page provides some “bits and pieces” of my precious
discussions with many world champions, famous bridge
authors, and world-class players. At the bottom of the
page you will see comments from the editors of different
bridge magazines, too.
reason I provide this is that I believe it gives you
the important perspective (not always favorable for
me) of undisputed experts – it would benefit you regardless
of your attitude towards Zar Points.
idea of such an article is terrific.
system most probably is an improvement over current
point count evaluation, but...it's too complicated for
statement is kind-of a “common” concern, and honestly
my “unbiased” opinion is that there isn’t such a “giant
leap of a difference” in complexity between:
calculating 3*v + 2*s + d (where v is the number of
voids, s is the number of singletons, and d is the number
of doubletons in the hand);
calculating (a+b) + (a-d)
where a, b, c, and d are the suit-lengths in descending
familiarity and convenience are probably some of the
factors here, but certainly the “perception” of complexity
that you point out is there to some extend.
“perception is reality” JThanx, Matt.
it looks good and I agree with almost every bid, I doubt
whether you can sell it to the general public because
it's a bit too involved - too many calculations.
always have to have your calculator handy in bridge,
Eddie J I definitely recognize your concern regarding the
general public, though.
luck with your new book!
interesting -- several authors (Marty Bergen, Edgar
Kaplan and others) have gotten interested in the subject
and have tried to develop alternate point count systems.Of course, this debate goes back to the Goren-Culberson-Lenz
would have to study more seriously to fully understand
-- it is more than casual reading! Thanks for the mention
of the LAW with reference to me.
pleasure, Larry - it’s just natural to direct the reader
to your publications when the LAW is the subject.
forward it to Marty -- but I know he gets overwhelmed
with e-mails and can't respond to them right away.
in advance – I am really looking forward to his comments
interesting and well-written article.
I suspect that Eric Kokish will also enjoy reading it. His e-mail address is
Thanx for the referral. I’ll get in contact with him today.
wish I could give you some more intelligent feedback
about your ideas, but I am afraid the only way to do
that would be for me to try playing bridge using your
methods of hand evaluation and see how it works. Given
my current schedule, this is unlikely to be possible
any time soon.
me, Fred – I didn’t expect you to throw everything away
and start playing Zar Points in the middle of a tournamentJ )
general sense after reading your article is that your
ideas do have merit. Perhaps if I spend some time with
the program you plan to create will be sufficient for
me to gain better insight into how well Zar points work
hope so – and I’ll keep you posted. Good luck with the
examined the article.I have seen similar attempts to quantify hand
evaluation before, and the problem is that things are
always missed. For example, I saw no mention of singleton
honors or intermediate cards.
honors are degraded the same way they are degraded now,
Mike. Also, all favorite conventions are available,
too (adjusted to the Zars).
cards - they are accounted for - 10's of fit-suits are
counted as 1 pt, while 10's in the short suits are worthless
these comments were about the first version of the article
where I really have missed to explicitly mention the
regular degrading for singleton honors, so Mike had
his point, as usual).
Zar Points would be useful for some players, but for
most experts I think the current system, intelligently
adjusted, works ok.
article certainly does NOT target the experts, though.
On the contrary - it targets the intermediate and "advanced"
players that do NOT have yours and Zia's expertise!
the whole point - how to try to bridge the gap between
the expert and the middle guy. I don't think you or
Bob Hamman or Zia
would EVER need the Zar Points.
actually think too many players are 'slave' to the 4-3-2-1
being a slave to the Zar Points system would be as big
a problem, just as some players now are slave to the
Law of total Tricks.
can replace thinking at the table, Mike - you know that
far, far better than me. The point is to provide "somewhat-better"
guidelines for the "middle-guy" who constantly
operates in a fog of uncertainty.
comprehensive system (like this) is too complicated
for at-the-table use. I see no real 'solution' (to being
an expert), except learning from reading and experience.
that’s certainly so … Reading
and experience – and learning from it rather than just
reading it and experiencing it J
Agree again, Mike. Thank you for both the time and the
article is interesting, to say the least...
indeed, Mike …
do have some brief thoughts however.
items you isolate to use in your evaluation are all
have not bothered to check to see if they are properly
weighted, but each contributes some important point.
discussed that with Fred Gitelman,
already (the proper weight). The proper weights are
a matter of equations calculations already so this cannot
be a concern (NOTE: this was again an early feedback
like the one from Michael Rosenberg so these were all
valid points as you might expect).
is one point that bothers me in that there is no allowance
for judgment. It looked to me as if misfitting
hands might overreach to game when they should not.
there is no fit, you need extra values to compensate.
