Calculating Covered Combinations in an Abbreviated Wheel

[ExpertLotto]

not exactly. you do need the list of all 5-number combinations that can be constructed from the numbers in your wheel. so if your wheel contains x uniques numbers you'll need a list of all pentads from those x numbers.

now you need to scan the wheel for each pentad in your list and compare it with each line in the wheel to see if the line matches the pentad in *exactly* three numbers.

let's assume that your list has e.g. 5 pentads only. then you may get results like this:
1. pentad - 0 matches
2. pentad - 2 lines match in three numbers
3. pentad - 5 lines match in three numbers
4. pentad - 2 lines match in three numbers
5. pentad - 0 matches

that means you have 40% chance of winning nothing, 40% chance of getting two 3-number hits and 20% chance of getting five 3-number hits.

if you were looking for 4if5 coverage then your results may look like:

1. pentad - 0 matches
2. pentad - 2 lines match in 4 numbers and 6 *other* lines match in 3 numbers
3. pentad - 4 lines match in 3 numbers
4. pentad - 2 lines match in 4 numbers and 8 *other* lines match in 3 numbers
5. pentad - 3 lines match in 4 numbers and 2 lines match in 3 numbers

then the collated results are:
20% chance of winning nothing
20% chance of getting four 3-number hits
40% chance of getting two 4-number hits *and* 6 to 8 3-number hits
20% chance of getting three 4-number hits *and* exactly two 3-number hits

(i hope it makes any sense and i didn't make any mistake )

 

[PAB]

Thanks for the Reply ExpertLotto,

Unfortunately I have still NOT been able to Resolve this.
I think I will just Accept the Fact that I am NOT going to be able to Achieve a Solution.

Thanks again to All those that have Replied.
All the Best.
PAB

 

[Grandmaster]

Hi PAB,

I think Nick Koutras knows the solution for your question, he is an expert in excel vba and his program Lotto designerXL calculates covered combinations in any abbreviated wheel,

But where is Nick koutras?


Regards

 

[PAB]

Hi Grandmaster,

I Appreciate the Reply, and you are Quite Right, Nick would have the Answer to my Request.
I have NOT seen Nick Around this Board for Quite a While, he is Probably Deeply Involved in the Setting Up of the Designs Library, which I am Quite Sure will be Well Worth the Time and Effort that LT & Nick are Putting in.

Once Again, Thanks.
All the Best.
PAB

 

[PAB]

Hi Everyone,

I thought I would Pick this Thread up and Run with it Again.
I am Still Unsure if I Completely Understand the Logic of the Calculations to Provide the Covered & Uncovered Scenarios.
In Order for me to Understand, would Somebody Kindly Produce the Coverage of the Following Examples Using Covermaster Please.
I Know a Wheel will Not have One Line but the information will Hopefully Clarify things a Bit,

Wheel 1

01 02 03 07 08 09

Wheel 2

01 02 03 07 08 09
01 02 03 06 08 10

Wheel 3

01 02 03 07 08 09
01 02 03 06 08 10
05 06 07 08 09 10

Thanks Very Much in Advance.
All the Best.
PAB

 

[Brad]

The lines were pasted directly into CM:

#1. CoverMaster recognizes the 'wheel' as a CM(9,6,3,6)=1

T if M    Tested Covered         % Not Covered     %
----------------------------------------------------
2 If 2 :      36      15  41.66667      21  58.33333
2 If 3 :      84      65  77.38095      19  22.61905
2 If 4 :     126     120  95.23810       6   4.76190
2 If 5 :     126     126 100.00000       0   0.00000
2 If 6 :      84      84 100.00000       0   0.00000
2 If 7 :      36      36 100.00000       0   0.00000
3 If 3 :      84      20  23.80952      64  76.19048
3 If 4 :     126      75  59.52381      51  40.47619
3 If 5 :     126     111  88.09524      15  11.90476
3 If 6 :      84      84 100.00000       0   0.00000
3 If 7 :      36      36 100.00000       0   0.00000
4 If 4 :     126      15  11.90476     111  88.09524
4 If 5 :     126      51  40.47619      75  59.52381
4 If 6 :      84      64  76.19048      20  23.80952
4 If 7 :      36      36 100.00000       0   0.00000
5 If 5 :     126       6   4.76190     120  95.23810
5 If 6 :      84      19  22.61905      65  77.38095
5 If 7 :      36      21  58.33333      15  41.66667
6 If 7 :      36       3   8.33333      33  91.66667

#2. CoverMaster recognizes the wheel as a CM(10,6,3,6)=2

T if M    Tested Covered         % Not Covered     %
----------------------------------------------------
2 If 2 :      45      24  53.33333      21  46.66667
2 If 3 :     120     104  86.66667      16  13.33333
2 If 4 :     210     206  98.09524       4   1.90476
2 If 5 :     252     252 100.00000       0   0.00000
2 If 6 :     210     210 100.00000       0   0.00000
2 If 7 :     120     120 100.00000       0   0.00000
3 If 3 :     120      36  30.00000      84  70.00000
3 If 4 :     210     141  67.14286      69  32.85714
3 If 5 :     252     230  91.26984      22   8.73016
3 If 6 :     210     209  99.52381       1   0.47619
3 If 7 :     120     120 100.00000       0   0.00000
4 If 4 :     210      29  13.80952     181  86.19048
4 If 5 :     252     110  43.65079     142  56.34921
4 If 6 :     210     161  76.66667      49  23.33333
4 If 7 :     120     116  96.66667       4   3.33333
5 If 5 :     252      12   4.76190     240  95.23810
5 If 6 :     210      46  21.90476     164  78.09524
5 If 7 :     120      64  53.33333      56  46.66667
6 If 7 :     120       8   6.66667     112  93.33333

