UWR - to Nick Koutras

G

Grandmaster

Member
Lottoarchitect,

I also want that WG1.4 optimized wheels, since you are the creator of WG1.4 wheels I won't show the wheel, I'll show only the results of Covermaster detail analysis comparing a C (8,6,5,6)=4 non optimized and C (8,6,5,6)=4 optimized with WG1.4.

First analysis LottodesignerXL UWR

Non-optimized LD( 8, 6, 3, 6) = 4 - 60
Optimized WG1.4 LD( 8, 6, 3, 6) = 4 - 65


Non optimized detail analysis using Covermaster:
6 5 4 3 % Total Acc %
--------------------------------------------------------------------------------------
- - - 1 32 57.14286 57.14286
- - - 2 24 42.85714 100.00000
6 5 4 3 % Total Acc %
--------------------------------------------------------------------------------------
- - - 4 16 22.85714 22.85714
- - 1 2 48 68.57143 91.42857
- - 2 0 6 8.57143 100.00000
6 5 4 3 % Total Acc %
--------------------------------------------------------------------------------------
- - 3 1 32 57.14286 57.14286
- 1 1 2 24 42.85714 100.00000
6 5 4 3 % Total Acc %
--------------------------------------------------------------------------------------
- 2 2 0 24 85.71429 85.71429
1 0 3 0 4 14.28571 100.00000

Optimized WG1.4 detail analysis using Covermaster:
6 5 4 3 % Total Acc %
--------------------------------------------------------------------------------------
- - - - 4 7.14286 7.14286
- - - 1 26 46.42857 53.57143
- - - 2 24 42.85714 96.42857
- - - 3 2 3.57143 100.00000
6 5 4 3 % Total Acc %
--------------------------------------------------------------------------------------
- - - 3 12 17.14286 17.14286
- - - 4 8 11.42857 28.57143
- - 1 1-3 40 57.14286 85.71429
- - 2 0-1 10 14.28571 100.00000
6 5 4 3 % Total Acc %
--------------------------------------------------------------------------------------
- - 2 2 13 23.21429 23.21429
- - 3 1 16 28.57143 51.78571
- - 4 0 4 7.14286 58.92857
- 1 0-2 1-3 22 39.28571 98.21429
- 2 0 2 1 1.78571 100.00000
6 5 4 3 % Total Acc %
--------------------------------------------------------------------------------------
- 1 3 0 6 21.42857 21.42857
- 2 2 0 14 50.00000 71.42857
- 3 1 0 4 14.28571 85.71429
1 0-1 2-3 0 4 14.28571 100.00000

Final comments,

The optimized wheel WG1.4 has a higher UWR than the non-optimized wheel, this means the non-optimized wheel is better acording to LottodesignerXL.

I think that using the optimized WG1.4 wheel take some risks, first If i hit 3 numbers out of 8 then I have a 7.14% chance of 0 wins, the non-optimized wheels always guarantees a 3 win if you hit 3 out of 8,

Another risk I see using WG1.4 optimized wheel is for example if you hit 6 numbers out of 8 then in the non-optimized wheel you guarantee 2 five and 2 four at least with 85.71%, in the optimized WG1.4 wheel you have a 21.43% chance of 1 five and 3 four, that is worst that the minimum guarantee by the non-optimized wheel.

At least in this wheel I can't see a better wheel than the original using WG1.4,

This is a constructive critic, what do you think?
 
L

lottoarchitect

Member
It is really unbelievable how far someone can go to prove a point that does not exist. GrandMaster, first of all, the close-cover database you have, is not optimized using WG yet. I have optimized several wheels but I haven't make the database available to the users yet. Any comparisons you make in the close-cover database ARE INVALID to prove anything against WG. And even if you prove something, WG still produces better wheels than Covermaster in terms of coverage on most cases I have tried it so far and some equivalent (possibly because we already reached an optimal level). So, I cannot understand again what you try to prove right now.

PLEASE read the previous posts again. For your information, the wheel you are assuming was created by WG, is in fact generated using Covermaster. So you compare two different wheels generated with Covermaster. I have optimized this wheel with WG and it turns out to be the same as the 1st wheel you post (you don't have this wheel in the LA database yet). Obviously, in 4 lines it is pretty easy to find the best arrangement which is the one of the 1st wheel. So, any complaints to Covermaster please.