100%, but I discuss these in the second version of the
article (the one on the Web) and you’ll see the developments
there – thanx once again for
the example and the rest of the feedback!
thought a lot about that, and the trouble stems from
the need that the correction should be simple enough
to be no burden for the players and in the same time
to be effective in the sense that in covers the suit
combination in both hands.
power of Zar Points is engendered by its simplicity
(oh, man … I meant ‘compexity’J ) and relative independence of the hand evaluation
(only fit adjustments are made). But I will certainly
continue thinking in that direction, Mike.
if I seem to be quibbling a little...
strong points, actually (as one might expect from Mike
)! Thank you indeed for the time to read the article
and think about counter examples!
your statement about bidding aggressive games is correct
and anything to encourage that is useful.
the main point indeed.
of the critics I received on the article boil down to
the “it is too complex” issue – it looks like counting
to 13 is already too complex J.
have to certainly keep the things as simple as possible,
though (but not simpler J ). Thanx again, Mike!
read the article quite carefully …
think you're on to something, although the world will
consider it too complex.
sitting around the bridge table, you already are into
something “too complex”, Eric J
key to everything is the two short suits and it impacts
on so much of the total count, as in 4-0 vs
2-2, for example.
believe that this stuff is worth publishing.
to hear it from your mouth, Eric – I’ve read so many
articles of yours…
by trying The Bridge World and Bridge Today, but don't
rule out any publication. IMP magazine in Holland is a likely candidate too.
you again. I definitely will.
me up to date.
certainly will. Thanx!
you for forwarding the article to me. Fascinating
reading and excellent content.
you, Ron. I am honored to hear that from you!
will be many (the ambitious) who will be influenced
by your approach, but the vast majority will fall into
your final four paras group.
Everything beyond 4-3-2-1 is too complex.
man … same refrain J
– let’s play bridge for fun J
have recently tried to encourage the average players
to ‘lower their standards’ by taking shape and controls
into account when opening the bidding --- attached are
excerpts from a couple of recent books --- and focusing
on many of the factors that you do, too, but Zar Points
are much more scientific and hence thorough.
good luck to the up-coming Bermuda Bowl – I’ll comment
on some of the boards there from Zar
and good luck!
have distributed your link to some 300 players on the
SABF mailing list.
you, Sid !
view expressed by an ex-Norwegian master is attached.
again – I’ll gave a look and
have engineering and mathematical academic background
and I must say that your point count is very, very clever.
am very excited to try it at the table.
Thanx Paul – at the table is all that counts J
to see some theoretical work done and see how it works
thanks again for this groundbreaking point count.
let me know if you hit a measurable success or failure
with Zar Points – I’d be pleased to explore both.
thanks for all the amazing research you've been doing!
all benefit from it.
you – I certainly hope so J
I right to assume that one partner alone can't use your
Zar point count if her partner is using the old faithful
Goren or Bergen counts?
good question, actually.
the answer is “yes, you can”. In fact Zar Points are
going to be used in the up-coming Bermuda Bowl (by a
very few teams of course) and one of the players is
going to use it EXACTLY that way – just to “back” his
decision-making process in though situations.
fine to me, Zar.
Kit – good luck at both the bridge table and the backgammon
example of opening with 7 HCP's is not permitted in
ACBL sanctioned events.
since you are the ACBL Tournament Division Manager,
you can take the appropriate steps to change that :-)
I am sure you do realise
that if you do not open the hand, you'll be "out
of breath" real soon. This is on top of the fact
that by opening you are pushing the opponents in defensive
you either play bridge or cricket :-)
A change to this would require approval of the ACBL
Board of Directors. I do not intend to propose such
The point is that when
I pick up my cards, the last thing I need is a Tournament
Director reaching and grabbing my jaw like the Big Brother,
whispering in my ear "Now you have to say P-A-S-S,
boy..." (did I scare you? :-)
Forgive my arrogance
of thinking that I have a couple of brain cells in my
head and I can decide whether to say "Pass",
"One Spade", or "Boy, oh, boy" :-)
You don't like my bidding
'extravagances'? I have an easy solution for you - just
pull the "X", enjoy the result, and say "Thank
This kind of a game
is called "Bridge".
If you continue the
line of ever-increasing restrictions, we'll end-up with
- third-hand MUST play
- second-hand MUST
- you MUST take all
finesses (in the trump suit only : -) etc.
I am not saying that
such a game is not gonna be interesting - all I am saying
is that it's gonna be interesting in a "different
Thanx for the input,
needless to say.
say it is a very fascinating article and I shall give
it some local publicity in a review here in Malta.
