BBO Discussion Forums: Zar points, useful or waste of energy - BBO Discussion Forums

tysen2k, on Sep 27 2005, 12:19 PM, said:

You resolve it by using tricks as the way to judge value, not points.

Hand one = 3 tricks if you we assume we play in our longest fit. 3 Dist and 0 whcp tricks.
Hand two=3+4=7 tricks again if we assume we play in our longest fit. 3 dist and 4 working hpc tricks 10/3=3.33 and round up to 4.

Note none of this depends on opening 1s only assumes our longest fit is not hearts our void.

In your example 2 in any event 4 working+3 dist=7 tricks expected on hand 2 example

In your example 3 you have zero dist tricks in hand one and 10/3= 4 working hcp tricks and other hand has zero and zero. In fact you could argue for negative one dist tricks because of duplication. so 4-(0 or 1)=

mike777, on Sep 27 2005, 11:54 PM, said:

Uh Mike...

Do you understand the notion of circular reason?

The methodology being used is grounded on using trick taking taking capability to measure the accuracy of different hand evaluation metrics.

Using trick taking capability to measure trick taking capability seems fruitless.

>
Average is the sum of all hands divided by the total number of hands. This is likely close to but not exctly the same as a 10 HCP hand.
<

Average Hand in Milton sense is a hand with 10 HCP (25% of the 40 HCP total in the deck). Average Hand in Zar Points sense is a hand with 24 points (10 HCP + 3 CTRL + 11 Distributional points). Average hand in Goren Sense is a hand with 11 Goren Points (10 HCP + 1 for the doubleton).

Note that ALL these comply with the WBF “Rule of the Queen” – they are all 1 Queen (2 points in terms of the corresponding “points” definition) BELOW the opening hand (12 HCP, 13 Goren, 26 Zar Points).

>
A 5422 hand has "x points" of distribution when it has honors but is worth "y points" of distribution with fewer/no honors, where y>x.
<

A 5422 hand has a distribution of … 5422. Don’t see how the DISTRIBUTION would change as the HCP changes. The RATIO between the distribution and the HCP will change obviously, but the DISTRIBUTION is just THERE for you to enjoy or suffer. Not only the RATIO, but the overall POTENTIAL will change, of course. The only thing that REMAINS unchanged is ... the distribution, hence the distribution POINTS. Am I missing something here?

>
If you define a yarborough as 0 working HCP, then the second hand has 10 "points" of working strength for initial evaluation since the second hand is worth 10 more points than the first. However, once partner opens 1♠, the second hand is now worth only 7 more points than the first.
<

Wait a min... we are now talking RE-evaluation in the light of PARTENR’s opening.

These are apples and oranges ...

>
♠ AKQxx
♥ AKQ
♦ xx
♣ xxx
♠ xxxxx
♥
♦ xxxx
♣ xxxx


With AKQ against void the issue is DUPLICATION and is also a subject of RE-evaluation rather than evaluation. I am not dismissing the RE-evaluation at all. We just have to be careful not to MIX these issues.

>
Using trick taking capability to measure trick taking capability seems fruitless.
<

May be we should try trick-losing instead :-)

I am measuring IMP-winning capability based on trick-taking potential. This is different from what you are suggesting. Making 10 or 11 tricks is not that important on the background of bidding or missing the game, right? That’s why the “match” measures UNDER and OVER bidding on the boundaries, rather than trick-taking by itself.


ZAR

Zar said:

Did you miss the distinction that hrothgar and Tysen were making? This is precisely what they wish to avoid using for 'average hand' [it's true that in each case the average over all hands accords with the numbers you give, but it is [i]not[/i] defined by these numbers, and the term 'average hand' is not reliant on any method of evaluation].

Zar said:

Yes, I think you are. Of course the distribution remains static, but you seem to take it as axiomatic that the "distribution points" (a representation of the trick-taking ability of the distribution) are independent of the HCP strength of the hand, which is precisely the notion being challenged. The only reason we have for believing it is that it makes everything easier to work out, and people are providing evidence that we should not believe it, which you are ignoring rather than debating.

Blofeld, on Sep 27 2005, 08:45 PM, said:

I am afraid we are running in circles here ... Or in parallel tracks ... The ability of a STATIC distribution to make tricks INCREASES with the HCP content - that's the reason why you COMBINE them. I have stated in a number of ocasions that a SINGLE hand does NOT take tricks - it's the COMBINED power of the 2 HANDS that makes tricks. Your KJx can make 0 tricks against xxx with 25% chance, or 2 tricks with the same 25% chance, and in the same time 3 tricks with 100% CHANCE against AQx. HOW can you incorporate that in the evaluation of the SINGLE hand? You evaluate YOUR hand (and re-evaluate during the bidding) an make only probability-based conclussions about the other 3 hands as the bidding progresses.