Second, if you read again my previous posts, you'll see that coverage only is not enough to claim a wheel is better than another. It purely depends on an subjective definition of what is considered a better wheel. UWR is IMHO is insufficient to provide accurate measure of the wheels quality. I ask Nick Koutras to have a look on this matter but it seems he is not interested. I don't use UWR as I have seen properties that are not covered.
I propose another measure: minimum possible hits. This directly illustrates more winnings and more winnings means better wheel. This was the example I presented with the C(6,14,5,6)=98 in a previous post.
So, please please please, read think and then post. I don't know what you have against me but this is not good.
 
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G

Grandmaster

Member
Lottoarchitect,

It is really unbelievable how far someone can go to prove a point that does not exist. GrandMaster, first of all, the close-cover database you have, is not optimized using WG yet. I have optimized several wheels but I haven't make the database available to the users yet. Any comparisons you make in the close-cover database ARE INVALID to prove anything against WG. And even if you prove something, WG still produces better wheels than Covermaster in terms of coverage on all cases I have tried it so far. So, I cannot understand again what you try to prove right now.
Click to expand...

As I told you before this is a CONSTRUCTIVE CRITIC

PLEASE read the previous posts again. For your information, the wheel you are assuming was created by WG, is in fact generated using Covermaster. So you compare two different wheels generated with Covermaster. I have optimized this wheel with WG and it turns out to be the same as the 1st wheel you post (you don't have this wheel in the LA database yet). Obviously, in 4 lines it is pretty easy to find the best arrangement which is the one of the 1st wheel. So, any complaints to Covermaster please.
Click to expand...

If I go to your webpage I could see the section "wheels" pick 6, 5 if 6 in 4 numbers and *4.

Then I find LEGEND * Wheels marked are optimized using WG1.4, then I compare this wheel of the program (I unfortunately buy).

I have full version with latest wheels, do you sell my crap wheels? Covermaster wheels? I was fooled then, because that means any of the wheels listed in your page are real to the final user.
Second, if you read again my previous posts, you'll see that coverage only is not enough to claim a wheel is better than another. It purely depends on an subjective definition of what is considered a better wheel. UWR is IMHO is insufficient to provide accurate measure of the wheels quality. I ask Nick Koutras to have a look on this matter but it seems he is not interested. I don't use UWR as I have seen properties that are not covered.
Click to expand...

At least UWR is trusted than your fake wheels.

So, please please please, read think and then post. I don't know what you have against me but this is not good.
Click to expand...

I don't believe anymore in WG1.4 wheels, your marketing strategy to sell your program is based in wheels that don't exist in the full version of your program.
 
L

lottoarchitect

Member
Grandmaster said:
Lottoarchitect,



As I told you before this is a CONSTRUCTIVE CRITIC



If I go to your webpage I could see the section "wheels" pick 6, 5 if 6 in 8 numbers and *4.

Then I find LEGEND * Wheels marked are optimized using WG1.4, then I compare this wheel of the program (I unfortunately buy).

I have full version with latest wheels, do you sell my crap wheels? Covermaster wheels? I was fooled then, because that means any of the wheels listed in your page are real to the final user.


At least UWR is trusted than your fake wheels.



I don't believe anymore in WG1.4 wheels, your marketing strategy to sell your program is based in wheels that don't exist in the full version of your program.
Click to expand...

Just one comment on al these as what you say is totally unfair. You bought the program on 11/12/2004. At that time, WG did not even exist. So, how do you expect to have WG wheels in the program? Furthermore, keep in mind that all programs around use wheels from several sources. Some wheels I have are from Covermaster. Now, if you call these crap, then you know where your comment refers to. As for the marked wheel, please read the legend below (green colour=to be updated in the next database version. The mark * indicates that the update will be a wheel from WG). The database version you have is on 1/12/2004) which is the latest available for users and obviously not optimized using WG.

Now think a bit, you attack me for any efforts I make to provide you with the highest quality wheels because everything I do is to have happy customers. Finally, you have WG wheels to compare, the 1st version of the open-cover database. I think you really overeacting. You just try to find something to hit me for a reason I don't know. Finally, nobody in here is interested in a fight between me and you, neither me. As for UWR, you have already made several tests on WG wheels and all of them had a better UWR, so you still believe on the comment you made? Still, UWR does not take into account all aspects of a wheel.
 
T

tomtom

Member
lottoarchitect said:
Finally, nobody in here is interested in a fight between me and you, neither me.
Click to expand...