Thank you in advance,
I get a headache thinking about all your stuff , but
truly, thanks a lot.
Sounds better than
I have expected, Mario :-)
Aloha, Ken !
I finished reading all 26 pages of your document, and
was VERY impressed.
Thank you, nice to
hear it from you.
I'll send a longer reply in a few days -- this looks
to be a busy week -- and look forward to seeing you
next summer (unless you can be persuaded to come in
January for our annual Regional, instead).
I'd love to, but the
current plans are to be in Japan by that time - I'll
let you know.
Thanx again - I am
looking forward to your further comments
First off, I really meant it when I said I was VERY
impressed with what you're doing.
I am really honored
There's a long history of attempts to improve on Culbertson's
honor count approach, but nothing has been able to displace
the Work count, at least in this country. The idea that
adding controls to Work is equivalent to the 6421 count
seems obvious (NOW), but I'd never made that connection.
And the (a+b) + (a-d) was totally new to me, and an
obvious improvement on Bergen's Rule of 20. You're the
king (or perhaps the (C)Zar) of hand evaluation.
Wow ... that certainly
goes beyond my expectations Ken. Nobody has gone that
far so far :-)
All this stuff has
been there since the time Mr. Harold Vanderbuilt invented
the contemporary Contract Bridge - I was just able to
see it and happy to report it.
To put it using the
famous sentence of Federico Fellini - "I just report
what I see" :-)
I dabbled in point counts briefly years ago, but quit
when no one seems to want to change from Work, and my
main interest was in system development rather than
A bit of history. I
joined the ACBL in 1950 while in graduate school, as
soon as I had passed my prelims, and was immediately
impressed by S J Simon (not so much by "Why You
Lose at Bridge" as by his other book, "Design
for Bidding", that talked about the tradeoffs involved
in building a system. That inspired me to send an article
to The Bridge World on an Americanized version of Acol
that, to my surprise, was published as a 3-part series
in 1957 when I'm sure I had less than 100 MPs. I quickly
decided I needed to learn the game before writing anything
else, and finally wrote "3-D and the MAFIA Club"
in 1981 that combined a forcing club/4-card major system
with some new ideas on competitive bidding, and had
favorable reviews in England and Australia, but only
lukewarm reviews here (because every bid would be an
alert). Then I retired, moved here, and did not play
for a few years while developing an automated publishing
system for the Navy. Then my daughter decided to join
me and wanted to learn bridge. That led to "Foundations
of Modern American Bidding" that tries to make
what people play today at least semi-intelligible.
I visited the http://northshorebridge.com/foundn.htm
site specifically for that, Ken. Trully impressive from
a variety of perspectives ... I am going through it
My main quarrel with American bidding is the emphasis
on 44-fits, since that often makes it more difficult
to locate the 53-fits (primary as well as secondary)
that provide a source of tricks for games and slams.
So my systems usually have a minimum biddable suit quality
of Q10xx, and I'll freely bid AKx (or even KJ10 or Axx,
in a pinch) before stooping to 8762, on the theory that
most defensive tricks are taken by high cards (or ruffs)
rather than by length, and if we don't have the high
cards, then the opponents must.
The net result of such
thinking is that I try to evaluate high-card strength
and distributional strength separately, with controls
determining which of the two is more important. This
is why I've been using, and teaching the Losing Trick
Count for measuring distributional strength. You (surprisingly)
didn't treat LTC in your comparisons, but with 9 possible
scores (0-8), it should rate as well as the best of
the non-Zar methods.
I've been around Romex
since my student years in the late 70-es and I would
say that LTC doesn't directly address the distribution
(or shape) per se. What I have in mind is the following
(examples directly taken from the LTC page of bridge-forum.com):
I am sure you see the
problems I have with LTC (actually the 2 TYPES of problems
I have hard time classifying
these points as Distribution Count ... They are more
relevant to the Footprints, if considered in both hands,
although the Footprints cover much more ground I believe.
I'm beginning to suspect that HCP is the least important
of the components in the Zar count, and that a workable
system might be possible with just Controls + (a+b)
+ (a-d), which I'll call the Zar Distributional Count
You are right about
the HCP. Its value is pushed back in two ways:
1) The amount of points
you get from distribution is BIG compared to the amount
of points you "collect" from the HCP (say,
a hand with 11 HCP and 5431 distribution will get 13
points for the distribution - more than the HCP itself);
2) You add the Controls,
which pushes the value of the HCP even further (say,
in the above-mentioned 11-HCP hand you'd get additional
5 points if the 11 HCP are A-A-K).
