[mikestar]

Ben,

Thus far I have only been discussing initial valuation. As to revaluation in case of a superfit 2 points per extra trump is fairly equiavlent to Zar's simplified 3 points per extra trump. I'll publish details about revaluation later.

[Zar]

Mike,

Let me get this straight since I intend to run some boards through the 1-3-5 valuation (some means like 100K of course, rather than a couple :-). You say "programmed for years to think in terms of 13/26/33/37, instead of 26/52/62/67" and I take that as you add the 1-3-5 for xx-x-void to the HCP and "flag" a Game if you get to 26, Small with 33, and Grand with 37. Prety much like with Goren, correct?

It will be the same set of boards that were reported in the "Reserch" section of the book on the website (where the xx-x-void are calculated via 1-2-3 though). Let me know.

Cheers:

ZAR

[tysen2k]

mikestar, on Apr 21 2004, 04:51 PM, said:

Thus far I have only been discussing initial valuation. As to revaluation in case of a superfit 2 points per extra trump is fairly equiavlent to Zar's simplified 3 points per extra trump. I'll publish details about revaluation later.

And see my articles on revaluation (although long and detailed). I think I mentioned them earlier in this thread:

[Improving Hand Evaluation Part 1]
http://tinyurl.com/25huc

[Improving Hand Evaluation Part 2]
http://tinyurl.com/383e6


Zar, in reference to how many hands I've tested it on it's over 2.8 million.

Let me just show some hard data so we're not talking about "IMHO."

           Tricks  Tricks  Tricks  Error   Error
           Real    ZAR     5/3/1   ZAR     5/3/1
4-3-3-3   0.000   0.000   0.000   0.000   0.000
4-4-3-2   0.296   0.400   0.333   0.235   0.030
5-3-3-2   0.339   0.600   0.333   1.061   0.000
5-4-2-2   0.595   0.800   0.667   0.447   0.055
6-3-2-2   0.660   1.000   0.667   0.655   0.000
4-4-4-1   0.810   0.600   1.000   0.133   0.109
5-4-3-1   0.864   1.000   1.000   0.241   0.241
6-3-3-1   0.918   1.200   1.000   0.276   0.023
7-2-2-2   0.999   1.200   1.000   0.021   0.000
6-4-2-1   1.154   1.400   1.333   0.286   0.152
5-5-2-1   1.183   1.200   1.333   0.001   0.073
7-3-2-1   1.208   1.600   1.333   0.290   0.030
5-4-4-0   1.519   1.200   1.667   0.127   0.027
6-4-3-0   1.624   1.600   1.667   0.001   0.002
5-5-3-0   1.643   1.400   1.667   0.054   0.001
7-3-3-0   1.697   1.800   1.667   0.003   0.000
6-5-1-1   1.703   1.600   2.000   0.008   0.063
7-4-1-1   1.712   1.800   2.000   0.003   0.032
7-4-2-0   1.923   2.000   2.000   0.002   0.002
6-5-2-0   1.964   1.800   2.000   0.018   0.001
               
                          Totals   3.862   0.842

We're looking at how many more tricks you take with certain hand patterns over a 4333 hand. The first column shows what the actual average difference is over the 2.8 million hands. The second column is what ZAR predicts the difference will be. Third column is what 5/3/1 predicts. Fourth and fifth are the squared errors weighted by frequency. The totals on the bottom show that ZAR has over 4.5 times as much error as 5/3/1. Note that I'm using 3 points per trick for 5/3/1 even though it should be slightly less since 26/29/33/37 aren't perfectly 3 point steps. If I change it to a little more than 3, then the 5/3/1 count gets even better.

Tysen

[mikestar]

Zar,

you understand me correctly.

[Zar]

Hi, guys:

I ran the Grand Slams for WTC and for the 1-3-5 evaluation.

I DO realize that in the Slam / Grand area Zar Points are hard to come close to and that 4S/4H (Games) is the more important one to get right. But still, here are the runs:


7 (GRANDs, 7813 boards)========Overall Results ===========

GOREN Points ( HCP + 3-2-1> 36 ) got 135 contracts
The WTC (Number of tricks > 12) got 667 contracts
The GOREN 135 ( HCP + 5-3-1> 36 ) got 1231 contracts
Basic Zar Points (no fit points) got 1925 contracts
Fit Zar Points (+3 extra trump) got 3760 contracts

I'll run the Games ( 5C/5D and 4S/4H) probably during the weekend (will try earlier). I'll also ZIP the files and make them available for download on the site.

