Hi LA:
Is WG incapable of making 5if5 wheels? (in pick6 games)
Whenever I try to make a 5if5 wheel with WG it seems like it can't even get close to a 1% coverage.
For example, a 5 if 5 guarantee (in a pick6 game) with 35 numbers [with 3 bankers] is doable with 171 combinations. But WG can't even get close to 1% with those many combinations.
Or a 5 if 6 guarantee with 35 numbers [with 3 bankers] is doable with 81 combinations but WG can't do it with under 133 combinations.
Are there any special settings that need to be adjusted when playing with bankers and/or higher win guarantees? Or is WG not able to deal with higher guarantees and more bankers?
I especially need to know how to get WG to work with 3 bankers to be able to deliver a 5if5 guarantee.
Any help would be appreciated.
Can WG create 5 if 5 wheels?
 lottoarchitect
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Re: Can WG create 5 if 5 wheels?
First, consider that when you request numbers as bankers in a wheel, you want that set to appear in each and every block of the covering. Now, for a pick 6 wheel with 3 bankers, you essentially want to form blocks like B1 B2 B3 X X X, where B1, B2, B3 are your bankers and X are the remaining numbers; the variable part. This is equivalent as forming the blocks like B1 B2 B3 + c(vBC, kBC, tBC, mBC), where BC is the bankers count (3 in your case). So, if you want to construct a 35,6,5,5 with 3 bankers, you create in practice a covering with the fixed part B1 B2 B3 + 32,3,2,2 wheel (in which case the 32,3,2,2 needs 171 blocks as you correctly state).
Now, bankers in WG are a very general mechanism, applicable within the overall design of number groups, which allows the fixed part B1 B2 B3 to show up in every block and to be part of a quite much more complex construction than the simple B1 B2 B3 + 32,3,2,2 construction you request. Given bankers operate at the logic of filtered construction (make a search for this term to find out more on filtered constructions), WG cannot compute the real achievable coverage of the filtered condition because this evaluation requires the covering to be in the form of v,k,t,k (m=k) but in this case here we have m<>k (5<>6). Thus WG display only the overall coverage and since you force part of a 35,6,5,5 to be a fixed B1 B2 B3, obviously this results in a covering less than 100% (actually it is impossible to create an unconditional 100% with a fixed part showing up in every block of the covering!). In fact the achievable coverage is less than 1% as you have observed here; nothing wrong with that really. WG can't show you the partial coverage achievement of the variable part c(vBC, kBC, tBC, mBC) due to the generality of its construction mechanism.
The same case is with the other covering 35,6,5,6 with 3 bankers. Here you check the overall (main) coverage but you should actually inspect only the filtered coverage indicated, given m=k here we can evaluate the filtered part of the wheel. A quick run with WG produced this in 85 blocks, running it a bit longer it would probably make this to 81 as well.
Bottom line is, the way bankers are implemented in WG are meant to operate in a much broader spectrum of possible constructions and still deliver the desired output but with the limitation of m=k because of the filtered mechanism. In order for WG to construct the wheels like the above you want, a special "bankers separation" function should be implemented that separates completely the fixed part (the bankers) from the internal covering construction of c(vBC, kBC, tBC, mBC), thus WG would specifically know it needs to evaluate the coverage of the vBC, kBC, tBC, mBC part only and attach internally the bankers.
Not sure if I have explained this adequately or if it is clear what you observe there, but this is what is happening.
If you can't make WG construct the desired bankers in your requested wheel, the simplest approach is to simply attach the bankers to the variable part c(vBC, kBC, tBC, mBC), after you construct the variable part.
I'll just give an example of the generality mechanism of bankers as implemented by WG. Just consider the case you want also a specific range of sums (or whatever combination of filters) to be allowed for your construction. Attaching bankers as is (what you are after), will easily violate your other requirements in many blocks. With WG's mechanism, provided the filtered coverage can be evaluated, you'll certainly pass all your other requirements alongside with your bankers too. This is the generality offered in WG,
Obviously WG can create any t if m wheel, including of course 5 if 5. The construction B1 B2 B3 + c(vBC, kBC, tBC, mBC) you want is in fact a special case of filtered constructions because the requirement here is the ability to evaluate the coverage of the variable part c(vBC, kBC, tBC, mBC) needed for this construction. Only a specially designed function in WG would allow that automatic separation and evaluation. I'll keep a note to this as a future addition to enhance the bankers operation further.