This might be a good approach for preemptive bidding.
I've never believed in prohibiting a Weak Two Bid with
a side 4-card suit, and this approach could legitimize
my violations of that prohibition. Since 26/13 = 2 (My,
I'm brilliant today!) it might make sense to divide
ZD by 2 and add it to HCP to get ZarCount/2 and thus
retain the familiar 13 to open/26 for game. Then people
could use ZC/2 for opening bids and ZD/2 for Weak Twos
I will study the idea
of "Zar-Pointing" the pre-emptive bids - it's
certainly worth it, thank you Ken.
As to the general conversion
(scaling back to 13 for opening by dividing the amout
of Zar Points by two), I did a similar thing for scaling
Zar Points (the distributive part of it, or the ZD-points
as you call them) to Goren points and then to Bergen
points - this was an idea of Jeff Rubens, the Editor
of "The Brige World", which I liked a lot.
This scaling is in
"The Conversion" section.
But I'll definitely
do the research of evaluating the preempts in Zar Points
- an excellent idea! Thanx Ken! I'll keep you informed
about the developments.
Thank you for the link - I want to study it more deeply.
After a first cursory glance I liked what I saw, especially
the fact that you use real-life deals played by experts.
I also am looking forward to see your analysis of the
coming Bermuda Bowl.
Thank you - it's the
same idea - see what the experts do and how you would
A hint: if you have the time and inclination, you may
want to check the Monte Carlo deals for:
- hands that were not
opened by champions although they were a Zar opening
- hands that were opened
light although Zar would not open them
The latter would REALLY surprise me - if I see
one I will DEFINITLY publish it under the Bermuda Bowl
link. Even the idea to check for that did never occur
to me ...
If ANY expert EVER opens a hand that does NOT have 26
Zar Points, this would be an indication that the expert
is drunk :-) The other case around - failure to open
a hand that does have 26 Zar Points would be an indication
that the expert is asleep :-)
Seriously, I challenge
you to present me a hand opened by an expert which does
not have 26 Zar Points. I believe this as strong as
I believe that I am writing these phrases in this moment.
But hey, experts live in their own world :-) I'll
be watching and please, so do you. Thanx a lot!
With the benefit of hindsight and standing on the shoulders
of Milton Work, Charles Goren and Marty Bergen, I would
approach evaluating hands differently. Milton points
only work well in NT contracts.
Agree 100% - there
is a section that acknowledges that, actually - the
one that considers the 1NT opening with two different
Another note - I have
the same benefit of standing on the shoulders of Milton,
Goren, and Bergen myself. I acknowledge and respect
that wholeheartedly. There would have been no progress
if we don't step on the shoulders of one another and
reach higher ...
The Goren distributional points only emphasize shortness
and do not take into consideration suit lengths .
Goren does not reflect
suit lengths DIRECTLY, but he DOES do so indirectly,
whether he intended that or not. I believe I gave a
good example with the 5-5 two-suiter. In Goren you get
3 points for that 5-5 lengths (either 2+1 for a singleton
and doubleton or direct 3 points for a void).
The Bergen method only emphasizes adding your two longest
suits and other adjustments.
True. But then again
- one can argue that Bergen gives 10 points for a void
or a combination of a singleton and doubleton in the
above-mentioned hand :-) All these correlations stem
from the fact that all the four lengths are "squeezed"
in a sum of 13.
Your article hits the nail on the head with the emphasis
on the 39 hand patterns. This should be the focal point
of hand evaluation. The 39 hand patterns should be mapped
into some quantitative structure .
what Zar Points (and Goren, Bergen and the rest for
that matter) are trying to do, indeed.
A 4-3-3-3 pattern should have a value of one , a 4-4-3-2
a value of 2 , a 4-4-4-1 a value of 3 , a 5-3-3-2 a
value of 4 etc up to your 13-0-0-0 pattern which has
a value of infinity if in spades.
Wow ... I don't know
about the value of infinity, but you are suggesting
a VALUABLE new idea here - the idea to COMBINE the lengths
and the suits they are actually in!!! In other words,
a length of 6 to yield different points if in CLUBS
or SPADES! That's worth exploring, Bob - and I believe
I'd do that! I actually "hint" such an approach
when adding 1 point for holding the Spade suit. I'll
explore this "cute" idea further ...
