        The online poker game concept is even harder to defend. You can
        have multiple servers and multiple programs running concurrently,
        and during play you only see a portion of the cards that are
        dealt, and never enough or close enough in sequence to be sure of
        just how the play is going to go. Every game should follow a
        reshuffle of the card deck, and the deal will vary according to
        the number of players at the table. For some games (not Hold'em),
        if a player folds, it will change the outcome of the rest of the
        game. Most players will not disclose their hold cards if they
        lose, so you have nothing there to add to your observations. And
        not all random number sequences are alike - some programmers
        chose to implement their own, or apply them in different ways.

        You cannot be sure if the same program is serving several tables
        at the same time, or if there are multiple instances of the
        program running. The a single program is serving several tables
        at once, using different decks, the random process will be split
        between the shuffles and deals done for those tables, so the
        information from one table would be incomplete. The only thing
        you can possible try to cue a forward reference from is the game
        number, but I see no evidence that the game number is directly
        associated with the random process for the hand that follows.

        If you want a challenge, try to figure out if observing a lottery
        or poker game would (1) provide enough information to determine
        if a PRNG is involved; (2) establish how long (how many games)
        it would take to reach this conclusion, and (3)whether the
        results could be used to project the winning picks or strategy
        for the game.

        Right now, it think people that have just a little bit of
        knowledge have gotten a bit fanciful in what they think you can
        do with that knowledge, and have added to urban legends in their
        efforts to persuade others by claiming that it really happened.

        Old Navy Chief, Systems Engineer, Systems Analyst, now semi-retired


          By the time BYTE is changed to LONG and the first FOR/NEXT is removed your
          code is almost the same as mine.

          I've put mine into a Sub but do not not employ RANDOMIZE within it. I
          execute RANDOMIZE in PBMAIN and forget about it.

          I only used it to generate large sets of sextuplets but since the code churns
          out about 10,000 sets a second on my 600MHz machine then a request for, say,
          2000 sets could see TIMER unchanged as it is only updated once per second.

          You probably know this trick but in case not if a Sub is used then we can use
          SUB GetSel( Picks() AS LONG)
          DIM balls(1 TO 53) AS STATIC LONG
          STATIC SecondEntry AS LONG
          LOCAL a AS LONG, b AS LONG
          IF SecondEntry = 0 THEN
            FOR a = 1 TO 53
              balls( a ) = a
            SecondEntry = 1
          END IF
          blah, blah, blah
          where balls() is set up only on GetSel's initial call.

          <So It's not like I didn't earn my titles or deserve my pay. But It
          just takes me longer to get a handle on the math involved.>

          The older I get the longer it takes me to get a handle on anything!

          <I guess I'm part of a small group that feels that coding is a better
          (and more practical) way of speaking the universal language.>

          When I read mathematics I didn't read it alongside a main subject,
          it <U>was</U> my main subject but it eventually splits into either
          a 'Pure' stream or an 'Applied' stream. I went the 'Applied' route
          but that split into a 'Statistical' stream or a 'Numerical' stream.
          I went with the 'Numerical' stream. As a Numerical Analyst I was a
          very different animal to my friends who were 'Pure' mathematicians.
          The 'Pure' mathematicians were almost invariably destined for academic
          life with the rest of us being able to speak mathematics and English.

          <Third, the order of the balls as they come up in the drawing is
          rarely reported - instead, we see the picks displayed in a
          numerical sequence. That would be disruptive to efforts to
          recognize the sequence of those numbers in the random sequence.>

          I don't figure this to be important especially since a particular
          number, if picked, will only be picked once a drawing.

          It's worth remembering that with multiple machines and multiple sets
          of balls the chosen equipment is not known a priori so any trends
          are analogous to trends of mankind rather than trends of
          ethnic groups.

          <Right now, it think people that have just a little bit of
          knowledge have gotten a bit fanciful in what they think you can
          do with that knowledge, and have added to urban legends in their
          efforts to persuade others by claiming that it really happened.>

          We could take that out of context and apply it generally.