:rolleyes:

There is no need for any fights...if someone paid some $$ believing in your product, he/she is supposed to be a valuable customer..... ?:rolleyes:

Sorry, it's not $$...that were some euros, right?
 
G

Grandmaster

Member
You bought the program on 11/12/2004. At that time, WG did not even exist. So, how do you expect to have WG wheels in the program? Furthermore, keep in mind that all programs around use wheels from several sources. Some wheels I have are from Covermaster. Now, if you call these crap, then you know where your comment refers to. As for the marked wheel, please read the legend below (green colour=to be updated in the next database version. The mark * indicates that the update will be a wheel from WG). The database version you have is on 1/12/2004) which is the latest available for users and obviously not optimized using WG.
Click to expand...

Final comments,

Covermaster is not crap, it generates good wheels for free, that's the difference,

I don't expect the full database optimized with WG1.4, I only expect the * wheels optimized, because you have them and they are no more than 30 with * in some sections.

But I understand that you are very jealous with your wheels and final customers like me don't deserve such wheels, only after 2 or 5 or 6 months or the moment you THE CREATOR decides.

Well, I won't do critics to your software or wheels anymore because you feel offended, feel better LA.
 
L

lottoarchitect

Member
Grandmaster said:
Final comments,

... or the moment you THE CREATOR decides....
Click to expand...

Creating an optimized database takes time. The same way we do not release products that are not ready for the users even if they demand it, the same way the new database is not ready to go out yet. You have already 412 WG optimized wheels. Given the WG works till 24/12/2004 and you already have 412 such wheels, I WONDER HOW YOU CAN COMPLAIN REALLY. TELL ME WHICH LOTTERY SOFTWARE PUBLISHER OFFERS YOU SUCH AFTER SALES SUPPORT. And you still complain. Some people are really unsatisfied no matter what they are being offered. I can't say anything else. NO more fights.
 
N

Nick Koutras

Member
UWR is a statistical test.
So to dispute the result is like disputing "Statistics"
It is very easy to generate/find an anova template in the net
and apply it to any design.
Check the math behind the p value.

If you wish I can send you such a spreadsheet.


Your effort to produce "optimized" designs is valiant and worthy.
Your optimization on the design(14,6,5,6)=98 is indicating
that you have to learn more about designs and what can make a design
better for the player.

Be more forward as of to what you wish to know.
Your thread should have been "Methods to optimize Lotto Designs"

My designs are free for every body to use and apply.


Try to match the one LottoDesignerXL v2.81 produced for the same
parameters in just 5 passes.
(The present algorithm did indicate that no more optimization is possible)
Bare in mind that with construction of designs this does change quickly...


LD(14,6,5,6)=98

1 2 3 4 5 6
1 2 3 4 7 8
1 2 3 9 10 11
1 2 3 5 7 12
1 2 3 12 13 14
1 2 4 5 6 8
1 2 4 6 9 13
1 2 4 6 10 14
1 2 4 7 11 12
1 2 5 9 11 14
1 2 5 10 11 13
1 2 6 7 8 11
1 2 8 11 13 14
1 2 8 9 10 12
1 3 4 5 8 11
1 3 4 6 7 8
1 3 4 8 9 14
1 3 4 8 10 13
1 3 5 6 11 12
1 3 6 11 13 14
1 3 6 9 10 12
1 3 7 9 11 13
1 3 7 10 11 14
1 4 5 7 9 10
1 4 5 7 13 14
1 4 9 11 12 13
1 4 9 10 13 14
1 4 10 11 12 14
1 5 6 10 12 13
1 5 6 7 8 11
1 5 6 9 12 14
1 5 8 9 12 13
1 5 8 10 12 14
1 6 7 9 12 13
1 6 7 10 12 14
1 6 8 9 10 11
1 6 8 12 13 14
1 7 8 10 12 13
1 7 8 9 12 14
2 3 4 5 7 11
2 3 4 11 13 14
2 3 4 9 10 12
2 3 5 8 9 13
2 3 5 6 8 12
2 3 5 6 11 12
2 3 5 8 10 14
2 3 6 8 9 14
2 3 6 8 10 13
2 3 6 7 10 13
2 3 6 7 9 14
2 3 7 8 11 12
2 4 5 10 12 13
2 4 5 9 12 14
2 4 6 7 8 12
2 4 7 9 11 14
2 4 7 10 11 13
2 4 8 12 13 14
2 4 8 9 10 11
2 5 6 7 13 14
2 5 6 8 11 12
2 5 6 7 9 10
2 5 7 8 9 13
2 5 7 8 10 14
2 6 9 11 12 13
2 6 10 11 12 14
2 7 9 10 13 14
3 4 5 10 12 14
3 4 5 9 12 13
3 4 6 8 11 12
3 4 6 12 13 14
3 4 6 9 10 11
3 4 7 10 12 14
3 4 7 9 12 13
3 5 6 7 9 14
3 5 6 8 10 14
3 5 6 7 10 13
3 5 6 8 9 13
3 5 7 8 13 14
3 5 7 8 9 10
3 5 9 10 13 14
3 6 7 8 11 12
3 8 9 11 12 14
3 8 10 11 12 13
4 5 6 10 11 14
4 5 6 7 8 12
4 5 6 9 11 13
4 5 8 9 11 14
4 5 8 10 11 13
4 6 7 10 11 13
4 6 7 9 11 14
4 6 8 9 10 12
4 6 8 11 13 14
4 7 8 9 11 13
4 7 8 10 11 14
5 7 9 10 11 12
5 7 11 12 13 14
6 8 9 10 13 14
9 10 11 12 13 14
 