I certainly agree that the trick-taking POTENTIAL of KJxxxx is much bigger than the potential of KJx, but this IS reflected in ANY method (more or less).

If we shove here the influence of fits, misfits, double-fits, super-fits etc., where does the point-of-discussion go? In that respect the misfits and superfits, double-fit etc. points are MUCH more relevant than the distribution-value-change of a SINGLE hand (whatever that means IF it means anything at all).

ZAR

Zar, on Sep 28 2005, 01:58 AM, said:

I agree. But is it not the intention that the ORIGINAL valuation should give rise to an indicated level of tricks such that subsequent re-evaluation (should any be required) is equally likely to give rise to an increase as to a decrease?

My point is that if I had 5-0-4-4 Yarborough and I knew that partner was initially valuing his hand under Zar (or any other currently recognised method for that matter), and he being in ignorance of my shape at the time, I would be expecting subsequently to devalue some of his high card values later in the auction. Contrast with when I hold 5-3-2-3 shape I would not have that expectation.

Ah, I think I saw a glimmer of light while commuting to work:

The initial value assigned to your distribution would appear to anticipate the effect that some of partner's high cards may be wasted opposite your shortage. That distributional value would initially assume that partner has an "average" hand. I am not sure whether that is a priori average or average in the context of your own hand, but that does not alter the principle.

Now, if you have a 5-0-4-4 Yarborough, have no opportunity to convey your distribution or values to partner, and partner has no opportunity to advise you of his distribution or location of honours but IS able to tell you his precise count (Zar or High Card I am not sure but may be important), then in re-evaluating your own hand in light of this information it is incumbent upon you to re-evaluate downward if partner has shown total values in excess of the expected average, upward if partner has shown total values falling short of the expected average.

Neat. I think.

Sorry for reviving such an old thread, but I was doing some research on hand evaluation methods and came across this -- a ton of very interesting data here to review.

I have a few comments and questions -- hopefully some of the members in this thread are still active and can give some insight to the following:

1) I've noticed all of Zar's published data lacks a comparison with a 3-2-1-.5 HCP value based system. Why is this? The reasoning given thus far is that players don't want to deal with fractions in evaluation. I think we should see the comparisons and then let the user/player decide what's more practical -- dealing with fractions or changing all boundaries to accommodate an entirely new scale. I suspect Zar has already done the comparisons and refuses to publish them because the data would suggest most of the improved accuracy of his system comes from the 3-2-1-.5 HCP values rather than from his distribution adjustments.

2) Have any comparisons been made using BUM-RAP 5-3-1 along with the adjustments that TSP uses (essentially keeping the 4.5-3-1.5-.75-.25 numbers + the adjustments Tysen proposes in TSP).

3) A question regarding adding value for combinations (cooperating values). I noticed in the TSP adjustments, this is given weight:

* Add 1 point for every suit that has 2+ honors (including the Ten)


This made sense to me, until I read the conclusions Thomas Andrews made in his study:

http://thomaso.best....onclusions.html

Does anyone know what data supports his opinion here:

Alex Martelli has noted that cards in combination are worth slightly less than cards in seperate suits, and that cards in long suits are worth less than cards in shorter suits. This appears to be true.

This certainly is counter-intuitive and I wonder what specific data backs this conclusion. Tysen seemed to ignore this conclusion for some reason.

4)Have any comparisons been made using GIB single dummy data?

dustinst22, on 2011-April-29, 10:25, said:

Some of the old threads are worth reviving every now and then

Quote

6-4-2-1 is exactly the same as 3-2-1-0.5 doubled - the relative weights are the same. As you say Petkov wanted to avoid fractions - but more to the point he also wanted the 2a+b-d formula for distribution and that would have overwhelmed the honour count in 3-2-1-0.5. Indeed, in my investigation of this 2a+b-d would have been better with 9-6-3-1 as two points for a 5 card suit is a lot to count.

Petkov essentially suggested the 2a+b-d formula for distribution - which is linear - and though quite good, it isn't linear as others discovered and as you have read, 1-3-5 for shortages (not a linear assessment) being better.

Quote

Again 4.5-3-1.5-0.75 is exactly the same honour count again. It also introduces .25 for tens - which is a sop to them being worth something particularly in NT - and also to HCP counters as the whole thing adds to 10. But counting tens is mainly a NT adjustment and the whole concept of the 3:2:1 ratio for A:K:Q is relevant to suit contracts. You need a different scale altogether for NT - I'm sure you'll have seen Andrews fifths scale 4-2.8-1.8-1-0.4 for judging 3NT contracts.

Quote

Again, if you read Andrew's stuff properly I think you'll see that he makes the point that honours in combination are a plus for opening values - as you know they'll work together regardless of whether partner has any sort of support or not. Single honours in partner's suits are worth their weight as you're sure they're useful - but counting anything too much extra is dangerous - as partner may have already upgraded for honours in combination in his/her hand.