The one liner answer is: WG evaluates the covering as v,k,t,m but in reality the special case of a set of b bankers requires evaluation of a vb, kb, tb, mb covering. In the case of k=m, WG can evaluate this correctly by inspecting the indicated filtered coverage (not the main coverage).
That's why 35,6,5,5 with 3 bankers needs 171 blocks, because 32,3,2,2=171 blocks. Also 35,6,5,6 with 3 bankers needs 81 blocks because 32,3,2,3=81 blocks.
Now, bankers in WG are a very general mechanism, applicable within the overall design of number groups, which allows the fixed part B1 B2 B3 to show up in every block and to be part of a quite much more complex construction than the simple B1 B2 B3 + 32,3,2,2 construction you request. Given bankers operate at the logic of filtered construction (make a search for this term to find out more on filtered constructions), WG cannot compute the real achievable coverage of the filtered condition because this evaluation requires the covering to be in the form of v,k,t,k (m=k) but in this case here we have m<>k (5<>6). Thus WG display only the overall coverage and since you force part of a 35,6,5,5 to be a fixed B1 B2 B3, obviously this results in a covering less than 100% (actually it is impossible to create an unconditional 100% with a fixed part showing up in every block of the covering!). In fact the achievable coverage is less than 1% as you have observed here; nothing wrong with that really. WG can't show you the partial coverage achievement of the variable part c(vBC, kBC, tBC, mBC) due to the generality of its construction mechanism.
The same case is with the other covering 35,6,5,6 with 3 bankers. Here you check the overall (main) coverage but you should actually inspect only the filtered coverage indicated, given m=k here we can evaluate the filtered part of the wheel. A quick run with WG produced this in 85 blocks, running it a bit longer it would probably make this to 81 as well.
Bottom line is, the way bankers are implemented in WG are meant to operate in a much broader spectrum of possible constructions and still deliver the desired output but with the limitation of m=k because of the filtered mechanism. In order for WG to construct the wheels like the above you want, a special "bankers separation" function should be implemented that separates completely the fixed part (the bankers) from the internal covering construction of c(vBC, kBC, tBC, mBC), thus WG would specifically know it needs to evaluate the coverage of the vBC, kBC, tBC, mBC part only and attach internally the bankers.
Not sure if I have explained this adequately or if it is clear what you observe there, but this is what is happening.
If you can't make WG construct the desired bankers in your requested wheel, the simplest approach is to simply attach the bankers to the variable part c(vBC, kBC, tBC, mBC), after you construct the variable part.
I'll just give an example of the generality mechanism of bankers as implemented by WG. Just consider the case you want also a specific range of sums (or whatever combination of filters) to be allowed for your construction. Attaching bankers as is (what you are after), will easily violate your other requirements in many blocks. With WG's mechanism, provided the filtered coverage can be evaluated, you'll certainly pass all your other requirements alongside with your bankers too. This is the generality offered in WG,
Obviously WG can create any t if m wheel, including of course 5 if 5. The construction B1 B2 B3 + c(vBC, kBC, tBC, mBC) you want is in fact a special case of filtered constructions because the requirement here is the ability to evaluate the coverage of the variable part c(vBC, kBC, tBC, mBC) needed for this construction. Only a specially designed function in WG would allow that automatic separation and evaluation. I'll keep a note to this as a future addition to enhance the bankers operation further.
The one liner answer is: WG evaluates the covering as v,k,t,m but in reality the special case of a set of b bankers requires evaluation of a vb, kb, tb, mb covering. In the case of k=m, WG can evaluate this correctly by inspecting the indicated filtered coverage (not the main coverage).