As for the values you
suggest assigning (1, 2, 3 etc...), John McLeod, the
"Guru of all Card Games" as I call him (and
the guy who runs www.pegat.com - check it out) suggested
an even more natural metrics for the sake of a different
argument we had - simply regard the distributions as
4-digit decimal numbers. That is, the distribution 5-3-3-2
has the value of 5 thousand, 3 hundred, and 32, the
4-3-3-3 distribution has a value of 4 thousand, 3 hundred,
and 33 etc. (John is the most knowledgeable card-games
guy I have ever seen, indeed).
The real question is
- what do you actually do with these assigned numbers?
Just watch them wandering how big or how small they
are? :-) I am sure you see the point.
This is what you are attempting to do with your length
subtractions and additions.
You are not hinting that I am doing something "complex",
are you? :-) Please, have mercy :-)
However, a better approach (if it is possible) ...
Let me tell you right away - it's impossible :-)
... would be to quantify the hand patterns and then
make adjustments for HCP's and controls.
I am a bit lost here ... forgive me ... I believe that's
what Zar Points actually do.
Hand Patterns are bridge . We defend and count using
hand patterns. In declarer play we visualize the lie
of the land with hand patterns and plan our play accordingly.
Squeezes and endplays are executed with the benefit
of hand patterns. We translate bidding into hand patterns
to visualize what partner is trying to communicate to
us by bidding . If it were back to the 1920's or 1930's
and I was trying to invent or quantify a method to evaluate
bridge hands, I would use hand patterns as the starting
point. 7-3-2-1 , 6-5-1-1 , 5-5-3-0 make HCP's almost
That's actually the
benefit of using Zar Points indeed. The above-mentioned
hands get 2 TIMES more points than the 4-3-3-3 distribution
gets, effectively pushing the HCP "portion"
of Zar Points back.
Teaching the average player to "think in patterns"
is a monumental step in their bridge development.
Again , well done in
your article .
Thanx Bob - I'll let
you know how the working of the "length-suit"
combo shapes out. Thanx.
Very Interesting article on hand evaluation.
Couple of quick questions:
a) Most of the examples
you have given are for suit contracts. Does the Zar
Point Count with continuous re-evaluation work equally
well for NT contracts?
There is a comment
on NT contracts immediately after the section SUMMARY
for the distributive hands (in red). BUT - the short
answer is - with balanced hands or on your way to a
NT contract, you re-work to regular "brute HCP
power" the way you usually do.
To make the point clearer
- if you have a 4-3-3-3 distribution, you shouldn't
even bother calculating Zar Points - just see where
the brute HCP power is and act accordingly.
If the regular sequence
in the field for a board is 1NT - 3NT, Zar Points are
not going to help you much. Neither would Goren or Bergen,
for that matter.
b) How well does pre-emption work with ZAR evaluation?
As with any other system,
indeed. Neither better, nor worse ... I love pre-emption
(when I do it :-).
Continue the good work.
Thanx, Venkat - let
me know if you hit an interesting board, be it positive
Thank you very much for your article on Zar Points.
looks as a great effort to improve and complete the
initial work by Jean-René Vernes, published in
1966 (Emile-Paul editor, Paris), and in which has been
firstly demonstrated the Law of Total Tricks, by an
approach similar to yours (solving a number of equations
to determine the values of a lot of parameters).
I have never heard
of the gentleman ... I DO remember that we were using
The Law back in the 70-es in Bulgaria in the university
bridge club, but even back then I didn't know who The
Law of Total Tricks was "invented" by ...
Now that you told me
that, I made a search on the Web and I was surprised
to read an interview, in which he talks about that and
the fact that he had discovered it back in 1955 and
started discussing it in 1958 ... interesting ... Here
is a "cut" of it:
la loi des levées totales vers 1955. J'ai commencé
à en parler, à partir de 1958, dans une
série d'articles, et je l'ai publiée sous
sa forme actuelle en 1966 dans " Bridge moderne
de la défense " .
I'll read the entire
interview, thanx a lot !
That's why I would greatly appreciate if you could tell
me what were the parameters you introduced in your equations
- values to be assigned to the different honors?
- values to be assigned to the four suits lenghts?
- values to be assigned to the six possible length differences?
- other variables and parameters?
Thank you in advance
Actually The Theorem
and the implication on The Law:
- if the opponents
have a superfit, YOU have at least 3 8-card fits yourself
- if the opponents
have a double superfit, YOU have a double superfit yourself
and the "easy"
form of it, grasped by the principle "The more
they have, the more we have", have been "manually"
proved via the Dirichlet Principle in math.