          David Roberts


            david, i think you might be interested in the posts from ion in
            this thread:
            he seems to be on a different track than you are, and you might
            enjoy. or at least be interested, in the discussion underway.

            old navy chief, systems engineer, systems analyst, now semi-retired


              <He seems to be on a different track than you are, and you might
              enjoy. or at least be interested, in the discussion underway.>

              From Ion,

              <Everything is ruled by mathematics, as all wise humans know by now. Didn’t wise
              Plato put this inscription at the frontispiece of his Academy?

              ”Let no one enter here who is ignorant of mathematics.”>

              I am in no doubt that he is on a different track to me.

              However, we are travelling in the same direction.

              From Ion,

              <Of course, there is no 100% certainty in lottery, either. But the main thing is to
              play smaller amounts of combinations at the most favorable moments. Yes, there are
              such favorable moments that lead to a profit.>

              I agree entirely. There have been many favourable moments.

              However, as far as I know, no one on this planet has ben able to predict them.

              I didn't find any accounts on Ion's site detailing his winnings in the last twelve
              months, for example.

              Added: Here's an idea for you to think about: Retrospective prediction.

              The UK lottery has had 945 drawings so far. Take the first 800, for example, and apply
              any historical method to predict the 801 drawing. Now move the base from '1 to 800'
              to '2 to 801' to predict the 802 drawing and so on. We can do this 145 times before
              we run out of data. Now analyse the results.

              David Roberts

              [This message has been edited by David Roberts (edited January 16, 2005).]


                Yeah, I tried that years ago. I also allowed for a sliding
                window that could be expanded or contracted, and to look from
                1 to ten drawings ahead. The results were disappointing. While
                I could look at the data and come up with a specific case or rule
                that appeared useful, the program would show that in the general
                case, there was no clear precursor or pattern.

                Old Navy Chief, Systems Engineer, Systems Analyst, now semi-retired


                  I'm not surprised.

                  Before this thread drifts into the ether I should mention another use
                  for the Hypergeometric probability function.

                  So far, we have used

                  N=population size
                  n=sample size
                  k=number of items in population labelled "success"

                  h(x; N, n, k) = ( kCx * (N - k)C(n - x) )/NCn ... [1]
                  where x = 0, 1, ... , k.

                  with, for example, N=53, k=6 and n=16 (ie the pool size)

                  Going in the opposite direction we can use k as a pool and sk as a
                  subset of k to denote an interest in the behaviour of singletons,
                  doubles, triplets and so on.

                  We now have

                  h(x; N, k, sk) = ( skCx * (N - sk)C(k - x) )/NCk ... [2]
                  where x = 0, 1, ... , sk.

                  For N=49 (as in UK), k=6 and sk=1, for example, we get

                  h(1)=0.12244897 (ie 1 - h(0))

                  So, the probabilty of a number from N not appearing in k is h(0).

                  For it not to appear in two consecutive weeks is 0.87755102^2.

                  For j weeks we have 0.87755102^j.

                  We can ask, how many weeks will a number need to be not selected for
                  that probabilty to be <= 0.05.

                  ie 0.87755102^j = 0.05

                  giving j = 22.93.

                  So, the chance of no selection for 23 weeks is < 0.05.

                  This morning, 19 Jan, for the UK lottery, 34 has not shown itself
                  for 28 weeks 34[28] and 21 has been absent for 23 weeks 21[23]. The
                  next four are 3[22], 2[20], 13[18] and 14[17].

                  Now, one school of thought would argue that 34 is a 'hot' number on
                  the basis that if non-bias rules then 34 will have to 'come back'.
                  However, this throws away some information, namely that 34 is <U>currently</U>
                  suggesting bias. Note that I refer to # 34 and not ball 34. We know,
                  only after the event, which sets of balls are used so we cannot consider
                  a particualar ball. We don't need to, # 34 is not behaving as expected.