Again, Grand Slam area is the "extreme" for Zar Points so the comparisson in the Small Slams and Games would be more interesting. One thing I noted immediately, though, is that 1-3-5 is almost 10 TIMES better than Goren 123 - it is much more interesting to go through all the 7813 boards and observe the specific differences.

Cheers:

ZAR

[mikestar]

I'm inclined to think that putting up with the brain cramp while changing my ways might be worth it.

Did you also allow for +1/2 HCP for each ace and -1/2 HCP for each queen in the 1-3-5 calculations? If not, then part of Zar's superiority is the more accurate honor count.

A fit version of 1-3-5 is easily defined-- add 2 points per extra trump instead of Zar's 3 to reflect the different size of the scales.

I suspect these two changes (or one if you already did the HCP adjustment) will bring 1-3-5 closer to Zar. It is also possible that the targets should be one point lighter--American beginners are taught 26 for game and European beginners are taught 25.

I wouldn't be surprised to see that Zar is still superior even with these adjustments to 1-3-5, but for me the test is how much superior--how much improvement do I get in exchange for the mental effort.

For anyone who can adjust to using Zar at the table easily, I'm sure the effort is worth it. I can envision that many people would find changing the targets easier than using half points as I advocate or quarter points as in BUM Rap. For me I find it harder to change targets.

[mikestar]

I wanted to share something I came up with during my mental meanderings aroung Zar points. Here is a formula for converting HCP/Goren point/Bergen point etc. bidding requirements to Zar points. First determine an appropriate base shape for the bid. For bids such as opening one bids that can be unbalanced but don't show extreme shape, I would suggest using 5-4-2-2: note that its 12 Zar DP is halfway between 11 Zar DP for 4-4-4-1 (the weakest unbalanced patern), and 13 Zar DP for 5-4-3-1 (the most common unbalanced pattern).

We assume that the point count requirement applies to a hand of the base shape with a normal number of controls. Proceed as follows:

1. Convert the requirement to HCP if it isn't already in HCP, by deducting the distribution points for the base shape.
2. Multiply the HCP by 1.3 to convert HCP to Zar honor Points.
3. Add the Zar DP for the base shape.

Some examples:

Goren opening one bid (13 Goren points):

Subtract the 2 Goren DP from 13 yielding 11 HCP.
Multiply 11 HCP by 1.3 yielding 14.3 Zar HP--round to 14.
Add the 12 Zar DP for 5-4-2-2 shape to the 14 Zar HP, yielding 26 Zarpoints

A Rule of 18 opening:

18 - 9 (Bergen value of 5-4-2-2) = 9
9 * 1.3 = 11.7, round to 12
12 + 12 = 24 Zar points


Precision 1C (with unbalanced hand):

16 HCP, no subtraction.
16 * 1.3 = 20.8, round to 21
21 + 12 = 33 Zar points

Romex Dynamic NT (with unbalanced hand):

(Converting Rozenkranz's more complex requirements to "Rule of 27")

27 - 9 =18
18 * 1.3 = 23.4, round to 23
23 + 12 = 35 Zar points

This technique might be useful for setting Zarpoint standards for premepts (with different base shapes, of course). For example, thet's say our partnership's minumum weak two is something like KQxxxx xxx xx xx. We chose 6-3-2-2 as our base, giving 13 Zar DP. Now

5 * 1.3 = 6.5, round to 7
7 + 13 = 20 Zar points

Note that we don't do any of this calculating at the table--this is done when we are coverting our system notes to using Zar points. At the table we just count Zars.

This post has been edited by mikestar: 2004-April-23, 18:19

[Zar]

*** Mikestar wrote: I'm inclined to think that putting up with the brain cramp while changing my ways might be worth it.
<

I hope it’s not a typo and you didn’t mean “brain crap” :-)

>
Did you also allow for +1/2 HCP for each ace and -1/2 HCP for each queen in the 1-3-5 calculations? If not, then part of Zar's superiority is the more accurate honor count. A fit version of 1-3-5 is easily defined-- add 2 points per extra trump instead of Zar's 3 to reflect the different size of the scales.
<

None of these, Mike – just what you told me, HCP and 1-3-5. These +-½ will neutralize in most cases I believe, but if you insist I’ll put them in ...

>
I suspect these two changes (or one if you already did the HCP adjustment) will bring 1-3-5 closer to Zar.
<

The fit +2 will, that’s for sure.

