Talk about anything Wheel Generator related which doesn't fit in the other forums
Sooz
Proficient Posts: 246
Joined: Wed Feb 09, 2011 12:24 am

Looking at the Current World Records made by Wheel Generator. But what does it all mean?

For example there is one :
18,6,4,6 = 33 FD 100% 2 Groups, 9 numbers per group, requesting 3 correct per group. Unconditional coverage 96.73%.

So I understand that WG finds 33 blocks, using combinations of 18 numbers. And that if 6 of those 18 numbers are the winning numbers, then at least one of those 33 blocks will have a 4-hitter.
I understand about WG taking 3 numbers from each group of 9.
This would be awesomely useful, after first asking GAT to find the best 3-hitters with 9 numbers predicted.
But what is FD 100% and what does "unconditional coverage 96.73%" mean? ie what does "unconditional coverage" refer to?
Thanks,

Sooz

lottoarchitect
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Joined: Tue Jan 15, 2008 5:03 pm
Location: Greece
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Hi Sooz, FD means Filter Driven constructions which means, the produced covering is allowed to use only blocks allowed by the defined filters which are in guide mode. Also FD is any construction that uses a mother covering as input (in practice, an imported mother covering and defining guide filters in WG is equivalent, what changes is the way the allowed blocks are defined).
So why do we use FD constructions? The simple answer is, we can reduce the total blocks needed and still get the desired guarantee by the introduction of additional constraints besides the initial m parameter constraint (the m parameter of a wheel is actually a constraint on its own, the constraint is we need to match at least m correct numbers to our selection of v numbers). The unconditional coverage is the coverage achievement when the m parameter is the only constraint.
Now, as soon as we introduce additional constraints (by the means of filters/mother covering) we effectively define that we expect one of the allowed blocks (those that are imported by the mother or defined and allowed by the filters in guide mode) to be also the winning combination, but of course we don't know which one this might be so to play it alone and win. So, we can utilize the FD construction capability and still get the defined t guarantee in fewer blocks, IF any of the allowed blocks as defined by the mother/guide filters is the winning combination.
In the example "18,6,4,6 = 33 FD 100%, 2 Groups, 9 numbers per group, requesting 3 correct per group" we state that we pick 18 numbers, we play 6 number tickets (k=6) we expect to have all correct numbers (m = 6) in our set of v = 18 numbers selection and we guarantee the t = 4 win 100% in only 33 blocks. FD 100% means that this t=4 win guarantee is 100% IF we have all 6 correct numbers picked (m=6, our first constraint) AND also qualify at the two additional constraints defined: 2 defined groups of 9 numbers each where the constraint here is to have exactly 3 correct numbers predicted in each group.
So, we have here three constraints:
1) m = 6
2) 1st group of 9 numbers to have exactly 3 correct (9 unique numbers from our v set, not used in other groups).
2) 2nd group of 9 numbers to have exactly 3 correct (9 unique numbers from our v set, not used in other groups).

If all 3 constraints above are fulfilled, then we have the produced wheel offer the t = 4 win 100% in 33 blocks. We use the terminology FD 100% to indicate that we have additional constraints defined beyond the m = 6 default constraint. If we remove constraints 2) & 3) then we talk for the default overall coverage, or to distinguish this from the FD, we name it "unconditional coverage". When you browse at the internet, all the available wheels are 100% unconditional coverage, unless if something else is specified.
One additional important note: we can evaluate constructions for their FD coverage only if m = k. So we cannot really compute an 18,6,4,5 as FD coverage because a requirement for FD evaluation is to have the winning combination to be one of the allowed blocks and this is obviously possible only if k = m. WG can also make k <> m constructions with additional constraints however in that case, you simply define the allowed blocks to be used (by the mother or the defined guide filters). Also when you plan to construct FD coverings, you have to also enable the function "Filtered over overall coverage at the coverage tab" so to give priority of the FD coverage over the overall one (unconditional). If you don't enable this whilst building FD, then a balance will be attempted by the engine for both the FD coverage and the overall (tries to maximize both at the same time) but really this isn't what you would like in FD constructions, so you have to enable this to get the best results.
The benefit of FD constructions is you can get the desired guarantee in fewer blocks. To see that benefit, I'll use the same example 18,6,4,6 = 33 FD 100%. Here you get that t=4 guarantee in 33 blocks, unconditional 100% would require 42 blocks (if I recall correctly). An additional menu appears when m=k is applicable named "Hits (filtered). This gives a detailed hits overview production provided the winning combination is any of the allowed blocks used to make the covering.
This would be awesomely useful, after first asking GAT to find the best 3-hitters with 9 numbers predicted.
Yes, that's the point of GAT's absolute mode, so to be used in FD constructions like the above.
So I understand that WG finds 33 blocks, using combinations of 18 numbers. And that if 6 of those 18 numbers are the winning numbers, then at least one of those 33 blocks will have a 4-hitter.
Yes, provided all the constraints are fulfilled.

