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wheel algorithms?

Topic closed. 42 replies. Last post 1 year ago by SergeM.

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United States
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July 25, 2012
67 Posts
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Posted: February 19, 2013, 3:14 pm - IP Logged

I am interested in learning about lottery wheel algorithms, specifically for abbreviated wheels.

And I am interested in techniques for proving that the resulting wheel is "mathematically minimal" (and "balanced"?)

(What makes a wheel "well-balanced"?  Is it just some subjective concept of the "variety" or "scope" of numbers; for example, 1 2 3 4 5 might be "poorly balanced", whereas 1 12 23 34 45 might be considered "well-balanced"?  Or is there a more-rigorous definition of "balanced"?)

Please note that I am interested in algorithms, not the wheels themselves.

So pointing me to the Lottery Wheels link is not sufficient, unless I overlooked a link to algorithms per se (where?).  Also, since I am not a gold or platinum member, the links there to particular wheels are not useful to me (other than as good examples).

However, there is a reference there to a book by Iliya Bluskov.  Does that book describe wheeling algorithms in sufficient detail to implement in a computer language?  Or does the book simply provide the wheels themselves?

(Or perhaps someone here can offer an algorithm in sufficient detail.)

A Google search has turned up some implementations.  I am still looking through the links.  However, the ones that I have seen so far are implemented in C++.  Although I have a lot of experience with C, I struggle to understand C++ implementations.  An implementation in C or VBA would be helpful.

In any case, I'm not sure I will know how to prove that the results are "good", much less "mathematically minimal".

For example, the wiki lottery wheel page (as well as a link in this forum's Lottery Wheel Pick-6 page) claims that an abbreviated wheel for 4-if-4-of-8 can be covered with as few as 7 tickets for 6-draw lottery.  I can easily do that in 15 tickets.  But I have not yet been able to pare that down to 7, even manually, much less algorithmically.  (Moreover, my algorithm is not extensible to more 8 favored numbers.)

I would be grateful if someone could show me a 7-ticket wheel for 4-if-4-of-8 for a 6-draw lottery.  Then at least I know what I am shooting for.

    SergeM's avatar - alas
    Economy class
    Belgium
    Member #123705
    February 27, 2012
    2726 Posts
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    Posted: February 19, 2013, 6:43 pm - IP Logged

    Could you post the C++ code?


      United States
      Member #116272
      September 7, 2011
      20244 Posts
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      Posted: February 19, 2013, 6:51 pm - IP Logged

      I believe the wheels on LP are for the use of premium members. I wish you the best on your project and hope you come up with some winning numbers that you can share with the rest of us. Welcome to LP.

      Wheel:  Pick 5 Abbreviated 4 if 4 of 8

      Tickets:  20

      Description:  Minimum 4-number match, if 4 numbers drawn fall within your set of 8 numbers.

      Input:  1, 2, 3, 4, 5, 6, 7, 8

      1. 01-02-03-04-07
      2. 01-02-03-04-08
      3. 01-02-03-05-06
      4. 01-02-04-05-07
      5. 01-02-04-05-08
      6. 01-02-04-06-07
      7. 01-02-04-06-08
      8. 01-02-04-07-08
      9. 01-03-04-05-06
      10. 01-03-05-07-08
      11. 01-03-06-07-08
      12. 01-05-06-07-08
      13. 02-03-04-05-06
      14. 02-03-05-06-07
      15. 02-03-05-06-08
      16. 02-03-06-07-08
      17. 02-04-05-07-08
      18. 03-04-05-06-07
      19. 03-04-05-06-08
      20. 03-04-06-07-08

        SergeM's avatar - alas
        Economy class
        Belgium
        Member #123705
        February 27, 2012
        2726 Posts
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        Posted: February 19, 2013, 7:00 pm - IP Logged

        I believe the wheels on LP are for the use of premium members. I wish you the best on your project and hope you come up with some winning numbers that you can share with the rest of us. Welcome to LP.

        Wheel:  Pick 5 Abbreviated 4 if 4 of 8

        Tickets:  20

        Description:  Minimum 4-number match, if 4 numbers drawn fall within your set of 8 numbers.