>
It is also possible that the targets should be one point lighter--American beginners are taught 26 for game and European beginners are taught 25.
<

I am taught 24 :-)

>
I wouldn't be surprised to see that Zar is still superior even with these adjustments to 1-3-5, but for me the test is how much superior--how much improvement do I get in exchange for the mental effort.
<

I have the feeling I am pulling your teeth with these Zar Points :-) Have you ever worked harder? :-)

>
For anyone who can adjust to using Zar at the table easily, I'm sure the effort is worth it. I can envision that many people would find changing the targets easier than using half points as I advocate or quarter points as in BUM Rap.
<

These quarters and halfs and rounding stuff ... How come none of them is a brain cramp for you? Cannot seize to wonder :-)

ZAR

[mikestar]

[Mikestar post]
I'm inclined to think that putting up with the brain cramp while changing my ways might be worth it.


[Zar reply]
I hope it’s not a typo and you didn’t mean “brain crap” :-)

[mikestar reply]
Not a typo (for once!)

[mikestar post]
It is also possible that the targets should be one point lighter--American beginners are taught 26 for game and European beginners are taught 25.

[Zar reply]
I am taught 24 :-)

[mikestar reply]
Always were an agreesive game bidder, weren't you? ;-)

[mikestar post]
I wouldn't be surprised to see that Zar is still superior even with these adjustments to 1-3-5, but for me the test is how much superior--how much improvement do I get in exchange for the mental effort.

[Zar reply]
I have the feeling I am pulling your teeth with these Zar Points :-) Have you ever worked harder? :-)

[mikestar reply]
Well, yes--not at bridge however. It seems I always resist a new idea most strongly before adopting it.

You show both the ability and the willingness to defend your ideas with excellent supporting data--that counts for a lot. Many new ideas never got adopted by me because their inventors couldn't defned them or couldn't be bothered to do so.

[mikestar post]
For anyone who can adjust to using Zar at the table easily, I'm sure the effort is worth it. I can envision that many people would find changing the targets easier than using half points as I advocate or quarter points as in BUM Rap.

[Zar reply]
These quarters and halfs and rounding stuff ... How come none of them is a brain cramp for you? Cannot seize to wonder :-)

[mikestar reply]
I don't actually count them: noticing a couple of aces and no queens, I add a point.

My bridge history with regard to hand evaluation has involved many different point count methods (plus non-PC methods like the LTC). All of the methods had 26 for game, however much they differed otherwise (with the exception of a couple which clearly had no merit--for example, one with a 5-4-3-2 scale for honors). So the equation of 26=game is more firmly rooted in my unconsious than any method of counting to 26. I think it fairly likely that my experience is atypical.

In any event, the fact that I am considering such a radical overhaul of my methods is a testimony to the great merits of Zar points--I don't have the time or mental energy to waste wrestling with something merely above average.

As a side note, I find it interesting that 1-3-5 even without a fit adjustment is so much better than Goren 1-2-3: you would think it would be more widley played, as the adjustment from 1-2-3 is so simple.

[inquiry]

Hi Zar,

I have a question. I was plugging through your example of 7 level grand slams and lookng at the hands. And I noted a few hands that the opitmal contract (double dummy solver) was 7 that I think 7 is not a good contract on.

This is when I noted that you don't show the EW hands, so for example if the double dummy solver will drop a singleton trump K offside to make slam missing 4 trumps would that show up as the optimal contract? Would the fact that a grand slam had precisely 50% to make, would it be included in the "grand slam" group if the hand actually dealt was one where 13 tricks could be made, but listed as a six level contract if it was one where six was limit by the position of the opponents cards? I note that most of the 63 ZAR point grand slams that I looked as so far, even looking at the hands (but not the opponents), that a small slam would be the preferred contract (actually as predicted by ZAR Points I guess).

Ben

[Zar]

** Mikestar wrote: the fact that I am considering such a radical overhaul of my methods is a testimony to the great merits of Zar points...
<

I am happy to see a “hardliner” like you doing it, Mike – thank you.