The Zar Points themselves
(the DISTRIBUTIVE part of it) were an independent "discovery"
which initially had the form of (a + b) + (c -d) and
was targeting the difference in playing power with 5-4
The comments of Eric
Kokish for example are regarding this first light version
where the current Zar Points were called "Recursive
Zar Points" and were presented as an improvement
over my initial count of (a + b) + (c - d). After I
ran a number of boards (equations) through them, the
first version was dropped since it was of the SAME complexity
as the first one, and (more importantly) it fit the
6-4-2-1 HCP count (Milton + Controls) closer. The equations
themselves DID already include the distribution part
of Zar Points in the form (a + b) + (a - d) and involved
the coefficients for Honors, Discount honor combinations,
Upgrades for 2-suit-concentration of Honors, and the
adjustments for additional length (over 8) and honors
in the partner suits. The Controls were "separated"
later from the 6-4-2-1 count for easier-to-remember
purposes (i.e. to preserve the Milton HCP 4-3-2-1 count
which people are accustomed to). The inclusion of the
Distributive points solved a lot of problems with length
calculations and adjustments and the way you combine
these lengths and differences in lengths. There were
other experiments which "didn't make the grade"
- plus the coeficients were rounded and the equations
re-run for regression testing, of course. The final
version is the one you know. Note also, that virtually
all the boards were either game in major or small slam
with virtually no duplication, since this was the initial
tagret I had in mind. The yielded values for the levels
were about 52 and 62 respectively for game in major
and slam, again - in the "no fat" or "no
duplication" cases (the corresponding values for
the (c-d) version were 48 and 58 and the openning level
was 24). That's the story.
Thanx again for the
pointer to the work of Mr. Jean-René Vernes on
The Law ! And the attention to The Theorem and its implications
on The Law - I was surprised that the entire attention
was focused on the Opening and the Upgrade of the hands
towards a Game and you are the FIRST one to even mention
The Theorem and implications on The Law. Thanx!
Congratuations on a
brilliant piece of work.
Thank you - brilliant
is a bit of a "stretch" I guess, though :-)
I write a small bridge magazine and do some teaching.
Recently I wrote an article relating to a bidding problem
that involved a 'very' light opening bid. I got thoroughly
rubbished by most of the so called 'experts' on a panel.
Would you like me to send you a copy of the article
and some of the panel's comments - maybe you could comment
on what I wrote.
Most certainly, Vil
- I'd be glad to.
Also, if I do any bidding problems in future, would
you be on the 'panel' and maybe you may also be interested
in contributing to the magazine by way of any articles
etc? Hoping to hear from you,
I'd be happy to. Keep
in mind that experts do not need people to teach them
- that's why they are experts :-) Don't get offended
by that - some times (I'd sasy MOST of the time) they
simply don't have .... TIME to deal with stuff they
don't need in the first place. Just take it easy and
keep going ...
Is it a coinsidence that your 6-4-2-1 scale is just
twice the old 4A's scale of 3-2-1-0.5? In case you are
not aware of it , this scale was discussed in Bridge
World by M.Schwartz in the Dec.2000 issue on p.4-8.Also,
if you multiply the 4A's scale by 1.5 you get the Martelli
It's just a matter
of coeficients solutions actually. The fact that 6-4-2-1
fits perfectly the "natural" for most readers
"counting" of HCP + Controls was the "lucky"
fact in this case. You can scale it up or down the way
it fits you needs (meaning your OTHER considerations
in the process of Hand Evaluation, whatever that might
I have NOT "inveted"
any of these, as you know :-)
Perhaps you are not aware that an eleven card suit missing
A+K counts as 23.5 Zar pts but it is likely to take
So you think that the
hand xx, QJxxxxxxxxx, -, - havs 23.5 Zar Points ...
Let's check that ... You have 3 HCP and 0 controls for
a total of 3 pt on the Honors side.
On the distribution
side you have 11+2 + 11-0 = 24 points.
On the trump length
upgrade (3 points for any trump FIT over 8) you get
an average 12 additional points (since you fir is between
11 and 13 cards) for another 12 pt.
So 3 + 24 + 12 = 39
The actual 39 is different
from 23.5 but the point is elsewhere.
Such a hand would qualify for a strong 2C opening bid
under ACBL rules proving the card shows 9+ tricks regardless
of HCP count.
You probably have not
read the "Critics Section" .... Read the emails
from Butch (the ACBL Tournament Division Manager - he
specifically COMPLAINS about me giving examples with
openings of hands which have BELOW 8 (EIGTH) HCP, since
that is AGAINST the ACBL rules.
