page provides the answers to some questions I've been
asked over and over again - so I just decided to put
them in FAQ-page for people to read whenever they decide
to ask me a question :-)
Are Zar Points too complicated to calculate?
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.
Can you use Zar Points "secretly" while your
partner continues to use
answer is “yes, you can”. In fact Zar Points have been
used in the Bermuda Bowl (by a very few teams of course)
and one of the players was using them exactly that way
– just to “back” his decision-making process in though
key points where you can use Zar Points that way are
at the opening-bid decision and at the point of "invitational"
sequences, be it for Game or Slam.
Do Zar Points comply with the WBF standards for opening
WBF defines an opening hand as "a hand which is
better than the average hand by a Queen-worth".
Thus, a hand with 12 HCP is the minimal opening hand
if you happen to do hand evaluation via HCP count -
10 HCP for the average, plus 2 for the Q.
you can read in the "Never Miss a Game Again"
article, the average Zar Points hands has 13 Zar Points
from HCP and Controls, plus 11 Zar Points from distribution
for a total of 24 Zar Points.
a hand of 24 Zar Points plus a Q-worth (2 points) =
26 Zar Points is an opening hand, so Zar Points
comply with WBF.
is interesting to note that all the 3 methods - Goren,
Bergen, and Zar - fit EXACTLY the minimal conditions
imposed by the World Bridge federation. Since the "average"
hand has 5-3-3-2 distribution with 10 HCP, here are
the three calculations:
Goren gets 10 for the HCP plus 1 for the doubleton
= 11 Goren Points for the average hand - a Queen-worth
from the opening bar of 13 Goren Points.
Bergen gets 10 for the HCP plus 8 for the 2 longest
suits = 18 - a Queen-worth from the opening bar of
20 Bergen Points.
Zar gets 10 + 3 = 13 for the HCP + Controls, plus (5+3)
+ (5-2) = 11 for the distribution for a total of 24
Zar Points - a Queen-worth from the opening bar of
26 Zar Points.
Do Zar Points comply with the EBL and ACBL standards
for opening hand?
European and American Bridge Leagues, contrary to the
World Bridge Federation, relate the opening bids to
HCP and state that an opening hand has to have 8 HCP
+ "compensating distribution". To quote the
EBL, for a hand with 9 HCP you have to have either a
"a 6 card, or two 5 card suits". I am not
going to argue the equivalence of 1 6-card suit and
2 5-card suits, but the point is that the rule allows
for some kind of distribution compensation.
the EBL states that for the opening bids "at the
one-level the "Rule of 18" shall serve as
the guideline for judging whether it meets normal opening
bid expectations". That is, the sum of your HCP
and the lengths of your longest 2 suits (a+b) should
be equal to at least 18. Zar Points comply with the
Rule of 18 also (see the article for proof).
Isn't the value of HCP diminished in Zar Points count?
is hard to say "diminished" since it is calculated
through tons of equations - the accurate way to say
it is that the values of HCP is "accurate"
(as it is the case with all the other components of
Zar Points, for that matter).
to the "normal" weight of HCP, their value
is "diminished" in two different ways:
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);
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
How does the Zar Points method compare with Losing
Tricks Count (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):
How does the Zar Points method compare with the Charles
article proves in 3 different ways that Zar Points are
3 times better than Goren and Bergen as hand
a general bidding performance, Zar Points are proven
to deliver 2 times better bidding performance
via a "head-to-head" comparison through over
300,000 boards in the zones of part-score, game in Major,
game on Minor, slam, and Grand slam. All the records
are available from the "Support" menu for
How does the Zar Points method compare with the Marty
Bergen Rule of 20?
article proves in 3 different ways that Zar Points are
3 times better than Goren and Bergen as hand
a general bidding performance, Zar Points cannot be
compared to Bergen since Bergen does not address the
bidding per se, but rather only serves as an indicator
for opening the bidding.
How can you scale the Zar Points to the Goren or Bergen
is a separate section called "The Conversion"
which addresses this point. It shows how to "convert"
or "scale" Zar Points (the distributive part
of it, of course) to Goren points and then to Bergen
points - this was an idea of Jeff Rubens, the Editor
of "The Bridge World", which I liked a lot.
is also shown there, that Zar Points are better than
Goren in Goren terms and better than Bergen in Bergen
terms - a very powerful tool for comparison indeed.
How does the Zar Points criteria for opening compare
with the experts' judgment?
are a lot of examples of "light" openings
by real experts in real tournaments throughout the article.
I have put it in a letter to one of the experts, "
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 :-)
Which distribution count is better - short suits (Goren)
or long suits (Bergen)?
don't know which one is better, but I hope you already
know which one is the best :-)
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).
Bergen method only emphasizes adding your two longest
suits, but 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.
How do you value the suits you hold (say clubs vs.
Points assign one point for having the spades suit,
but you can only use that point in borderline decisions
- say, you have 25 Zar
and hesitate to open ... Now, if you have the spades
suit (4 cards at least) you can say that you have 26
Zar Points actually and to open the bidding.
the rationale? Not only the convenience to outbid the
opponents at the same level, but the convenient re-bid
after your partner bids something on level one. As a
general rule, you should know in advance what your eventual
re-bid would be prior to opening the bidding, That's
where holding the spades suit counts.
Does Zar Points count work for NT contracts?
Zar Points were originally calculated via tons of boards
in the suit Game and Slam areas. However, there were
many regression tests performed on NT contracts (all
DB-records are available for download here under the
"Support" menu)- and the results as you may
see there were consistent with the results for suit
realize, of course, that the reason for that is simple
- it's in the ratio between the HP and DP portions of
the Zar Points. With NT-oriented hands, the portion
of the HP (HCP + Controls) will be much more heavier,
compared to the corresponding picture in the suit-oriented
hands and contracts.
Has anyone before tried an approach similar to Zar
best way to answer that is via the discussion with Roger
Eymard from France:
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"
"J'ai découvert 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 " .
How did Zar Points evolve?
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 two-suiter between
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 coefficients 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
target 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 opening level
was 24). That's the story.