A

aluc8rd

Member
Hi Nick,

I would like to receive this spreadsheet in my email and am thankful very if you he will be able to make this.

Best regards,


Freehand
<<< email addy deleted - thanks to all who reported >>>
 
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G

Grandmaster

Member
Great wheel Nick!

Also great wheel LA, both are optimized wheels (14,6,5,6)=98,

Your effort to produce "optimized" designs is valiant and worthy.
Your optimization on the design(14,6,5,6)=98 is indicating
that you have to learn more about designs and what can make a design
better for the player.
Click to expand...

Analysis:

LottoDesignerXL UWR

WG1.4 LD( 14, 6, 5, 6) = 98 - 32973
Nick k. LD( 14, 6, 5, 6) = 98 - 32946

The optimized wheel WG1.4 has a higher UWR than the Nick Koutras wheel, this means the Nick K. wheel is better acording to UWR.

The detail report of Covermaster shows better coverage for Nick Koutras wheel.

WG1.4 wheel result is very close to latest version of Nick K. LottodesignerXL wheel, that means WG1.4 is generating very good wheels but as Nick recommends you have to learn more about designs to make a better design for the player.

My designs are free for every body to use and apply.
Click to expand...

Thank you Nick, your wheels are the best :agree2:
 
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L

lottoarchitect

Member
Nick Koutras, of course I don't doubt statisics in anyway. I'm a mathematician myself. What I ask is what UWR evaluates and some proof why this result is valid, or at least an intuitable discussion of the validity. We do not apply directly ANOVA & p-value on the wheel's tickets. Furthermore, each statistical test has the null hypothesis and an alternative. What is your hypothesis and compared to which sample?
We have been given UWR. Good. It is better than nothing of course. People that don't know maths, they accept it as is because they told it evaluates wheels and they use it blindly. Me, as a mathematician, I query what UWR evaluates, given the subject of coverings has more parameters involved. I don't say I know everything about coverings but I'm willing to learn. From what I have read in the posted links, UWR evaluation based solely on the coverage achieved.

I'll present 3 different cases. Please try to favor or go against their validity.

Case 1: Increasing the overall coverage on average, we have a better wheel (UWR).
Case 2: Increasing the minimum possible hits achieved on average, we have a better wheel.
Case 3: Reducing the variance (x^2) of tickets dependency, we have a better wheel.

More cases can be derived too. The above illustrate simply some examples of what might be considered a better wheel. Intuitively, case 1 & 2 seem to be valid. However I don't see a reason why case 2 is lesser than case 1 or vise-versa. Both define an improvement. Case 3 cannot directly related to improvement but deeper thought can realise it does, although players don't directly benefit from this. However, each case offer a different means of improvement, but still is an improvement.
My opinion is that case 2 is more directly related to players than case 1. Of course case 1 is desirable too. More coverage of everything is preferable. As I said before, case 1 & 2 do not go hand-by-hand (at least this is what I observe). Improvement of one usually degrade the other. Your designs are based on coverage achievement. My designs based on multiple hits achieved + coverage + dependency (lesser).

So, the questions that arise are simple:
- Do we need to define more UWR evaluators to cover all such cases based on the improvement we try to achieve?
- Can we combine all these in one UWR?
- Do really case 1/2/3 represent improvements of wheels? This one directly queries what is considered a better wheel.