        Input:  1, 2, 3, 4, 5, 6, 7, 8

        1. 01-02-03-04-07
        2. 01-02-03-04-08
        3. 01-02-03-05-06
        4. 01-02-04-05-07
        5. 01-02-04-05-08
        6. 01-02-04-06-07
        7. 01-02-04-06-08
        8. 01-02-04-07-08
        9. 01-03-04-05-06
        10. 01-03-05-07-08
        11. 01-03-06-07-08
        12. 01-05-06-07-08
        13. 02-03-04-05-06
        14. 02-03-05-06-07
        15. 02-03-05-06-08
        16. 02-03-06-07-08
        17. 02-04-05-07-08
        18. 03-04-05-06-07
        19. 03-04-05-06-08
        20. 03-04-06-07-08

        1234
        1235
        1236
        1237
        1238
        1245
        1246
        1247
        1248
        1256
        1257
        1258
        1267
        1268
        1278
        1345
        1346
        1347
        1348
        1356
        1357
        1358
        1367
        1368
        1378
        1456
        1457
        1458
        1467
        1468
        1478
        1567
        1568
        1578
        1678
        2345
        2346
        2347
        2348
        2356
        2357
        2358
        2367
        2368
        2378
        2456
        2457
        2458
        2467
        2468
        2478
        2567
        2568
        2578
        2678
        3456
        3457
        3458
        3467
        3468
        3478
        3567
        3568
        3578
        3678
        4567
        4568
        4578
        4678
        5678
          lottoarchitect's avatar - waveform

          Greece
          Member #2815
          November 18, 2003
          485 Posts
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          Posted: February 19, 2013, 7:51 pm - IP Logged

          The only known to me available source for wheeling code is the old Cover32 program (not sure if it is still somewhere available). What source code do you refer to, because such things are really hard to find mostly because abbreviated wheel development is based on unique heuristics and nobody really wants to share his own work (I also have developed mine from scratch because I really couldn't find any source to work on - the same problem you face).

          Also Iliya Bluskov's books do not contain any info on wheel development. Most of his wheels are based on theories and are optimal or near-optimal constructions. I also have a few wheels of mine in his lotto 6 book made by my program simply because no optimal theory-based solution has been found for those few instances.

          For your final question on 4if4if8, the general case is that we cannot approach the theoretical minimum. Given a covering v,k,t,m=b, the computed general theoretical minimum assumes the covering can be made as "pack design" which means every combination that must be covered to offer 100% guarantee, it is covered by one and only one block of the covering. Such a property is possible in some t=m constructions and maybe very few t < m constructions (if any). Therefore the general theoretical minimum is just a lowest boundary which can't be reached in most cases. Very advanced mathematics can compute a better lowest bound (higher than the general theoretical) for some classes of v,k,t,m coverings but even these may not be possible to reach. So your 4if8, given it is a t < m construction it will not approach the theoretical minimum simply because there is an unavoidable overlap among the blocks of the covering.

          By the way, 4if4of8 means nothing, you need 4 parameters to define a wheel.

            Avatar
            Florida
            United States
            Member #135620
            November 27, 2012
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            Posted: February 19, 2013, 11:03 pm - IP Logged

            I've created a system myself and have been struggling with how to best wheel the result. My main fault seems to be that I'm going for the gold, a straight. I could position the numbers I play and play them boxed but... hopefully that's not me just being greedy.

            As for wheels themselves, I think that depends greatly on what system is being used, how the numbers are generated, etc. I would think (with my limited experience) that trying to create a blanket wheel that covered all circumstances would be a lesson in futility.

            Although, if you come up with a wheel that isn't around or maybe a modification you'd like to see on an existing wheel, let me know. If you'd like to work together, I've been toying with the idea of adding some wheels to my site but I have to do more research...

              BobP's avatar - bobp avatar.png
              Dump Water Florida
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              Posted: February 20, 2013, 3:14 am - IP Logged


              Balanced is taken to mean each number on the wheel appears the same number of times.  It is not always possible for a wheel to be perfectly balanced and optimal / tightest at the same time.

              If you mean (8,6,4,4)=7 CoverMaster made this in about one second.

              1 2 3 4 5 6
              1 2 3 5 6 7
              1 2 3 5 6 8
              1 2 4 6 7 8
              1 3 4 5 7 8
              2 3 4 6 7 8
              2 4 5 6 7 8
              100% (8,6,4,4)=7 not balanced

              BobP


                United States
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                Posted: February 20, 2013, 4:58 am - IP Logged

                Dont get crazy trying to develop wheels, unless you plan to sell them.  But you will have LOTS of competition.

