[Frank C]

Tysen,

You checked the Zar point system against other hand evaluators and I have a few questions about your approach.

1) Some of the hands you were looking at belonged in notrump, right?
2) Some of the hands you were looking at make less than 9 tricks in their best contract, yes?

The reason for these two questions is that Zar doesn't claim to be accurate in notrump evaluation and Zar doesn't claim to work (without adjustment) for low partscore hands.

The notrump problem is obvious. Adding all the control points makes aces and kings too valuable compared to queens jacks for notrump purposes. Also Zar distribution points are too heavily weighted on notrump hands.

The partscore problem is a little more subtle. Zar sets a 5 zar pt range between each trick level. This is only accurate at the top of the scale. So if 52 zars equals 10 tricks and 57 zars equals 11 tricks, it doesn't follow that 42 zars equals 8 tricks. This result shouldn't surprise you. In Goren land it takes 26pts to take 10 tricks, +3 more (29) to take 11 tricks, but +4 more (33) to make a small slam and +4 more to make a grand slam. So you see that the scale is not evenly spaced all the way across.

If you want to convince me that Zar points are less accurate than other evaluators (except Binky-- which is basically impossible to use at the table anyway) then restrict your data set to hands which #1 belong in a suit as opposed to NT and
#2 are rated by double dummy analysis to take at least 9 tricks.

Maybe you have already done that, I don't know. But I get the feeling that you are looking at a random sample of hands for which some belong in NT and some are low partscore deals.

[tysen2k]

Frank C, on May 5 2004, 11:34 AM, said:

1) Some of the hands you were looking at belonged in notrump, right?
2) Some of the hands you were looking at make less than 9 tricks in their best contract, yes?

1) Yes that's right and I agree with your reasoning as well. However, all the evaluators have to deal with NT hands at the frequency they come up. My current "best and simple" evaluator counts 5/3/1 points for distribution always. It has to cope with the same problems with NT and does so better. You can't just pretend the NT hands don't exist b/c they do exist. One of the know problems with Zar is that it goes overboard with a misfit. This happens.

2) Yes and No. When I reported the average error in tricks, that was based on a random sample of all hands. However, when I reported the average IMP's won/lost based on the evaluator, that was based on the side that "won the bidding" which is usually the side that can take more tricks, which is usually 9+.

I can try this all again eliminating the NT hands and only looking at 9+ tricks hands as well. That shouldn't be too hard.

Tysen

[tysen2k]

Okay, let me first post some of my original data for comparison:

All Hands  
             ERROR  SCORE
HCP          1.23  -0.49
HCP+321      1.07   0.00
HCP+531      1.05   0.07
Zar          1.05   0.08
BUMRAP+321   1.03   0.14
BUMRAP+531   1.02   0.21
Binky        0.99   0.32

This compares different methods of evaluation looking at ~2.8 million hands. ERROR is the average number of tricks that you are off between your evaluator's prediction and actual tricks. This error can never reach zero even if you knew your partner's hand perfectly, since you still don't know the location of the opponents' cards. SCORE is an estimation of the number of IMP's you would gain (or lose) per hand using this evaluation against a team using an unimaginative HCP+321

Now here are the results looking only at the hands where the best contract is not NT and where we can take 9+ tricks:

No NT, 9+ tricks  
             ERROR  SCORE
HCP          0.87  -0.31
HCP+321      0.79   0.00
HCP+531      0.76   0.10
Zar          0.76   0.10
BUMRAP+321   0.77   0.08
BUMRAP+531   0.74   0.19
Binky        0.71   0.30

No real surprises here. Everything becomes more accurate since we are only dealing with the subset of stronger hands. Zar gets better in comparison, but not much. Using raw HCP+531 gives practically equal results to Zar and BUMRAP+531 still does better. Binky (although not usable at the table) is still the best but it slips a tiny bit since it's optimized over all hands and not just the good ones.

Tysen

[tysen2k]

I’ve been doing a little research into what the “correct” values are for initial distribution. Interestingly, if you want to assign values to various suit lengths, the optimal values turn out to be:

Length  Points
0        4.8
1        2.5
2        0.9
3        0.0
4       -0.2
5       -0.1
6       -0.1
7        0.0
8        0.0
9        0.2
10       0.3

If you wanted to do it similar to the Zar or Bergen way of assigning coefficients to the relative lengths, these turn out to be the best values to use:

0.79*Longest + 0.62*Next – 0.87*Shortest

These are relative to “normal” points so the “ideal Zar” coefficients would have to be multiplied by 5/3 or be:

1.31*Longest + 1.03*Next – 1.46*Shortest

Tysen

[Frank C]

Tysen,

Great post! I find it very interesting.

