The Zar-Points theory is a result of exhaustive
research of hundreds and hundreds of “aggressive”
game contracts bid by world-class experts like Hamman,
Wolff, Meckwell, Lauria, DeFalco, Zia, Helgemo, Chagas,
Sabine Auken, Karen McCallum (I have great respect
for the women experts) and many others at various
world-class tournaments. It is backed by a research
and regression testing on literally hundreds of thousands
of boards which are all available for download from
the “download” page of the “Support” menu.
The initial evaluation (just as you pick up
your cards and have a look at what’s in there) captures
the three standard important aspects of every hand:
the shape, the controls, and the standard (Milton
Works 4-3-2-1) HCP. The re-evaluation covers the placement
of the honors and the suit-lengths in the light of
partner’s and opponents’ bidding.
Calculating the Zar Points has 2 parts – calculating
the High-card
Points (HP) and the Distribution
Points (DP).
For the
high-card points we use the 6-4-2-1 scheme which
adds the sum of your controls
(A=2, K=1) to your standard Milton HCP, in the 4-3-2-1
scheme (A=4, K=3, Q=2, J=1). You will see WHY
we have adopted this HP counting in the second part
of the article.
Calculating distribution
points addresses the 39 different possible
distributions in a bridge hand. In Zar Points we assign
a specific value to all of these 39 shapes by adding:
-The difference
between the lengths of the Longest and the Shortest
suits (we call it S2)
-The sum
of the lengths of the Longest 2 suits (we call it
L2);
The reality of Zar Points is that we add ALL the 3 differences of your suits:
( a – b) + (b – c) + (c – d).
But wait … look what
happens when you drop the parenthesis – both b and
c disappear and the expression becomes very
simple:
(a – d)
So …
The entire amount of the Distributional
Zar Points is:
(a + b) + (a – d)
So you have calculated the HP
portion first, and then have added the DP portion for the Distributional Zars.
Now, if the sum is 26
or better, you have an Opening
Hand. Here are some examples, to get your feet
wet:
11+4+3+8=26
11 HCP
K J x x x
K x x
x x x
A x
10+4+4+9=27
10 HCP
x
K x x x x
K x x x
A x x
8+4+5+9=26
8 HCP
A x x x
A 10 x x x
x x x x
___
10+3+4+9=26
10 HCP
Q 10 x x
A x x
x
K J x x x
9+2+5+10=26
9 HCP
K Q x x x
K J x x x
x x x
___
7+3+6+11=27
7 HCP
K x x x x x
A x x x x
x x
___
If you read the “Never Miss a Game again,
you will see how we arrive at the following
SUMMARY:
1) With 8 HCP - you need AT LEAST5-5,
6-4 or 5-4-4-0 distribution with
2 Aces
2) With 9 HCP - you need AT LEAST5-4-3-1
distribution with 2
Aces
3) With 10 HCP - you need AT LEAST5-4 distribution
4) With 11 HCP - you need EITHER a 5-card suit OR 5
controls
What kind of weight to put on the components
you consider valuable is not a matter of "expert
judgment", but a simple matter of solving a series of equations with unknown coefficients -
an obviously overdetermined system of equations (you
enter hundreds of equations based on the hundreds
of boards you feed in, for finding the value of several
of coefficients – the weights you are interested in).
How do you create the equations for a specific
board in order to calculate the “right” weights? We
will illustrate that by an example that is very familiar
to you - we’ll count HCP points and distribution points
for void, doubleton, and singleton (kind of Goren
style) with 3 points for void, 2 for singleton, and
1 for doubleton. Here is the equation:
You make a collection of hundreds and hundreds
of boards that have a game (4 in major) and solve
the overdetermined system of equation to find the
values of the unknown coefficients. Simple.
For the board above (4 Spades), if we consider
the plain 4-3-2-1 Milton Works points, assigning 4
for A, 3 for K etc. and assign Goren distribution
points (3 for void, 2 for singleton, and 1 for doubleton),
we see that those ARE a solution for our first (and
only for the time being) equation:
so you have to “collect” 25 points to get a game with Milton / Goren
points. The same way we have run the systems for the
Zar Points which have much more variables to calculate.
Now that we know that we need 26 Zar Points to open, let’s ask
the question “How low in terms of HCP can you get?”.
Let's explore this avenue a bit - here are several hands that
will provide the answer to that:
7+3+6+11=27
7 HCP
K x x x x x
A x x x x
x x
___
6+2+6+12=26
6 HCP
K x x x x x
K x x x x x
x
___
5+1+7+13=26
5 HCP
K x x x x x x
Q x x x x x
___
___
4+2+7+13=26
4 HCP
10 x x x x x x
A x x x x x
___
___
Looks a little aggressive, doesn’t it? Well ... that’s because
it IS aggressive.
It may even look like kinda crazy to you ....
The article will let you make the difference between crazy
and aggressive. Better yet, it will make you stop
being crazy and start being aggressive.
K J x x x 
K x x 
x x x 
A x