                I would focus on learning on how to pick the correct numbers!!!!Idea

                Three power number wheels are generally the best in IMHO. But make sure you get them right!Mad

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                  Cape Town
                  South Africa
                  Member #66343
                  October 23, 2008
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                  Posted: February 20, 2013, 5:16 am - IP Logged

                  This might be a useful place to start:

                  www.lotterypost.com/thread/228056/1968766

                    SergeM's avatar - alas
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                    Posted: February 20, 2013, 7:17 am - IP Logged

                    Great program!

                      SergeM's avatar - alas
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                      Posted: February 20, 2013, 7:21 am - IP Logged
                      12345
                      12346
                      12347
                      12348
                      12356
                      12357
                      12358
                      12367
                      12368
                      12378

                      In Belgium you get forms for this, upper box for key numbers and lower box for wheel numbers in all combinations. Full wheels also are offered, just put more crosses in one box. For a 10 number wheel, you just cross ten numbers on the form, for 10 euros, I believe. All you have to do is picking the right numbers.

                      Coffee


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                        Posted: February 22, 2013, 4:23 am - IP Logged

                        An Abbreviated Lottery Wheel generates a combination that is much less in number
                        than that generated by full wheels to guarantee wins other than the jackpot. The
                        design of an abbreviated wheel itself is not a simple matter; there is no
                        formula for it and is mostly a result of iterations and trials and errors. In
                        fact, in mathematics, it is called Covering Design and belongs to a
                        branch of mathematics called Combinatorics.

                        Thinking of...

                          helpmewin's avatar - dandy
                          u$a
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                          Posted: February 22, 2013, 7:19 am - IP Logged

                          An Abbreviated Lottery Wheel generates a combination that is much less in number
                          than that generated by full wheels to guarantee wins other than the jackpot. The
                          design of an abbreviated wheel itself is not a simple matter; there is no
                          formula for it and is mostly a result of iterations and trials and errors. In
                          fact, in mathematics, it is called Covering Design and belongs to a
                          branch of mathematics called Combinatorics.

                          Thinking of...

                                   Thinking of...

                                           

                            Avatar
                            bgonçalves
                            Brasil
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                            June 9, 2010
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                            Posted: February 22, 2013, 7:53 am - IP Logged
                            Hello, let's try to innovate, wheels to catch small awards through an array with mirrors example of an array 49/6
                            Matrix 7 x 7 =
                            Then, the example below also do vertically,
                            0000xxx
                            0
                            0
                            X
                            X
                            X
                            0
                            Goal, and see small segentos in 7 rows and 7 columns with 3 and 4 segments with mirror,
                            Note has cross threads with 0000 xxx column line, catching so accumulated hits segments, and aainda see the positions, but in order to fit this need help from more advanced members of the lp. Keep under the brim of hat. ahhh!!!
                            When it mounts the eescolher 7 x 7 array in rows and columns randomly distributed, couple take the gain setting within the thread, normal and mirror
                            12, 02, 15, 26, 35, 48.49
                            15. ...
                            08
                            26
                            35
                            39
                            40
                            Unique Wheels
                            x x  o o o x x
                            o x x o x x o
                            o x o x o x o

                            Mirror Wheels
                            x x x o o o o
                            o o o o x x x

                            x x o x o o o
                            o o o x o x x

                            x x o o x o o
                            o o x o o x x

                            x x o o o x o
                            o x o o o x x

                            x x o o o o x
                            x o o o o x x

                            x o x x o o o
                            o o o x x o x

                            x o x o x o o
                            o o x o x o x

                            x o x o o x o
                            o x o o x o x

                            x o x o o o x
                            x o o o x o x

                            x o o x x o o
                            o o x x o o x

                            x o o x o x o
                            o x o x o o x

                            x o o o x x o
                            o x x o o o x

                            o x x x o o o
                            o o o x x x o

                            o x x o x o o
                            o o x o x x o

                            o x x o o x o
                            o x o o x x o

                            o x o x x o o
                            o o x x o x o

                            Wheel 3 = X
                            Wheel 4 = o 
                            The least used wheel in lottery;
                            x o x o o o x
                            x o o o x o x
                              SergeM's avatar - alas
                              Economy class
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                              Posted: February 22, 2013, 1:47 pm - IP Logged
                              XXXOOOO
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