>
As a side note, I find it interesting that 1-3-5 even without a fit adjustment is so much better than Goren 1-2-3: you would think it would be more widely played, as the adjustment from 1-2-3 is so simple.
<

I mentioned in another thread (read all the 3 threads on Zar Points here) that “...the “1-3-5 method” suffers the same “merging” deficiencies as Goren (since they assign values to the SAME parts of the 39 shapes). Not as bad as Drabble, but still 6-3-3-1 is same as 4-4-4-1 or 5-4-3-1 for example, or 5-4-4-0 is the same as 7-3-3-0 etc. meaning having 2 additional cards in a suit may not be reflected in any way.” I am sure you wouldn’t like someone to pull-out 2 cards from your longest suit from time to time, while you are playing a high-stake rubber bridge :-)

Another VERY important point that remains unnoticed. If you check the records from the experiments and read “The Research” section of the book, you’ll see that Zar Points is #1 in the “Not OVERBIDDING” comparisons!!! Being #1 is a 2-side coin – bidding the most Games and Slams and NOT OVERBIDDING part scores on Games and Games on Slams. I would have never published Zar Points if they didn’t demonstrate their ability to NOT overbid and I was happy to see Zar Points leading the comparison in the “NOT-overbidding” contest (see the records on the site).

Otherwise here a system for the previous “GRAND-slam” experiment that will beat both Goren 5-3-1 AND Zar Points – just bid a GRAND every time the bidding comes to you :-)

ZAR

P.S. I posted this reply by mistake to the other thread first, sorry.

[Zar]

*** Ben wrote: I was plugging through your example of 7 level grand slams and lookng at the hands. And I noted a few hands that the opitmal contract (double dummy solver) was 7 that I think 7 is not a good contract on.
<

I see you really think of me as a VERY hard-working guy, while I am just smart :-) I don’t check every single board of the millions I have in the databases. ALL of them are only played on Double-dummy by the (same :-) computer. There is a couple of them off – sure, but that’s a drop in the sea.

Now, here is an IMPORTANT note for you – WHY is Double-dummy SHARP for analysis? Here is why. The Double-dummy programs indicate an average 1.0 tricks MORE than you and I would make AGAINST THE COMPUTER, simply because “these guys” never make a mistake allocating the missing cards, never play in ruff-and-discard, never jump against forks etc. However, there was a study on 25 MILLION plays calculating that the average defender in those 25 million plays gives away 1.1 tricks as a defender!!! Yes, you and me too, my friend. Defense is not flagged as the hardest part of the game by chance.

That’s why I put the “AGAINST THE COMPUTER” in caps above – because it’s different at the table where there are 2 other PEOPLE (rather than computers) who are often willing to help you out. And you see that the 1.1 and 1.0 are close to neutralizing each-other.

>
This is when I noted that you don't show the EW hands, so for example if the double dummy solver will drop a singleton trump K offside to make slam missing 4 trumps would that show up as the optimal contract?
<

The direct answer is “yes”, but see above.

>
I note that most of the 63 ZAR point grand slams that I looked as so far, even looking at the hands (but not the opponents), that a small slam would be the preferred contract (actually as predicted by ZAR Points I guess).
<

Yes, I am glad you noticed that – Zar Points were the best performer in the NOT OVERBIDDING comparison and I value that equally if not more than the best performance in bidding Games and Slams. See my reply to Mike above.

Cheers:

ZAR

[Zar]

I owe you an appology for the GRAND slam comparison - it turned out that I
have left a filter throwing away hands with over 31 HCP (I make all kinds of
experiments and this filter was left from previous series). BUT - the good news
is that I have now run the GRANDS through several different filters and the
results will be of interest to you.

First, the GRANS slam area with no filters, meaning that the HCP restriction
is 40 points. Here are the numbers:


HCP_3-2-1 1427
WTC 1543
HCP_5-3-1 2913
Zar_NoFit 3753
Zar_Fit 5729


So in this "No-Filters" GRAND slam area where the HCP restriction is 40 HCP,
we can say that:


1) HCP_5-3-1 performs 2 TIMES better than HCP_3-2-1

2) Zar_Fit performs 2 TIMES better than HCP_5-3-1


This is the "worst-case-scenario" comparison for both 5-3-1 and Zar, meaning
that the lower you go on HCP the better their relative performance.

Here are the numbers for GRANDS with less that 35 HCP:

HCP_3-2-1 1232
WTC 1424
HCP_5-3-1 2718
Zar_NoFit 3567
Zar_Fit 5543


Here are the numbers for GRANDS with less that 31 HCP:

HCP_3-2-1 135
WTC 667
HCP_5-3-1 1231
Zar_NoFit 1925
Zar_Fit 3760


Here are the numbers for GRANDS with less that 27 HCP:

HCP_3-2-1 0
WTC 103
HCP_5-3-1 133
Zar_NoFit 224
Zar_Fit 1098


You see that the more aggressive the contract (in terms of low HCP), the bigger
the advantage of the Zar Points method, which is expected.