On your latest post I have a suggestion. Do a search and cull out only the boards where the best contract in a suit scores within + or - 20 pts if played in notrump. i.e. best contract is 3d +110 but notrump makes +90 or best contract is 3D +130 but notrump makes +120.

This is the way to select those hands that are reasonably suitable for notrump play. Then if you do the same calculation that you just did (how many points for inititial lengths) we would have a good working number for the value of distribution in Goren for notrump purposes. I believe this would be good data, as zar or 531 +bum rap already covers the suit hands. So having proper values for distribution points on notrump hands would be a good idea.

[tysen2k]

Frank C, on May 11 2004, 04:40 PM, said:

On your latest post I have a suggestion.  Do a search and cull out only the boards where the best contract in a suit scores within + or - 20 pts if played in notrump.  i.e. best contract is 3d +110 but notrump makes +90 or best contract is 3D +130 but notrump makes +120. 

This is the way to select those hands that are reasonably suitable for notrump play.  Then if you do the same calculation that you just did (how many points for inititial lengths) we would have a good working number for the value of distribution in Goren for notrump purposes.  I believe this would be good data, as zar or 531 +bum rap already covers the suit hands.  So having proper values for distribution points on notrump hands would be a good idea.

I ran the same test with the hands you suggested. It suggests these values:

Length [space]Points
0 [space] [space] [space] [space]2.1
1 [space] [space] [space] [space]1.3
2 [space] [space] [space] [space]0.6
3 [space] [space] [space] [space]0.0
4 [space] [space] [space] -0.2
5 [space] [space] [space] -0.1
6 [space] [space] [space] [space]0.1
7 [space] [space] [space] [space]0.7
8 [space] [space] [space] [space]1.6
9 [space] [space] [space] [space]1.7
10 [space] [space] [space] 1.5

0.72*Longest + 0.24*Next – 0.25*Shortest

(Zar)
1.19*Longest + 0.40*Next – 0.41*Shortest


But I think these values are worthless. Picking all hands that give a NT contract within 20 points of the best suit contract seems sort of arbitrary. Sure, you get more balanced hands than a random sample, but there are still plenty of unbalanced hands in the mix that do okay in NT. For example you might get these hands that make both 3♥ and 2NT:

Q9432
987
94
K98

K
AKJT654
QJT
J2

Is this what I want to be counting? Do I care how many NT tricks I can take? Not unless I’m looking at slam, and in that case I’m not going to be using “points” to tell me if I should be there.

There is actually a lot of noise in the numbers above and that furthers the notion that they shouldn’t really be counted. I’ve looked at other evaluations when NT is the best contract. In those cases distribution matters very little. Simply adding 1 point for having a 5+ suit is about the best you’re going to do.

Tysen

[Zar]

Hi, guys:

Didn't know about this thread.

I'll go through it tomorrow, but for now just a quick remark. I cannot find the thread where we discussed the 5-3-1 method versus Zar Points, WTC (Winning Trick Count) etc. To avoid duplicate posting, I just want to say that I posted the extended results in the original thread "Zar Points - Useful or waste of energy".

I'll go through this thread tomorrow and see if there are any unanswered questions.

Make it a great day:

ZAR

[Zar]

*** FrankC wrote: "Zar doesn't claim to be accurate in notrump evaluation and Zar doesn't claim to work (without adjustment) for low partscore hands.
<

I promissed to get back to this thread and never did, sorry.

Actually I have never said Zar Points do not work on part score contracts. In fact, as some of the posted sets of boards indicate, they behave very well in partscore AND in respect to not going overboards when there is no prospect for a higher play - one of the Japan articles discussed that too.

As far as the sets of boards for testing, I agree with the majority of the posters that the "right" thing to do is to go over a "standard" and "public-access" sets of boards rather than generating "targeted" sets where you can twist things the way you please.

In any event, the bottom line is that you have to feel comfortable with the method you use from any perspective of the game - even if you feel uncofortable with a "side effect" like the chance that a very light opening caries risks for your partnership understandings (and penalty-doubles on low-level part-scores), you may decide to go with STRONG openings JUST for that reason alone - nothing wrong with that.

ZAR

[tysen2k]

Zar, on Jun 13 2004, 01:16 PM, said:

As far as the sets of boards for testing, I agree with the majority of the posters that the "right" thing to do is to go over a "standard" and "public-access" sets of boards rather than generating "targeted" sets where you can twist things the way you please.

Okay, how about this. The only criteria for limiting the hands is that "our side" can take equal or more tricks than "their side." No limitations on 9+ tricks or no NT contracts, etc.

Sound good?