wheel algorithms?

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.

Could you post the C++ code?

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.

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.

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...

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

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!!!!

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

This might be a useful place to start:

www.lotterypost.com/thread/228056/1968766

Great program!

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.

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.