#3. CoverMaster recognizes the wheel as a CM(10,6,3,6)=3

T if M    Tested Covered         % Not Covered     %
----------------------------------------------------
2 If 2 :      45      33  73.33333      12  26.66667
2 If 3 :     120     117  97.50000       3   2.50000
2 If 4 :     210     210 100.00000       0   0.00000
2 If 5 :     252     252 100.00000       0   0.00000
2 If 6 :     210     210 100.00000       0   0.00000
2 If 7 :     120     120 100.00000       0   0.00000
3 If 3 :     120      54  45.00000      66  55.00000
3 If 4 :     210     180  85.71429      30  14.28571
3 If 5 :     252     252 100.00000       0   0.00000
3 If 6 :     210     210 100.00000       0   0.00000
3 If 7 :     120     120 100.00000       0   0.00000
4 If 4 :     210      44  20.95238     166  79.04762
4 If 5 :     252     158  62.69841      94  37.30159
4 If 6 :     210     198  94.28571      12   5.71429
4 If 7 :     120     120 100.00000       0   0.00000
5 If 5 :     252      18   7.14286     234  92.85714
5 If 6 :     210      71  33.80952     139  66.19048
5 If 7 :     120      89  74.16667      31  25.83333
6 If 7 :     120      12  10.00000     108  90.00000

 

[Brad]

Not sure if this helps but were you to change Wheel #1. to say 1,2,3,8,9,10 then CM would recognize it as CM(10,6,3,6)=1

It may help to look at the stats keeping '10' throughout. Notice though that the coverage is lower, as expected, compared to picking from 9 numbers.

T if M    Tested Covered         % Not Covered     %
----------------------------------------------------
2 If 2 :      45      15  33.33333      30  66.66667
2 If 3 :     120      80  66.66667      40  33.33333
2 If 4 :     210     185  88.09524      25  11.90476
2 If 5 :     252     246  97.61905       6   2.38095
2 If 6 :     210     210 100.00000       0   0.00000
2 If 7 :     120     120 100.00000       0   0.00000
3 If 3 :     120      20  16.66667     100  83.33333
3 If 4 :     210      95  45.23810     115  54.76190
3 If 5 :     252     186  73.80952      66  26.19048
3 If 6 :     210     195  92.85714      15   7.14286
3 If 7 :     120     120 100.00000       0   0.00000
4 If 4 :     210      15   7.14286     195  92.85714
4 If 5 :     252      66  26.19048     186  73.80952
4 If 6 :     210     115  54.76190      95  45.23810
4 If 7 :     120     100  83.33333      20  16.66667
5 If 5 :     252       6   2.38095     246  97.61905
5 If 6 :     210      25  11.90476     185  88.09524
5 If 7 :     120      40  33.33333      80  66.66667
6 If 7 :     120       4   3.33333     116  96.66667

Btw, CM will not recognize 1,2,3,4,5,6 as a wheel ... it needs at least 7 numbers from which to pick, ie: 1,2,3,4,5,7 <-- this would be considered as CM(7,6,3,6)=1.

Cheers

 

[anxious]

I have noticed that CM misrecognizes wheel designs in general. Dont have an example handy right now, have noticed this behaviour of CM in the past.

 

[PAB]

Thanks Very Much for the Response & Information Brad, it is Appreciated.

All the Best.
PAB

 

[PAB]

Hi lottoarchitect & ExpertLotto,

I am Trying to get the Exact Interpretation and Logic of what a Group is ( 2 if 3 for Example ) because a Friend of Mine said he will Help me Write some VBA Code for this.
I have Written the Below and would Appreciate it if you would Look through it and make Any Comments Necessary Please.
Here we go :-

Write a VBA Procedure that Counts the Number of Unique 2 if 3 Combinations in the Wheel ( in Cells G13:L17 for Example ) by Looping through the Wheel One Combination ( Row ) at a Time.
For Each Combination ( Row ), Generate Every Combination of 2 Values from 6 and Store them Somewhere ( Scripting Dictionary for Example ), when Done, Count the Unique Items. Every Combination of 2 has to be an Subset of a Combination of 3.

Following on from here, lets Assume that we have 6 Numbers in Each Combination …
01 02 03 08 09 10
etc
etc
… for Example.

If we just Concentrate on the 2 if 3 Scenario, the Code Needs to do the Following :-
Because the Maximum Number in the Combination in this Case is 10, we Need to Calculate and Store ( Scripting Dictionary for Example ) the 120 Combinations ( =COMBIN(10,3) = 120 ) Produced for 3 Numbers from 10 Numbers.
Then Loop through Each 3 Numbers Stored ( Scripting Dictionary for Example ) and Count How Many of those 120 3 Numbers have Exactly 2 Numbers in Our Combination of 01 02 03 08 09 10. The Answer in this Case for Combination 01 02 03 08 09 10 should Equal 80.
The Macro Basically Needs to Loop through Every 3 Number Combination and Compare it to Each Individual Combination in Our Wheel. If Exactly 2 Numbers in Any of Our Wheel Combinations Match Exactly 2 Numbers in Any of the 3 Number Combinations then that is Counted and the Macro Moves on to the Next Combination etc.
Or the Macro could Loop through the Wheel and Compare it to the Numbers Stored ( Scripting Dictionary for Example ).

All the Best.
PAB

 

[PAB]

<< Replicated Post in Error >>

 

[PAB]

Hi,

When you Calculate the ? if ? Categories do the Numbers have to Match at "LEAST" or "EXACTLY".
For Example, if we Use the 2 if 5 Scenario, does it have to Match in at "LEAST" 2 Numbers or have to Match in "EXACTLY" 2 Numbers.

Thanks in Advance.
All the Best.
PAB