Also, given WG is only 2 months in life and LottoDesigner is some years now, I'm more than satisfied I have achieved these results. Who knows what I'll have prepared in the following months/years regarding this matter. Of course, I do not doubt the quality of LottoDesigner, indeed the wheel you present is better in terms of coverage. Should we consider the other cases too?
 
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L

lottoarchitect

Member
Now, till Nick Koutras reply, I have a good question for all people who want to participate here. Please post your opinion and most important, the reason you made a selection.
I'll provide you with two wheels C(49,6,3,6)=163 in the next two posts. For now I'll display their detail analysis as obtained by Covermaster detail reports, which is sufficient to have a clear view about the wheels. I want your comments on which wheel you choose and why. Please also mention the reason you rejected the other wheel. I'll later post the wheels too.
 
L

lottoarchitect

Member
Wheel A
----------

Information on 3 Hits
6 5 4 3 % Total Acc %
--------------------------------------------------------------------------------------
- - - - 15417 83.67890 83.67890
- - - 1 2828 15.34954 99.02844
- - - 2 142 0.77073 99.79917
- - - 3 11 0.05970 99.85888
- - - 4 18 0.09770 99.95658
- - - 5 5 0.02714 99.98372
- - - 6 3 0.01628 100.00000

Information on 4 hits
6 5 4 3 % Total Acc %
--------------------------------------------------------------------------------------
- - - - 113157 53.40718 53.40718
- - - 1 75762 35.75771 89.16489
- - - 2 8657 4.08588 93.25077
- - - 3 3277 1.54666 94.79743
- - - 4 7968 3.76069 98.55812
- - - 5 463 0.21852 98.77664
- - - 6 131 0.06183 98.83847
- - - 7 33 0.01558 98.85405
- - 1 0-6 2411 1.13793 99.99198
- - 2 2-5 17 0.00802 100.00000

Information on 5 hits
6 5 4 3 % Total Acc %
--------------------------------------------------------------------------------------
- - - - 336798 17.66222 17.66222
- - - 1 966680 50.69422 68.35644
- - - 2 154528 8.10369 76.46013
- - - 3 78181 4.09993 80.56007
- - - 4 217600 11.41129 91.97135
- - - 5 25635 1.34434 93.31569
- - - 6 11208 0.58777 93.90346
- - - 7 4035 0.21160 94.11506
- - - 8 1760 0.09230 94.20736
- - - 9 346 0.01814 94.22550
- - - 10 7470 0.39174 94.61724
- - - 11 76 0.00399 94.62122
- - - 12 16 0.00084 94.62206
- - - 13 12 0.00063 94.62269
- - 1 0-10 98267 5.15328 99.77597
- - 2 1-9 3093 0.16220 99.93817
- - 3 1-6 190 0.00996 99.94814
- - 4 3-6 11 0.00058 99.94871
- 1 0-2 0-9 978 0.05129 100.00000

Information on 6 hits
6 5 4 3 % Total Acc %
--------------------------------------------------------------------------------------
- - - 1 3595746 25.71362 25.71362
- - - 2 3261643 23.32441 49.03804
- - - 3 1114905 7.97282 57.01086
- - - 4 2858548 20.44183 77.45269
- - - 5 476971 3.41088 80.86357
- - - 6 223556 1.59868 82.46225
- - - 7 93980 0.67206 83.13431
- - - 8 64089 0.45831 83.59262
- - - 9 37278 0.26658 83.85920
- - - 10 220944 1.58000 85.43920
- - - 11 11270 0.08059 85.51979
- - - 12 3665 0.02621 85.54600
- - - 13 1290 0.00922 85.55522
- - - 14 348 0.00249 85.55771
- - - 15 139 0.00099 85.55871
- - - 16 29 0.00021 85.55891
- - - 17 6 0.00004 85.55896
- - - 18 8 0.00006 85.55901
- - - 20 2476 0.01771 85.57672
- - 1 0-17 1781368 12.73878 98.31550
- - 2 1-15 165076 1.18048 99.49598
- - 3 1-13 25917 0.18534 99.68132
- - 4 0-10 2138 0.01529 99.69661
- - 5 2-7 207 0.00148 99.69809
- - 6 0-7 53 0.00038 99.69847
- - 7 3-5 8 0.00006 99.69852
- - 9 2 1 0.00001 99.69853
- 1 0-4 0-15 41942 0.29993 99.99846
- 2 1-2 3-8 44 0.00031 99.99878
- 3 0 4-7 8 0.00006 99.99883
1 0 0-3 0-13 163 0.00117 100.00000
 