Compared to the 5-3-1 method, the difference grows from 2:1 for anay GRANDS,
to 10:1 for the aggressive GRANDS with less that 27 HCP.

Basically the same 10:1 ratio holds for 5-3-1 against 3-2-1 in the aggressive area,
and the same 2:1 advantage holds in the 40 HCP are. So:


1) HCP_5-3-1 performs 10 TIMES better than HCP_3-2-1

2) Zar_Fit performs 10 TIMES better than HCP_5-3-1


I guess it is safe to say that at any range, Zar Points are as much better than the
5-3-1 method as the 5-3-1 method is better than the 3-2-1.

These differences will get smaller and smaller as the Level of the contract goes down,
and eventually will disappear at the low-level partscores, where basically "all
methods are good enough for the 1 Club contract" :-)

Cheers:

ZAR

[inquiry]

It will be interesting to compare the ZAR fit with 5-3-1 using the corrections for Fit that Mikestar mentioned, but these ZAR numbers seem very impressive. I have definetly started trying to use ZAR points evalution during my bidding, and have started redefining some of my raises in terms of Zar points.

Ben

[Zar]

*** Ben wrote: "It will be interesting to compare the ZAR fit with 5-3-1 using the corrections for Fit that Mikestar mentioned, but these ZAR numbers seem very impressive.
<

I think I have mentioned in a previous post - for the 5-3-1 ONLY the HCP plus the distribution assignments are calculated, and for Zar Points ONLY the basic points AND the +3 per supertrump (in the case of Zar_Fit method) - no other adjustments of any kind. Similarly, for Goren ONLY the HCP and the 3-2-1 points are considered, despite the fact that obviously no expert plays bridge without any adjustments :-)

Ben, on the "Cavendish" thread (which surprised me), I can send you the 2000-2003 comparisons (I don't have your email address). In two words - the approach there is MUCH more exhaustive and scientific, so to say - every contract is played against the "Average Cavendish Defender", menaing all the results are "calibrated" against every single table on the Cavendish, rather than picking a single number. I guess you'll like it, and I'll try to do a session from the 2004 the same way. I'll certainly discuss the Cavendish thread once I go through it.

Cheers:

ZAR

[inquiry]

Zar, on May 18 2004, 08:34 AM, said:

*** Ben wrote: "It will be interesting to compare the ZAR fit with 5-3-1 using the corrections for Fit that Mikestar mentioned, but these ZAR numbers seem very impressive.
<

I think I have mentioned in a previous post - for the 5-3-1 ONLY the HCP plus the distribution assignments are calculated, and for Zar Points ONLY the basic points AND the +3 per supertrump (in the case of Zar_Fit method) - no other adjustments of any kind. Similarly, for Goren ONLY the HCP and the 3-2-1 points are considered, despite the fact that obviously no expert plays bridge without any adjustments :-)

Ben, on the "Cavendish" thread (which surprised me), I can send you the 2000-2003 comparisons (I don't have your email address). In two words - the approach there is MUCH more exhaustive and scientific, so to say - every contract is played against the "Average Cavendish Defender", menaing all the results are "calibrated" against every single table on the Cavendish, rather than picking a single number. I guess you'll like it, and I'll try to do a session from the 2004 the same way. I'll certainly discuss the Cavendish thread once I go through it.

Cheers:

ZAR

My email address is easy....it is my name (inquiry) at the bridgebase.com address. You can email me by simply clicking the email button at the bottom of this message (and private message me by clicking the PM button).

Ben

[tysen2k]

Zar, on May 17 2004, 10:08 PM, said:

HCP_3-2-1 1427
WTC  1543
HCP_5-3-1 2913
Zar_NoFit  3753
Zar_Fit  5729


So in this "No-Filters" GRAND slam area where the HCP restriction is 40 HCP,
we can say that:


1) HCP_5-3-1 performs  2 TIMES  better than HCP_3-2-1

2) Zar_Fit performs  2 TIMES  better than HCP_5-3-1

Please, please, please stop saying that this methodology shows that x method is 2 times better than y. If my system bids a grand on every hand, it would be shown to be the best method out there by this logic!