That's why 35,6,5,5 with 3 bankers needs 171 blocks, because 32,3,2,2=171 blocks. Also 35,6,5,6 with 3 bankers needs 81 blocks because 32,3,2,3=81 blocks.

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Re: Can WG create 5 if 5 wheels?
Hi LA
I have a question for you, in a system with 4 Bankers [if V=30, K=10 and if m=6 and and I would look for a t=3] lets assume I don't get any Bankers right, what will be minimum guarantee in this scenario? Is is it 3 right "only" if some of these Bankers hit or I can still get a three hit even I don't get any Bankers right?
Is there any way to know what would be the minimum t value if none of the Bankers hit right.
I have a question for you, in a system with 4 Bankers [if V=30, K=10 and if m=6 and and I would look for a t=3] lets assume I don't get any Bankers right, what will be minimum guarantee in this scenario? Is is it 3 right "only" if some of these Bankers hit or I can still get a three hit even I don't get any Bankers right?
Is there any way to know what would be the minimum t value if none of the Bankers hit right.
 lottoarchitect
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 Posts: 1450
 Joined: Tue Jan 15, 2008 5:03 pm
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Re: Can WG create 5 if 5 wheels?
The guarantee of a wheel with bankers is computed differently. There are two parts that contribute to the overall guarantee, the bankers part and the c(vb, kb, tb, mb) part.
Just for one moment, omit completely the bankers part. What is left is the variable part (the actual wheel). This variable part contains the remaining numbers (vb) and it will deliver the designed guarantee tb, given mb is met.
To display this as per the wheel we discuss, the variable part will be (since you have 4 bankers) c(26,6,?,2) because you construct a 30,10,3,6 wheel (which includes the bankers as well). I have marked with ? the t parameter because 3b = 1!
Obviously any wheel will always have a guarantee > 0 (even an open cover wheel have greater than 0 guarantee), therefore requesting t=3 at the overall equation c(30,10,3,6) is not possible.
So, let's assume you design the variable part to be a c(26,6,1,2) (t is set to 1 but you can also use an open cover wheel with less than 100% coverage for 1 hit). For simplicity let's say the actual variable part is 100% for t=1 hit. You have here the minimum 1 hit guaranteed. Now, attach the bankers part, in which case you may hit 0, 1, 2, 3 or all 4 bankers as well. Therefore, the attainable hit performance of
B1 B2 B3 B4 + c(26,6,1,2) is [0..4] + 1. So, your minimum guarantee is 1 (from the variable part) and the maximum is 5 is you match all 4 bankers for a t=1 wheel. Of course, you may also achieve 2 or more (up to 6) hits at the variable part but the design B1 B2 B3 B4 + c(26,6,1,2) can guarantee 1 up to 5 numbers hit.
Just for one moment, omit completely the bankers part. What is left is the variable part (the actual wheel). This variable part contains the remaining numbers (vb) and it will deliver the designed guarantee tb, given mb is met.
To display this as per the wheel we discuss, the variable part will be (since you have 4 bankers) c(26,6,?,2) because you construct a 30,10,3,6 wheel (which includes the bankers as well). I have marked with ? the t parameter because 3b = 1!
Obviously any wheel will always have a guarantee > 0 (even an open cover wheel have greater than 0 guarantee), therefore requesting t=3 at the overall equation c(30,10,3,6) is not possible.
So, let's assume you design the variable part to be a c(26,6,1,2) (t is set to 1 but you can also use an open cover wheel with less than 100% coverage for 1 hit). For simplicity let's say the actual variable part is 100% for t=1 hit. You have here the minimum 1 hit guaranteed. Now, attach the bankers part, in which case you may hit 0, 1, 2, 3 or all 4 bankers as well. Therefore, the attainable hit performance of
B1 B2 B3 B4 + c(26,6,1,2) is [0..4] + 1. So, your minimum guarantee is 1 (from the variable part) and the maximum is 5 is you match all 4 bankers for a t=1 wheel. Of course, you may also achieve 2 or more (up to 6) hits at the variable part but the design B1 B2 B3 B4 + c(26,6,1,2) can guarantee 1 up to 5 numbers hit.
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