[VM1973]

Anyone who's known me for awhile knows I've learned about Zar Points recently and I'm quite taken with them. However, I was pleased to find the link at http://bridge.thomas...a/suittable.txt
and I decided to put Zar Points to the test.

I am focusing only on the most common hand shape patterns namely:

4-3-3-3
4-4-3-2
5-3-3-2
5-4-2-2
6-3-2-2
5-4-3-1
6-3-3-1
6-4-2-1
5-5-2-1

So at first I just took all the raw data and dumped it into Excel, multiplying the percentages by the number of tricks taken to come up with raw numbers. So what I came up with was:

4-3-3-3 776,3
4-4-3-2 807,2
5-3-3-2 812,5
5-4-2-2 839,4
6-3-2-2 849,7
5-4-3-1 867,9
6-3-3-1 876,0
6-4-2-1 901,7
5-5-2-1 902,9

(please check my math).

So then assuming that 4-3-3-3 is the base count (worth 8 points) and that each ZP is worth 0,2 of a trick I arrived at the conclusion that 4-4-3-2 apparently takes 0,309 tricks better than 4-3-3-3 and therefore should be worth about 9.5 ZPs in distribution. Proceeding along these lines I came up with the following table.

4-3-3-3 8,0
4-4-3-2 9,5
5-3-3-2 9,8
5-4-2-2 11,2
6-3-2-2 11,7
5-4-3-1 12,6
6-3-3-1 13,0
6-4-2-1 14,3
5-5-2-1 14,3

But then I thought, "Why am I including those hands on which you end up taking 4 tricks or something? You're not bidding on those." So I redid the numbers only including those hands on which you take 7+ tricks and I came up with new numbers, namely:

4-3-3-3 630,6
4-4-3-2 686,6
5-3-3-2 694,3
5-4-2-2 744,3
6-3-2-2 762,7
5-4-3-1 787,7
6-3-3-1 801,3
6-4-2-1 844,2
5-5-2-1 846,0

Which yielded the following distribution ZP table:

4-3-3-3 8,0
4-4-3-2 10,8
5-3-3-2 11,2
5-4-2-2 13,7
6-3-2-2 14,6
5-4-3-1 15,9
6-3-3-1 16,5
6-4-2-1 18,7
5-5-2-1 18,8

So what I'm looking for is the following opinions:

A) Is raw double dummy play data valid for distribution? Why or why not? Be specific.
B) Which methodological approach is better or are both screwy? Why should 7 (or 6 or 8) be the arbitrary cutoff? Be specific.
C) How should fractions be handled? Be specific.
D) How should said table be adjusted for IMPs? How should said table be adjusted for Vulnerable IMPs? Be specific.

[Free]

VM1973, on 2011-September-02, 16:16, said:

But then I thought, "Why am I including those hands on which you end up taking 4 tricks or something? You're not bidding on those."

I've been in 1NT-3 or 1NTx-3 on several occasions, even scoring good when the vulnerability is right... It can also go 1m-p-p-p for a number. So you do bid some of these hands.

[Zelandakh]

Raw double dummy data is imo useful if you confine your investigation to a specific range where things tend to even out. For example, if you concentrate on pairs of hands that take 10-11 tricks in 4M. When you go down to low part scores you need to be careful about the double dummy effect which starts to favour defending over real world data. Therefore I would personally probably not go below 8 tricks in such a methodology if specifically looking at constructive bidding. The fractions you need to handle according to the evaluation method you are proposing. For example, I could re-write your table rounding out to whole numbers:-

4333 ... 8 ... -1 ... 1 ... 0
4432 ... 11 ... 2 ... 0 ... 1
5332 ... 11 ... 2 ... 0 ... 0
5422 ... 14 ... 5 ... 1 ... 2
6322 ... 15 ... 6 ... 2 ... 2
5431 ... 16 ... 7 ... 1 ... 3
6331 ... 16 ... 7 ... 1 ... 2
6421 ... 19 ... 10 .. 2 ... 4
5521 ... 19 ... 10 .. 2 ... 5

The first column is the distribution; second is your calculated numbers rounded to an integer; third column is this value approximately normalised to standard distributional methods; fourth column is the error from 5/3/1 shortage count, doubled to take account of this being in ZP; sixth column is the ZP error. Interestingly 5/3/1 scores significantly better than Zars in your calculated numbers. This is normally the case in such studies but in this case the difference is greater than normal so I assume there must be an error somewhere in your calculations.