The comprehensive data that I posted under the "Zar accuracy question" post shows that HCP+531 (no fit) is close to Zar (no fit), but still worse than Zar. However, that's using raw HCP. Zar, you said a few weeks ago that you would run experiments using A=4.5, K=3, Q-1.5, J=0.75, T=0.25 and see how that does. Have you looked at that yet?

Again let me reiterate that I'm not trying to push one method over another and I'm not trying to trash Zar. I just want to make sure that experiments and statistics are reported in a scientific and not in a misleading manner.

Tysen

[Zar]

*** tysen2k wrote: “The comprehensive data that I posted under the "Zar accuracy question" post shows that HCP+531 (no fit) is close to Zar (no fit), but still worse than Zar. However, that's using raw HCP.
<

I have no idea what you mean by “comprehensive”. You have to realize that computers:

1) do WHAT you make them do;
2) do it the WAY you make them do it;
3) do it on the SET of boards that you feed them in with.

That’s why I have exhaustively explained WHAT I do and the WAY I do it, and POST all the hundreds of boards I actually use, for a download. Now THAT is what I call “comprehensive”.

In your “comprehensive approach” nobody can answer ANY of the these 3 questions, so nobody can judge whatever you are doing any way – positive or negative alike. We simply have no information other than your claims “this is THIS way, that is THAT way, because my analysis is the best” :-)

>
Zar, you said a few weeks ago that you would run experiments using A=4.5, K=3, Q-1.5, J=0.75, T=0.25 and see how that does. Have you looked at that yet?
<

I cannot remember saying that I’ll run boards throy these 0.75, 0.25 etc. – it’s just going into computer-bidding where we can use all kinds of computed coefficients like mine 6.18 for an Ace etc. Here we are discussing methods for at-the-table use (I think).

>
Again let me reiterate that I'm not trying to push one method over another and I'm not trying to trash Zar.
<

You can trash it all-day-long by “please, please, please, it’s bad, bad, bad” :-) but I specifically don’t attach much attention to it. Simply because I don’t have any information on the secret methods you are using.

>
I just want to make sure that experiments and statistics are reported in a scientific and not in a misleading manner.
<

I love that sentence coming out of you mouth :-)

Cheers:

ZAR

[inquiry]

Hola Zar,

Tysen2K is advocating BUM RAP + 5-3-1 for distribution. To be fair, you did suggest you would run it on your hands. See this link where you said so....

Post were Zar accepted the challenge

Now BUM RAP + 5-3-1 must be "really, really good" because tysen2K already published his own study (well, with no hands, etc), showing that BUM RAP +3-2-1 was heads and shoulders above ZAR points. His study can be found here....

Tysen2K study on BUM RAP + 3-2-1

To peak your interest, I will provide one quote from the above study, and one comparisoin of ZAR points to BUM RAP + 3-2-1....

       "I'm surprised at Zar's poor performance. I guess more
       complicated doesn't always mean more accurate. BUM RAP is
       a simpler method that gives better results." - taken from second link above


The result was in a table form comparing the two systems, where the higher the number, the better the system (and this was compared to Goren).

Zar points Earned 0.08 (with Goren getting 0), while
BUM RAP+ Earned 0.32

My math skills are poor, but this data seems to suggest BUM RAP + 3-2-1 is 4 times better than Zar points, and if using 5-3-1 improves the evalation, Bum rap will kill Zar points. Of course, there is nothing but the summary table to support the claim.

Ben

[Zar]

*** mikestar wrote: To do testing, simply change the Goren distribution figures from 1-2-3 to 1-3-5 and chance the HCP to 4.5-3-1.5-1 --even with no further adjustments it tracks more closely with Zar points than the other methods.
<

This is not something with the fractions of 0.25, 0.75 etc though ... you certainly realise that.

***
Zar points Earned 0.08 (with Goren getting 0), while
BUM RAP+ Earned 0.32

My math skills are poor, but this data seems to suggest BUM RAP + 3-2-1 is 4 times better than Zar points, and if using 5-3-1 improves the evalation, Bum rap will kill Zar points. Of course, there is nothing but the summary table to support the claim.
<

I don't know about these 0.08 and 0.32, WHAT they represent, HOW they have been calculated, WHAT boards have been used, ANY explanation of ANY kind. Just don't have time really to pay attention to any numbers out the air. I can tell you that in "another studdy" BUM got 0.01, RUM got 0.002, and Zar got 100,000.47. Does that help? :-)

ZAR