L

lottoarchitect

Member
Wheel B
----------

Information on 3 Hits
6 5 4 3 % Total Acc %
--------------------------------------------------------------------------------------
- - - - 15164 82.30569 82.30569
- - - 1 3260 17.69431 100.00000

Information on 4 Hits
6 5 4 3 % Total Acc %
--------------------------------------------------------------------------------------
- - - - 91421 43.14835 43.14835
- - - 1 96834 45.70315 88.85150
- - - 2 20186 9.52727 98.37877
- - - 3 986 0.46537 98.84414
- - - 4 4 0.00189 98.84602
- - 1 0 2445 1.15398 100.00000

Information on 5 Hits
6 5 4 3 % Total Acc %
--------------------------------------------------------------------------------------
- - - - 195231 10.23822 10.23822
- - - 1 659418 34.58092 44.81914
- - - 2 662624 34.74905 79.56819
- - - 3 246341 12.91851 92.48670
- - - 4 35237 1.84788 94.33458
- - - 5 1881 0.09864 94.43322
- - - 6 39 0.00205 94.43527
- - 1 0-4 105135 5.51344 99.94871
- 1 0 0 978 0.05129 100.00000

Information on 6 Hits
6 5 4 3 % Total Acc %
--------------------------------------------------------------------------------------
- - - - 97004 0.69369 0.69369
- - - 1 874323 6.25239 6.94608
- - - 2 2762387 19.75417 26.70025
- - - 3 3972107 28.40503 55.10528
- - - 4 2836287 20.28264 75.38792
- - - 5 1032011 7.38004 82.76796
- - - 6 192977 1.38000 84.14796
- - - 7 17837 0.12755 84.27552
- - - 8 839 0.00600 84.28152
- - - 9 17 0.00012 84.28164
- - 1 0-7 2103888 15.04516 99.32680
- - 2 0-5 51819 0.37056 99.69736
- - 3 0-2 103 0.00074 99.69810
- 1 0 0-4 42054 0.30073 99.99883
1 0 0 0 163 0.00117 100.00000
 
S

SRM

Member
History:
49-6-3-6=163 found by Rade & Dragan some years back

System is made from 22-6-3-3=77, a perfect system which absolutely can not be improved upon.
Add to this 27-6-3-4=86.

So any improvements made must be contained within the 27-6-3-4.
This was a very talked about / debated subject on RGL June 2004.
From memory the system posted at merseyworld/lottery had a better covering than the original Rade/Dragan system.

Rgds..
 
L

lottoarchitect

Member
Ok, I don't know why nobody posted his opinion, I'll present mine here and I hope this time you'll understand what I'm talking about.
Wheel A is the Rade&Dragan's world record wheel.
Wheel B is another contruction.

What I'll present here is a discussion of why UWR is not a good measure of wheel's quality.

UWR for wheel A=around 48500
UWR for wheel B=29465

Based on UWR, we should choose wheel B. However the following comments will suggest why wheel B is worse than wheel A.

Let's begin:

We'll have a look at both wheels coverage. As expected, wheel B has better coverage than wheel A (UWR indicates that too):

Wheel A
T if M Tested Covered % Not Covered %
----------------------------------------------------------------------
2 If 2 : 1,176 582 49.48980 594 50.51020
2 If 3 : 18,424 18,424 100.00000 0 0.00000
2 If 4 : 211,876 211,876 100.00000 0 0.00000
2 If 5 : 1,906,884 1,906,884 100.00000 0 0.00000
2 If 6 : 13,983,816 13,983,816 100.00000 0 0.00000
2 If 7 : 85,900,584 85,900,584 100.00000 0 0.00000
3 If 3 : 18,424 3,007 16.32110 15,417 83.67890
3 If 4 : 211,876 98,719 46.59282 113,157 53.40718
3 If 5 : 1,906,884 1,570,086 82.33778 336,798 17.66222
3 If 6 : 13,983,816 13,983,816 100.00000 0 0.00000
3 If 7 : 85,900,584 85,900,584 100.00000 0 0.00000
4 If 4 : 211,876 2,428 1.14595 209,448 98.85405
4 If 5 : 1,906,884 102,539 5.37731 1,804,345 94.62269
4 If 6 : 13,983,816 2,016,925 14.42328 11,966,891 85.57672
4 If 7 : 85,900,584 22,898,862 26.65740 63,001,722 73.34260
5 If 5 : 1,906,884 978 0.05129 1,905,906 99.94871
5 If 6 : 13,983,816 42,157 0.30147 13,941,659 99.69853
5 If 7 : 85,900,584 884,838 1.03007 85,015,746 98.96993
6 If 7 : 85,900,584 7,009 0.00816 85,893,575 99.99184


