Appropriate Block Size

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jrichardson83
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Appropriate Block Size

Post by jrichardson83 » Sun Oct 30, 2016 12:00 am

Anastasios,

In the WG Help file, under the section Covering Parameters, you write "Wheel Generator is put into play simply by inserting one’s design values...The user should acquaint themselves with typical values of (ie from the known covering repositories where one can find typical values for numbers of blocks to be generated for the numbers used ([v]) and the guarantee parameters ([t] & [m]) in the design) for the size of the covering to be optimized."

With that in mind, I play a 5/36 game and set my covering parameters to 21,5,4,5. Inputting 21,5,4 at LaJolla gives me C(21,5,4) <=1247, this was a wheel you produced timestamped 2008. I have several questions about this. First, At LaJolla what does "size" mean and why is that number 1247? Is it correct to read this covering as a 1247 block?

Again, from the help file you write "...if the Total Points [v] =15 for a 6 ball lottery eg ([k] = 6) and a 4 if 6 guarantee ([t] if [m]) is sought then the block number specified to ensure this guarantee is satisfied should be at least 19." Is this number derived from a general mathematical formula that can be applied to any covering? If so, what is that formula. The problem I'm having is determining the proper integer value for [m] and the appropriate block size for my particular lottery. Is [m] simply the guaranteed win sought?

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lottoarchitect
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Re: Appropriate Block Size

Post by lottoarchitect » Sun Oct 30, 2016 4:57 pm

Hi jrichardson83, to your questions
With that in mind, I play a 5/36 game and set my covering parameters to 21,5,4,5. Inputting 21,5,4 at LaJolla gives me C(21,5,4) <=1247, this was a wheel you produced timestamped 2008. I have several questions about this. First, At LaJolla what does "size" mean and why is that number 1247? Is it correct to read this covering as a 1247 block?
C(21,5,4) as presented by LaJolla means a 21,5,4,4 wheel (t=m). Size is indeed the total blocks of the wheel needed. So the current known record for 21,5,4,4 is <= 1247. We present this as <= because the top bound is currently at 1247 blocks but there may be possible to make this in even fewer blocks (or size as mentioned by LaJolla). However, there is a minimum possible bound for any covering - the general lowest bound equation, which is discussed here
viewtopic.php?f=11&t=35
This is the same value indicated by Wheel Generator at the Th. Min value at the bottom-right of the progress screen. No matter what we do or how we do it, it is impossible to construct a covering that goes below that Th. Min indicated. Quite often this value is really impossible to reach too, proved by other theoretical and more detailed mathematical analysis which indicates a higher value to that Th. Min. So any wheel really will be constructed within the range [Th. Min=general lowest bound equation or another lowest bound (higher to Th.Min) indicated by more advanced analysis] <= C(v,k,t,m) <= [current known blocks (size)].
So this C(21,5,4) is currently at 1247 blocks, its theoretical minimum (Th.Min indicated) is at 1197 blocks but the currently known record is at 1247 blocks. It may be possible to construct this same covering in e.g. 1246 blocks or even lower but it cannot go below 1197 blocks (or another theory may indicate a higher lowest bound).
from the help file you write "...if the Total Points [v] =15 for a 6 ball lottery eg ([k] = 6) and a 4 if 6 guarantee ([t] if [m]) is sought then the block number specified to ensure this guarantee is satisfied should be at least 19." Is this number derived from a general mathematical formula that can be applied to any covering? If so, what is that formula. The problem I'm having is determining the proper integer value for [m] and the appropriate block size for my particular lottery. Is [m] simply the guaranteed win sought?

Same as above, the Th. Minimum for 15,6,4,6 is indicated as 8.412 blocks or 9 blocks (cannot have decimal blocks really), thus 9 <= C(15,6,4,6) <= 19 which is the current known best record. In reality, 99.9% of wheels will always require more blocks compared to the Th.Min indicated. The parameter m is a value you specify by yourself; it represents "how many correct numbers you expect to have among the drawn numbers and your v numbers selection". Parameter t is the guaranteed win setting. You define all the 4 parameters, v,k,t,m and when you have these you can lookup to repositories to determine a meaningful value for b (blocks needed or size if you use LaJolla).

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