So, any covering that states FD followed by %, this automatically implies a v, k, t, k construction (m = k) with additional constraints beyond the default m parameter. Of course you can produce even open cover FD versions (e.g. at 90% guarantee) to reduce even further the blocks if so desired. Any other case that defines filters in guide or uses a mother as input which is m <> k is also an FD construction, but we can't evaluate the FD % in that case so we simply call these Filtered. In all those cases, the filters/mother "drive" the construction and define what blocks can be used, thus the Filtered and Filter Driven (FD) terminology.

To expand this FD in more depth, from general to specialized:

A) Any covering that does not use mother or have any filters in guide produce normal coverings (unconditional) which is the default operation and these constructions are similar to those found at the internet. Here we can use filters in normal mode to try and reduce those blocks that possibly fall outside our desired constraints.

B) If we introduce at least one filter in guide mode or use a mother, we enter the Filtered constructions era (not FD yet) which is a super-set of Filter Driven coverings. Here we simply define which are the allowed blocks to use for the construction. We can evaluate the covering only as unconditional and we enforce the blocks used to follow the defined constraints (mother or guide filters).

C) If m = k we produce FD constructions and we can also evaluate FD % coverage. So the term FD practically is used only if m = k. Here we can use any type of guide filter (sums/odd/even/import mother etc). From this point, we can also reduce blocks and still get the defined t win guarantee if we reach FD 100%.

D) If additionally to the above we have:
1) Constraints ONLY at the form of numbers groups (and nothing else i.e. sums or mothers):
2) each group indicates a unique set of numbers not found in any other defined number group.
3) the defined numbers of each group belong to our v numbers selection
then we have what we call Matrix constructions.

E) If additionally to the above we have:
4) Requesting an exact amount of correct numbers from each group.
5)The sum of "exact amount of correct numbers from each group" to be equal to k *
6) t < m
then we have Abbreviated Matrix constructions which is a unique WG feature. It has the property, if you miss one number from a group, the wins are transposed at the next lower division.

F)If additionally to the above we have
7)t=m=k

Then we talk about Serotic coverings (I use the terminology Jackpot Matrix as the official term for this) which have the property to directly produce the jackpot combination if all the defined constraints are fulfilled. However to be precise, Serotic also had each number group be equal in size and request the same amount of numbers correct from each group so in that sense Serotic is even more specialized. However WG is much more flexible and still maintain the properties of Serotic without those additional limitations. WG does not allow optimization when t=k=m, so to get these F) constructions, we use the "save filtered construction" from the covering menu. Also these coverings cannot get reduced further i.e. let WG optimize it (this is why WG doesn't allow optimization anyway).
* There is also the expanded version of Abbreviated/Jackpot Matrix which allows to define even more groups (so from one point of view it violates rule 5 above). This is possible to do if you also enable as requested numbers the value 0 (using the individual values feature). This is also explained at the help file. These are still Jackpot Matrix coverings and allow even more numbers to be used.

That's all more or less about FD constructions. So this 18,6,4,6 = 33 FD 100% is an abbreviated matrix.

Sooz
Proficient Posts: 246
Joined: Wed Feb 09, 2011 12:24 am