Wheel B
T if M Tested Covered % Not Covered %
----------------------------------------------------------------------
2 If 2 : 1,176 1,175 99.91497 1 0.08503
2 If 3 : 18,424 18,424 100.00000 0 0.00000
2 If 4 : 211,876 211,876 100.00000 0 0.00000
2 If 5 : 1,906,884 1,906,884 100.00000 0 0.00000
2 If 6 : 13,983,816 13,983,816 100.00000 0 0.00000
2 If 7 : 85,900,584 85,900,584 100.00000 0 0.00000
3 If 3 : 18,424 3,260 17.69431 15,164 82.30569
3 If 4 : 211,876 120,455 56.85165 91,421 43.14835
3 If 5 : 1,906,884 1,711,653 89.76178 195,231 10.23822
3 If 6 : 13,983,816 13,886,812 99.30631 97,004 0.69369
3 If 7 : 85,900,584 85,894,432 99.99284 6,152 0.00716
4 If 4 : 211,876 2,445 1.15398 209,431 98.84602
4 If 5 : 1,906,884 106,113 5.56473 1,800,771 94.43527
4 If 6 : 13,983,816 2,198,027 15.71836 11,785,789 84.28164
4 If 7 : 85,900,584 25,540,468 29.73259 60,360,116 70.26741
5 If 5 : 1,906,884 978 0.05129 1,905,906 99.94871
5 If 6 : 13,983,816 42,217 0.30190 13,941,599 99.69810
5 If 7 : 85,900,584 890,143 1.03625 85,010,441 98.96375
6 If 7 : 85,900,584 7,009 0.00816 85,893,575 99.99184

As you can see, wheel B indeed offers some good increase of coverage on several categories. Does that mean wheel B is better for playing C(49,6,3,6)=163?

Understanding what is wrong with wheel B:
2 flaws can be found
- the 3if6 category does not offer 100% coverage.
- the hits have been 'killed'

What that suggests is that although we have managed to increase the overall coverage, however, we do that on categories we really do not care about their coverage. As you can see, the 2if2 has been improved by about 50%! Pretty amazing result but... do we care? NO! Why? Because there is no way to win anything anyway if we match 2 numbers only. Thus, this category is of no use even if we improve it. And still, UWR shows this huge rate improvement because it considers this category a valuable one, when it should not be considered at all. The other categories are more important and there, coverage increase is welcome.
So according to the 1st flaw (no 100% coverage on 3if6), the wheel should be considered already worse, as our selection of wheel (3if6) suggests that we want this category to offer the best possible first. I really can't imagine how a person can feel, if he matches all 6 numbers and don't win something because of this loss of coverage... and still UWR suggests this as a better wheel:rolleyes:
The second flaw, and even more important, is the 'killing' of wins. Just watch the detailed reports above. The best we can hope with wheel B is mediocre wins. No multiple hits, no nothing. Unfortunately, this is the result of trying to improve coverage on irrelevant categories (eg 2if2). Still, UWR suggests wheel B is better. Well, how can this be with the above 2 flaws?

Is UWR a valid measure?
UWR is defined correctly in terms of mathematics. It does evaluate correctly coverage improvements. However, what is wrong about that is the assumption that if we increase all categories, we have a better wheel. The above example illustrates the defeats we have trying to increase categories that do not offer wins anyway. Also, this is the main reason UWR could not be considered a good measure for the overall wheels performance. It is the best measure to evaluate wheels in terms of coverage but better coverage does not necessarily means better wheel. And finally, better coverage is not what the player wants; he wants better hits and not 'dead' wheels in terms of hits like wheel B does, even if it offers better coverage.
If you have any comments for the above analysis, feel free to post your opinion. My conclusion is that UWR should not be used at all as a measure of quality; only if we are interested in coverage improvements. And even in this case, still lacks accuracy as it assumes all categories are equal which they are not.
 
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