                  I would argue for excluding both 34 and 21 and, perhaps, 3 ie treat
                  them as 'cold' numbers.

                  Excluding all three reduces my selecting from 49 to 46.

                  49C6 = 13983816
                  46C6 = 9366819

                  No great shakes but better than a poke in the eye with a sharp stick.

                  It should be remembered that the excluded numbers are not prohibited
                  numbers so they may appear in the next draw but this does not contradict
                  our argument. On the contrary, 5 weeks ago 34 had been absent for 23
                  weeks so its exclusion would have been correct <U>to date</U>.

                  The point of this approach is that it is a suggested better tack than
                  'assuming non-bias then...' because if non-bias then prediction is pointless
                  and we should simply generate a random selection.

                  On the other hand if a hint of bias at this point in time then, IMO, back it.

                  If the argument is false then we break even.

                  If we end up reducing our chances then this proves bias but we chose the
                  wrong direction.

                  My two cents is on exclusion.

                  In [2] above we can use sk = 1 to 6.

                  Added: One web site has <Most 'overdue' numbers> = 34, 32, 21, 3, 2, 13
                  even though last Saturday saw 32 being drawn.

                  I agree with them if I go back to last Friday so, it would appear, they
                  haven't updated their calculations yet. The moral here is to use your own
                  data and your own apps. No change there then.

                  David Roberts

                  [This message has been edited by David Roberts (edited January 19, 2005).]


                    <My two cents is on exclusion.>

                    Just lost two cents.

                    I checked out the first (946-800) weeks (except the first 26) of the UK lottery.
                    The first 26 was skipped so as to be more than 22, our criteria.

                    On 1953 occasions a number was found to be 'overdue' by more than 22 weeks.
                    On 236 occasions one such number occurred the following week.

                    Looks good? Nope.

                    By the same token, on 1953 - 236 occasions one such number didn't occur the following week.

                    ie a probabilty of (1953 - 236)/1953 = 0.8792

                    We have already found that the probabilty of <U>any</U> number not appearing is 0.87755102.

                    I then used, instead of 800, 100 to 700 and got,

                    0.8704, 0.8742, 0.8767, 0.8845, 0.8797, 0.8745, 0.8776

                    Another idea bites the dust.


                    BTW, I've done a chi-squared test on the UK lottery.

                    A test giving < 5% would suggest an unusual behaviour.
                    10% is inconclusive but worthy of keeping an eye on.

                    I got between 50% and 75%. At that level the chi-squared tables
                    don't bother with precision as there is absolutely no evidence of
                    anything unusual.

                    However, chi-squared belongs to the L~2-space group of algorithms including
                    the least squares method of curve fitting which tend to give little credence
                    to 'rogue' values unlike algorithms which reside in L~infinity-space. This is
                    why I considered the 'long runs of non-appearance' approach.


                    My first post in this thread said.

                    <Lotteries are determinate systems and as such the theoretical odds against
                    winning whatever strategy is used is the same for each and every one.>

                    I should read my own press.

                    David Roberts

                    [This message has been edited by David Roberts (edited January 19, 2005).]


                      That's deep, Dave. Real deep. I'm going to have to struggle
                      through that a few times.

                      But I think the arguement got down to the discussion of whether
                      there was ever a favorable moment when a certain strategy might
                      beat the odds. We agree that by hindsight, such moments do
                      seem to appear. We also agree that over the course of the lottery,
                      those moments are lost in the "normalization" of the lottery. No
                      pattern can persist without showing evidence of an underlying bias.

                      So I think the focus is now on two remaining issues: (1) What
                      determines that we are on the advent side of such an occasion, and
                      (2) what strategy does that apparent opportunity tend to support?

                      In other words, instead of sliding off again towards the long
                      view, we are trying to look at the lottery in some sort of myopic
                      manner that resembles the moment of decision when we would try to
                      decide what to play. It may seem rediculous, but it's key to
                      whether there are any prospects there at all. Is there something
                      we should be looking at that might give us a bit of an edge? I
                      don't really believe in this, you understand, but it basis for
                      trying to run the numbers again from a variety of perspectives.