Quote

I'm sure someone did comparisons with double dummy and average expectations from human single dummy play - I think it was OKBridge data. The conclusion was that at the 4 level, single dummy expectation and double dummy analysis are, on average, about equivalent - but for higher contracts, double dummy slightly overestimates true expectation at the table (declarer has enough stuff that he is in control usually) - and for lower levels double dummy data slightly underestimates expectation (as DD will always make the right leads and discards and the defenders, at lower levels, usually have some cards to do damage with).

Nick

NickRW, on 2011-April-29, 11:28, said:

Hey Nick, yes I know -- I was merely using the reduced version. My point is, the comparisons done by Zar have been using evaluation systems with a 4321 metric rather than a variation of the more accurate 6-4-2-1 (i.e. 4.5-3-1.5-.75-.25, 3-2-1-.5, or even a slightly more rudimentary 4.5-3-1.5-1 variation). I'd like to see more comparisons made to evaluation schemes using these ratios.

NickRW, on 2011-April-29, 11:28, said:

Thanks, I will have to find that in Andrew's studies. I admittedly have not read through all of his articles yet, but had found the comment I posted above regarding honors in isolation being more valuable as counter-intuitive.


Thanks for the comments.

Jlall, on 2005-August-29, 13:14, said:

!

Have we gone any further in this regard?

My conclusion from back then was that we were approaching the problem incorectly. Instead of evaluating a single hand additively,we needed to evaluate the hands as a combination and treat constructive bidding as variance reduction. This seemed to give results that made sense --the difference between your longest combined suit and the shortest combined suit is the biggest impact -- so trumps and splinters. Then controls and etc., just like normal bidding except we could probably improve some corner cases.

I'd have liked to teach TSP to help beginnes get some better guidance starting out, but that it really only worked well for suit contacts meaning you'd have to teach normal HCP for NT and build a bidding system that accommodated this. Plus there was no easy way to convert TSP to HCP in your head. So BUMRAP+531 it was and the other TSP adjustments had to be learned as judgement calls. Plus there wasn't a straight forward way to calculate BUMRAP without some elaborate rule or lots of fractions: e.g. As adjustments for card combinations.

But there is a book from MasterPoints honors series about optimal hand evaluation. Is it any good?

Has there been any further work on this topic?

MaxHayden, on 2019-August-31, 01:53, said:

I wanted to follow up on this.

Lawrence Diamond's _Mastering Hand Evaluation_ references and summarizes much of what has been written in English. It would be a good reference for someone who was doing research or someone who wanted an overview.

But Patrick Darricades' books are more interesting. He didn't do any original research, his goal was simply to summarize the state of the art based on what had already been written. He starts with the entire corpus of statistical work done by J-R. Vernes (including his 1995 book) and adds in more recent findings with a coherent set of point values so that you have an actual system instead of a list of considerations. Importantly, the focus is on adjusting your valuation to incorporate new information you get from your partner and to guide you bidding decisions about what information would be most helpful.

He has two versions: the Honor's Book _Optimal Hand Evaluation_ and a book from Tellwell, _Optimal Evaluation of Bridge Hands_. I bought both of them. The Honors book is an edited down more focused version of the Tellwell one. It's easier to follow if you are trying to *use* the method. But the Tellwell one made it easier to understand how he arrived at it, though I can't point to anything in the extra 50 pages of material that really stands out.

He hand-checked the method using about 7000 contracts over the period of 2 years. He says that a 50% odds contract will have at least the right point-value 95% of the time and one that have poorer odds will be below that threshold 95% of the time. The errors tend to be within 1-2 points. Typically you'll be 2 points high because of not knowing exact honor placement and having 1-2 points of wasted honors that weren't accounted for. Or you'll be be about 1 point too low because you had multiple deductions for lacking kings, queens, having mirror suits, and having 4333. The rounding errors accumulate in extreme cases and you subtract too much.

Since his results were by hand, I would love to rerun the numbers like we did for BUMRAP and TSP above so that we could put everything on the same footing and get an apples-to-apples comparison. Does anyone know if you can still access Tysen2k's databases and easily run the numbers like he did?

There are two benefits of Darricades' approach that I didn't really appreciate until I tried it. First, being based on the normal 4321 scale really does make it easier to deal with despite having to track half-points. Second, because it is a 6-increment scale instead of the 5 for Zar or TSP, you always have a good or bad intermediate and never a straight middle value.

The need for editing and computer statistics aside, there are only two things I'd want to add.

First, a better way to teach people to use the count. He has a few ways to explain the pieces in ways that avoid memorization, but I'd have liked a comprehensive presentation that helped people learn how to do this quickly at the table.