I have a friend who
sais that he will be comfortable if the "formuilae"
shows Level 6 when you hold 12 Spades to the A and singleton
Now, with 12 spades
to the A you can count on 12 tricks :-) Such a hand
would collect basically 4 more poins in HCP and 3 more
in controls, for a total of 46 Zar Points which still
doesn't reflect the fact that you have cold 12 tricks.
Can you make the Evaluation
System SOLVE that - sure - you can just change the values
assigned to additional trumps (abovr an 8-card fit)
accordingly (say, instead of assigning 3 points for
ANY additional, trump, you will start assigning 4 for
the 10th, 5 for the 11th etc.). Is it WORTH it is the
Is it WORTH it to clutter
the counting system with all kinds of artificial "additions"
and "subtractions" for the sake of "covering
it all", or ist better to take my approach, which
is "keep it simple and instruct the guy to use
You can find the answer
In the first version of Zar Points - (a+b) + (c-d),
the objection was that the difference between 5422 and
5431 was 2 points, which is equal to a Q. But since
your point total is twice that of a standard counting,
if follows that 2 pts for the 3-1 short is equal to
1 pt, not a Q.
Not really. As we mentioned,
the first version of Zar Points was calculating (a+b)
+ (c-d) and the current ZAR Points (a+b) + (a-d) were
presented as an improvement (at that time they were
called "Recursive Zar Points"). Now, what
happens in the previous version is the following:
If I change your distribution
from 5422 to 5431 I'll get 2 more points, right? If
I add one more Q to your hand I'll get AGAIN 2 more
points, which was too much for the experts.
Now, note, that with
the Recursive Zar Points (the current Zar Points that
is) you get ONLY ONE point for getting from 5422 to
5431 -> from 12 to 13 Zar Points.
I look forward to trying
out your system. I feel like a pioneer!
He-he ... nice feeling,
How long has it been in use? There is certainly a lot
of inertia to overcome.
is a very good way to put it, actually Geoffrey. People
just keep looking forward to the next board, as if it
will change things by itself :-)
I forwarded your article to a bridge pal of mine after
trying to give him my take on it verbally.
Thank you - "word
of mouth" is the best way to go ahead ...
ACBL might be willing to use your article in the "Bulletin"
and perhaps you could be a guest columnist defending
challenges to it or answering the inevitable questions.
The editor of "The
Bridge Buletin" is in communication with me, indeed.
But perhaps you're not interested in adding any more
to your plate which must be quite full already!
It is - but I enjoy
communicating with people. Different people have different
take on things and make you think in directions you
would never consider heading to ...
Good luck and I'll be watching for your name in the
Jeff Rubens, “The Bridge World” editor :
simplifications can be made (on the technical side).
Assuming that "controls" means high-card controls,
what we now call 2-1-points in The Bridge World (it
is hard to say as no example has a singleton), you are
adding two for an ace and one for a king,
The other controls (singletons and voids) are "implicitly
covered" by the S2 - the sum of all the 3 differences
in suit lengths – Zar Points do not attach explicit
points for distributional controls.
case you are in effect using 6-4-2-1 points, which we
have discussed at some length in fairly recent issues.
Because you are adding lengths (points) to 6421 points
rather than 4321 points, the lengths count for relatively
Note, that you still have 6 points difference from distribution
relative balance is a very important point indeed.
the years, we have considered many proposed such valuation
methods. After technical glitches are ironed out, the
basic tradeoff seems to be: Is the extra work worth
the additional accuracy?
really seams to be the major concern - although I personally
do not see the system as something "sophisticated"
or "complex" or "too much of an effort".
definitely the “extra effort”, as you put it, is something
all experts mention in one way or another.
main point “in points” is to quantify judgment, as hard
as that might be. And to do so for the so called “intermediate
and advanced” players, not for the experts, who will
do just fine anywayJ.
actual reason I started to think about the Zar Points
were 2 consecutive boards in which a casual partner
in a club raised me from 1 SP to 2 SP with Kxx in spades and 7 HCP.
in the first one he had 4333 distribution and 7 pt –
a K with 2 Qs, while in the second one he had “similar”
7 pt and Kxx in trumps, but
a K and an A plus a void! As you can guess, we went
down 1 on the first one and we made +2 on the second
one. For him, though, these were just “normal” 1-to-2
raises with Kxx in trumps
and 7 pt… or at least his bid showed them “the same”.
interesting thing is that he DOES realize that the two
hands ARE different, but the fact that he knows that
doesn’t help him much for 3 reasons:
He does not know by HOW MUCH these hands are different.
He does not know by how much WHAT (meaning denomination
or measure) they are different.