                      Old Navy Chief, Systems Engineer, Systems Analyst, now semi-retired


                        (1) What determines that we are on the advent side of such an occasion?

                        (2) What strategy does that apparent opportunity tend to support?

                        I reckon that the answer to (2) will be obvious when we have the answer to (1).

                        With any population there is a minimum sample size below which any conclusions
                        will be suspect. Any conclusions drawn with the minimum sample size are unlikely
                        to change with greater sample sizes. With a lottery we can determine a minimum
                        sample size given required confidence limits. However, our conclusions are likely
                        to be that nothing unusual is going on. If any unusual behaviour exists then it
                        will be short lived otherwise we'd have a different conclusion. So, we should
                        restrict our analyses to sample sizes below the accepted minimum for making general
                        conclusions. I'd already determined that your last 60 months of drawings was less
                        than this minimum sample size.

                        So, you are already employing a myopic stance.

                        Of course, getting suspect conclusions is exactly what we want and we want them to
                        persist for at least one drawing.

                        Every time that I thought I'd found something suspect by examining a particular
                        condition I found that the odds did not differ when that condition was removed. [1]
                        By 'Every time' I mean when I last looked at lotteries at the end of '99.

                        Take my 'long runs of non-appearance' approach. The chance of a 'long runner' not
                        being selected turned out to be no different than the chance of any number not being
                        selected. I excluded the three found above and # 34 was selected.

                        I tried a lot of ideas with my old Atari but some I couldn't try because of a lack
                        of memory and lack of CPU crunch. In fact, some of the things I've done in the last
                        few days I'd have run on the Atari, gone to bed and examined the results after
                        breakfast. With multi-tasking and the GUI the perceived advance isn't that great.
                        On pure number crunching, our machines today are staggeringly fast in comparison.

                        Anyway, as you infer the 'Holy Grail' is to find an approach where [1] is false.

                        I doubt intuition will help and it will probably be a process of elimination. That is,
                        keep trying different conditions until one looks promising.

                        Bit like gambling really. Looking for that one bet which will recoup every thing we've
                        lost so far.


                        David Roberts

                        [This message has been edited by David Roberts (edited January 20, 2005).]


                          Originally posted by Robert DeBolt View Post

                          Apparently, the lottery program was using a PRNG (Pseudo-Random Number
                          Generator). In his book, "Art of Computer Programming," (I don't
                          remember which volume (1 of three)), Donald E. Knuth has a very detailed
                          discussion on PRNGs and how to determine if the output string of numbers
                          are truly random. PRNGs are notorious for eventually repeating the random

                          Take the most recent 90 drawings (or less) and number then from 1 to 90
                          consecutively with 1 being the oldest and 90 being the most recent drawing.

                          You will probably also construct a 90 x 6 matrix of integers, where each
                          row consists of the 6 winning numbers for that particular drawing. This is
                          the source matrix.

                          Construct a 90 x 90 matrix of one-character cells. Draw a line through
                          the main diagonal and disregard the upper half of the matrix above the
                          diagonal. Number the rows down the left-hand side from 1 to 90, and the
                          columns across the top from 1 to 90. This is the target matrix.

                          Each row of the target matrix represents the comparison of that drawing's winning
                          numbers. Each column also represents a winning panel and is a repeat of the row.

                          Now go to row #2. Under column #1, where it intersects row #2, compare the
                          contents of drawing #1 to the contents of drawing #2 in the source matrix.
                          You will have anywhere from zero to six hits. You can then enter either the
                          digits 1 thru 6, or simply enter a non-blank character into that cell (2,1)
                          of the target matrix. If the number of hits is zero then leave that cell blank.

                          Now go to row #3. Under column #1, where it intersects row #3, compare the
                          contents of drawing #1 to the contents of drawing #3. Alter cell (3,1) as
                          described above. Then under column #2, where it intersects row #3, compare the
                          contents of drawing #2 to the contents of drawing #3. Alter cell (3,2) as
                          described above.