Finally, you are trying to work out evaluations based on trick-taking potential. Since tricks are not equal in IMP scoring I think it would be a mistake to try and then find some formula to convert this to IMPs and especially a second formula for vulnerable IMPs. I think it is also worth pointing out that this kind of work has been done many times over, sometimes by people with considerable statistical knowledge. I am not sure what you think you can bring to the table beyond that but, if you think you can, then it is very important that you do so from a neutral point of view and not from an interest in Zar Points. Otherwise it is extremely easy to misuse whatever statistical data you produce.

[VM1973]

Actually I've figured out it's completely unworkable. There just isn't enough information in the table and anyway my second set of numbers were based on several assumptions that are just not justifiable.

The point of working out how much distribution is worth assumes that you can look at (let's say) 10,000 hands with a certain amount of cards and two different shapes to see how they fare.

So at first I just assumed that in the long run the hands will have the same amount of strength on average. Later that night I realized that 4-3-3-3 must always be 0-37 HCPs. Whereas 5-5-2-1 must always be 0-31 HCPs. Assuming that, over the long run, those two shapes will average out to have the same number of HCPs is an unjustifiable assumption.

I'm now working on a second, more thought-intensive and non-empirical method of evaluating the value of shape. For example, if you hold:

AKJ2
AKQ
AKQ
AKQ

and partner has 0 cards with 4-4-3-2 (the most common shape) you calculate 10 ZPs for your partner and 55 ZPs for you for a total of 65 (63/5 = 12.6 tricks) which is about right since you can win any lead, cash ♠A, ♣AK, ruff the ♣Q and finesse the Jack. It's slightly more than 50-50 because the ♠Q might drop on the ♠A so those shapes seem all right in terms of their distributional value.

Whereas if partner has xxxx, xxx, xxx, xxx (8 ZPs) then you end up with 12.2 estimated tricks, which might be a little low, since the ♠Q might fall on ♠AK although it is definitely less than 50 percent chance probably more like 12.4 tricks.

The same thought process will have to be done with hands that are not so stratospheric in their card values and it may well work out that the distributional values are different at different card levels.

[VM1973]

I realized while thinking about it last night that I probably explained myself quite badly.

What I meant to say was that a hand like:

AKQJ
AKQ
AKQ
AKQ

evaluates to 57 ZPs. Accordingly we can say that with 57 ZPs in hand you can contract for 7 without worrying about partner's hand.

Holding:
AKQJ
AKQJ
AKQ
AK

We see that we have lost a queen, and gained a jack. Yet we still know we can make 13. The conclusion is that the 4-4-3-2 shape is better than the 4-3-3-3 shape. By how much? By the difference between a queen and a jack, which in this system is 1 point.

Whereas holding:

AKQJ2
AKQ
AKQ
AK

We have lost a queen and gained a two. Still, we are good for 13 tricks. So we can say that 5-3-3-2 is a queen better than 4-3-3-3.

In reality, however, perhaps this is an overly optimistic view. In hand 1, partner rated to have, on average, a jack (wasted). Whereas in hand 3 partner rates to have, on average 5/3 HCPs wasted in cards so 5-3-3-2 might be worth slightly less than a queen better than 4-3-3-3.

[Zelandakh]

Using a single extreme is rarely a good basis for extrapolation. For example, I have some bacon, if I leave it at room temperature it goes off in time x. If I put it in the fridge it lasts x-y. Hence to maximise the shelf life of bacon I simply need to cool it to -300 degrees celsius or so. Yes, there is a flaw in this argument.

Similarly, if you are serious about this kind of methodology then use hands somewhere in the 10-16 hcp range as a starting point and then take samples further out to check your results. Warning, this is alot of work, most of which has been done by others.