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.