                          Now proceed down the matrix, working from top to bottom and left to right.

                          I chose a 90 x 90 matrix because it fit well on a couple of sheets of paper
                          on my dot-matrix printer using the smallest type font.

                          Now, examine your printout. Where there are columns of unbroken sequences,
                          it suggests that there are drawings that are "related." That is, they share
                          common integers. An unbroken column of arbitrary length would indicate a
                          trend in that set of drawings. How long should a sequence be to be significant?
                          That's your arbitrary decision. Of course you only want to consider "runs"
                          which intersect the row of the most recent drawing.

                          Now take the union of the drawings indicated by the "runs" described above, and
                          that becomes your wheeling set.

                          Of course I wrote the programs about 20 years ago using C in DOS and the Borland
                          3.2 C compiler.

                          [This message has been edited by Robert DeBolt (edited January 11, 2005).]
                          Hi Robert, after so many years since this post you wrote, this post came to my eyes as I was looking for an old post of a small program published (I don't remember which forum member) that tried to find a reduced set to always get 2 numbers from the 6, however they are drawn, for a total of only 19 combinations, valid in a 6/49 lottery.

                          From this post, I was very intrigued by your matching process between the source matrix (the winning numbers) and your matching matrix of the numbers contained in the tickets to be played.

                          Do you still have code related to this research of yours, to better understand the practical process?
                          And I would also like to learn more about your references for evaluating the goodness-of-fit of random number generators. Do you still have that C code you have a long time ago?

                          I very much hope you will find the time and desire to respond to my post. In the meantime, wishing you much good health and a radiant day.


                            Originally posted by Mimmo Labate View Post
                            I very much hope you will find the time and desire to respond to my post....
                            Post you are quoting is dated 2005.
                            Robert Debolt:
                            Last Activity: 29 Jan 2013, 11:51 AM
                            ​I strongly doubt that you will get an answer:

                            And I would imagne that he has realised the folly of this whole thread by now.
                            Naive analyses of a limited number of lottery results is pointless, even if there is a minor. bias in the method to generate the numbers.

                            In the ensuing 18 years, there have been a LOT of threads on random numbers and "randomness" tests

                            That said, even then David Roberts was doing a good job of demonstrating the fallacies of the ideas espoused in the thread by others. He's spent a lot more time working on RNG etc since then


                              I did an extensive test on a pick 3 where there are 3 drawings a day which has a long history. Not worth playing, but very low odds compared to history. Over its life the combinations with the highest odds had a very-very slight advantage.

                              Long time since I did this so it may not be correct now. Some private gambling houses are restricted to taking out 10% of the pot. Some government affiliated lotteries take out 50%. It’s hard to overcome 50%.

                              If the lottery has a wild card, 6 slots + wild card slot, it’s impossible to attempt. Say there’s 60 wild card possibilities, you must buy 60 tickets to try one variation.

                              The only type I would consider attemptable is something like a pick 6 where all possibilities are unique.
                              All of this is a waste of time but kind of fun to play with and you learn from it.

                              I came up with a little program I called Assertion. You make any kind of assertion, no matter how stupid, and it’s either true or false. A false really bad assertion will be a really good assertion. An obvious bad assertion is that the numbers will be in a sequence of one.

                              I had a scheme that would have worked on the pick 3 if they didn’t pull 50% of the pot.
                              Where I live a pick 3 ticket is 50 cents.
                              3 or 4 numbers per drawing.
                              If you lose, still 3 or 4 numbers per drawing but more than on ticket on a number.
                              If you win, the winnings will depend on the quantity of tickets for that number.
                              The idea being you pull some money out of your playing pot along the way.
                              Running it over the history of the lottery, it could stay afloat for a long time.
                              But due to the 50% pull, it would eventually burn.

                              The patterns are just an illusion. If I was going to waste time on it again I’d try to come up with some kind of anti-pattern algorithm.