He does not know how this knowledge should be reflected
in the bidding.
he knows that they are different by EIGHT and these
EIGHT ARE Zar Points (2 from the controls and 6 from
the distribution) and that these 8 points may result
in TWO LEVELS difference (depending on re-valuation).
Compared with what is currently popular, using Zar points to evaluate
distributional strength will lead to more aggressive
evaluations with significantly-distributional hands.
Goren makes the following
distributions EQUIVALENT (all getting 3 points, see
the table in the article):
while for the SAME distributions
Zar Points vary from 14 to 17.
That's a 4 points diapason for hands considered EQUIVALENT
in Goren (with all due respect, needless to say).
If you look at the 2-points range, ALL of the following get 2-points
while in Zar Points they
range from 11 to 14 - again a 4 points diapason.
In any case, it seems reasonable to combine 6421 adjusted to the usual
scale with Zar shape points adjusted to the usual
scale. This would enable
a player who wanted to get better answers in a familiar
context to use your results.
Thank you very much
– I actually did that and you can see it by the end
of the article, Jeff. Thank you again – it was your
idea to do that and I am grateful for it.
convincing to show that Zar Points are better than Goren
in Goren terms and better than Bergen in Bergen terms
MarekWójcicki, “Bridge” magazine editor
will translate your article (in Polish) on the new method
of hand valuation.
article will be published (in Brydz
Magazine) under your name of course.
you once again.
let you know if I come up with some modifications.
The article was published in the April issue of “Bridge”,
“Bridge in Russia” editor.
article looks interesting and if you allow me to printed
it in the “Bridge in Russia" magazine, I will translate it in Russian and
print it in the first issue of 2004.
you, Alex. I would be pleased to see it published in
Russia, too. I can help you with the translation – I am Bulgarian
Canadian, but I know Russian, too.
You in advance!
best wishes in your theoretical investigations!
let you know if I make some modifications (most likely
And just a couple of "Regular
It is really nice to hear from the
"regular guys" which Zar Points are intended
for, as mentioned several times (don't ask Zia if he's
playing Zar Points next time around - he'd ask back
"What is 'points'?"':-).
I get lots of such emails and I'll
mention a couple - just for the heck of it :-)
Dimry Gip :
Wow ... what a begining,
Dimri :-) Thanx.
Good morning to you.
I am very - very thankful
to you for this so interesting system.
My pleasure, Dimry.
Yesterday I won a six-table pair tournament JUST by
using the basics of your system, i.e.
= 26 in opening hand.
This is so nice ...
A six-table local pairs-tournament
is a long way from Bermuda Bowl, but it still feels
So it's not that kind
of "hard calculations", I guess ... No rocket
science, as long as you have passed grade 1 and know
how to count ... :-)
I actually passed a few hands ,which I would have opened
Zar Points work both
ways - they make you more CONSERVATIVE with BAD hands
and more AGGRESSIVE with GOOD hands. I see that you
realise that already.
I will request you to send me some more deals played
using the Zar Points system.
Did you check the link
to Bermuda Bowl at the top of the page?
I'll provide "live"
reviews in Zar Points from the World Championship EVERY
day - so just check the site regularly and you'll have
"fresh" and "actually played" deals
from "the cream of the experts" :-)
It is really a very effective and simple system.
I am glad to hear that
- good luck using it!
Magnus Skaar :
I would like to thank you for a great article and a
very interesting theory on hand evaluation.
My pleasure, Magnus.
The system simplifies calculating points for distribution.
I am really glad to
hear that - I usually get the opposite responce from
the experts - "it's too complex, Zar" ...
I'm trying to use zar-points, and so far it looks great
Thanx - and good luck.
Let me know if you hit an interesting board, good or
I have a simple example from a teams match ( skipped).
The Zar-Count is 27 (12+14+1) so I was happy to open.
I am glad to see you
considered adding the 1 point for the Spade suit - people
often neglect that. HOWEVER, you should not do that
here since you have an opening hand anyway - it would
have been necessary if you had 25 "regular"
Zar Points plus the Spade suit - now you add it and
"collect" the 26 necessary for the openng.
In the other room this hand was (obviously) not opened
with only 10 hcp, and a lay-down game was missed.
This kind of AGGRESSIVE
game bidding are easy to notice and get excited about
because you "feel the joy" on the spot. As
you have probably noticed, though, Zar Points work both
ways. The other way is being CONSERVATIVE with BAD hands.
Usually the result of this type of boards is "simply
a double-score" and people do not pay attention
that much, although if you do the math, the gain is
comapable with the gain of a non-vulnerable aggresive