Second, when you use just HCP, it's very easy to figure out what opponents have based on what you have. But once you start adjusting for various factors, that becomes harder. I'd like something systematic that shows you how to make these inferences. (You could figure it out from his point value table, but it would be painful. So it should have been part of the book.)

If anyone looks into this work further, please let me know. I've been a big advocate of teaching advanced hand evaluation for a while and I think that Darricades' book is a huge step in the right direction. I think we can go further, but I'm glad that someone took the time to sit down and put what we already know in one place for easy reference.

MaxHayden, on 2019-August-31, 01:53, said:

The evidence I saw back in the day when this was a hot topic is that ZP are an improvement over Milton for suit contracts but the difference between ZP and modified Milton using a 4.5-3-1.5-1 scale with 5-3-1 for distribution is quite small and, if anything, the modified Milton scale has perhaps a tiny advantage. So yes, ZP are useful, but I think for most people using Milton and upgrading for aces, downgrading for queens and treating distributional features aggressively in combination with the usual upgrades and downgrades is more than adequate and probably easier to handle.

That's the conclusion that Darricades reached as well, and it took it much further than Tysen2k did.

I'd love to run Tysen2k's numbers for this new count. And I'd like to work out some shortcuts for doing it if it really gives a significant improvement.

The Zar Points are not as accurate as other simpler methods. That's my conclusion from analyzing 700K double dummy deals (downloaded from GIB site a long time ago).

Numbers below are for deals with a 9-card fit. (Results are similar for 10/11-card fit.) Columns are: points, average tricks, average error, cumulative percentages of making 8 to 12 tricks, number of deals. Each unprotected honor in a short suit is treated as the next lower-ranked honor. Distributional points are counted for both hands.

4321-531

Pts Trks Err 8 9 10 11 12 Deals
24 9.1 0.93 96 76 34 5 0 31076
25 9.4 0.93 98 86 49 11 1 30373
26 9.8 0.93 99 92 64 21 2 28169

This is the baseline with Works and 5-3-1 distributional points for void-singleton-doubleton. On average 25 points make 9.4 tricks with an error of 0.93 trick. 49% deals make 10 tricks or more.

Zar

Pts Trks Err 8 9 10 11 12 Deals
50 9.1 0.94 96 76 33 05 0 21882
51 9.4 0.94 98 84 45 10 1 21732
52 9.6 0.93 99 89 56 14 1 20469
53 9.8 0.93 99 92 66 21 2 19836

On average 52 Zar points make 9.6 tricks with an error of 0.93 trick. 56% deals make 10 tricks or more. The average error is comparable to the baseline.

6421-531

Pts Trks Err 8 9 10 11 12 Deals
30 9.1 0.89 97 76 31 4 0 22832
31 9.3 0.89 98 84 43 7 0 22328
32 9.6 0.89 99 90 55 13 1 21607
33 9.8 0.87 99 94 67 20 2 20705

The plain 5-3-1 evaluation for void-singleton-doubleton is more accurate than Zar's (a+b)+(a-d). The average error drops below 0.9.

BUMRAP-531

Pts Trks Err 8 9 10 11 12 Deals
24 9.0 0.88 96 72 26 3 0 29724
25 9.3 0.89 98 84 42 7 0 29389
26 9.6 0.88 99 91 58 14 1 27907

Now let's turn to BUMRAP with A=4.5, K=3, Q=1.5, J=0.75 and T=0.25. 50% game is between 25 and 26 points. The average error is comparable to 6421-531. Since no bidding systems can communicate fractions of a point, the points in both hands are rounded to the nearest integers before they are added together.

5321-531

Pts Trks Err 8 9 10 11 12 Deals
26 9.1 0.89 97 76 31 4 0 27252
27 9.4 0.88 98 86 46 9 0 26679
28 9.7 0.88 99 92 60 16 1 25460

If one doesn't like dealing with fractions, a simple way is to count A as 5 points and the accuracy for a game decision is still comparable to BUMRAP. To make the point scale compatible to 4321-531, one can still count A as 4 points but compensate that by subtracting 1 point for an ace-less hand and adding 1/2/3 points for 2/3/4 aces. Results are the same except that the relevant point range for a game decision changes from 26-28 to 24-26.

macroxue, on 2020-January-11, 16:14, said:

Apologies for the late reply. Times have been regrettably interesting.

I really appreciate you taking the time to post this. It seems like BUMRAP and TSP are about the same and that it's just a matter of calculational ease and preference.

Is this an analysis that you can run at will? As-in, could you run this analysis on the additional adjustments from the Darricades book if I posted them or messaged you?

His complete list of adjustments takes about 2 pages. I feel like I do most of these in my head anyway though. So I'm curious as to how much error reduction you get with each additional piece using the numbers he's assigned.