Zar Points are based on extensive
research on boards in the Game – Slam area.
This includes:
-Over 100,000 boards with 4
/
contracts;
-Over 70,000 boards with 5
/
contracts;
-Over 30,000 boards with 6
/
/
/
contracts;
-Over 10,000 boards with 7
/
/
/
contracts;
-Over 20,000 boards with NT contracts;
ALL these boards have been played on Double-Dummy to ensure accurate and independent assessment
of the playing level of the board.
You can download all the research boards with the detailed
Zar Points analysis of each
and everyone of them from
the website.
I have run different sets of boards, between 10,000
and 60,000 portions to ensure that the results provided
by the software I’ve written for the analysis
is stable. Below, I discuss the results of the research
and these samples of hundreds of thousands of boards
and the behavior of Zar Points in these experiments.
First let’s have a look
at the facts presented by the computer report.
For the Games in minors I ran
2 sets of boards, all played in double-dummy as usual.
The first set comprised 63,057
boards whose Best Contract indication by the Double-Dummy
play was either 4 or 4. Here is the very bottom of the report, including the last board (so
you get a feel of what’s actually reported on
each board) and the final statistics. NOTE: control
points are the points you get from the card that
brig you controls – 6 for A and 4 for K.
Board
#63057
North:
KT
KJ86
AQ
AQJ92
South:
Q863
T92
T532
T5
BEST
contract, actually played on double-dummy, is 4HE,
Controls = 6, ControlPoints
= 20
SP_len N = 2, HE_len N = 4, DI_len N = 2, CL_len N = 5
SP_len S = 4, HE_len S = 3, DI_len S = 4, CL_len S = 2
The fitin this contract
is 7-card, N has 4, S has 3
a_N = 5, b_N = 4, c_N = 2, d_N = 2
a_S = 4, b_S = 4, c_S = 3, d_S = 2
N - Zar Points (a+b) + (a-d)
= 12
Controls N = 6, HCP N = 20----------------------->
NZar Points = 38
S - Zar Points (a+b) + (a-d)
= 10
Controls S = 0, HCP S = 2------------------------>
S Zar Points = 12
Hands
below 50 Zar + FitPointsfor 63057 boards is 2573
Hands below 48 Zar + FitPointsfor 63057 boards is 662
So the average Zar Points with
the 3 pt. Fit calculations (rather that the Zar Ruffing
Power calculations which are a bit more sophisticated
and depend on both your fit and shortness in the side
suits) is about55 Zar Points.As you remember, the 4-level mark was 52,
which is 3 points below the average. This means that
the bottom level is only 5% below the average! So you have
an idea about the precision Zar Points work with.
Let’s have a look at
the “missed” boards. When you calculate
the rough 3-points-per-additional-trump, the missed
boards fell more than 2 times to only 2,500 out of 63,000+ boards. If you
download the 63,057 analyzed boards from the website,
you’ll see that 90% of the “missed”
boards are boards with double-fit which the program does not calculate. If you add the calculations
for double-fit, you
are in the 99% Game Bidding coverage!
Let’s have a look at
the second sample of 4-in-Major Games. It contains 42,756 totally different
Games:
Board
#42756
North:
KQJ53
A973
9
Q42
South:
976
K84
AJ3
AT85
BEST
contract is 4SP, Controls = 8, ControlPoints
= 26
SP_len N = 5, HE_len N = 4, DI_len N = 1, CL_len N = 3
SP_len S = 3, HE_len S = 3, DI_len S = 3, CL_len S = 4
The fitin this contract
is 8-card, N has 5, S has 3
a_N = 5, b_N = 4, c_N = 3, d_N = 1
a_S = 4, b_S = 3, c_S = 3, d_S = 3
N - Zar Points (a+b) + (a-d)
= 13
Controls N = 3, HCP N = 12------------------------>
NZar Points = 28
S - Zar Points (a+b) + (a-d)
= 8
Controls S = 5, HCP S = 12------------------------>
SZar Points = 25
Hands
below 50 Zar + FitPointsfor 42756 boards is 2947
Hands below 48 Zar + FitPointsfor 42756 boards is 901
Again the drop of “missed”
boards is over 2 times, if counting the fit-points.
Also, the “missed”
boards are about the
same 5%!
When you add the double-fit
adjustments (you can see that the majority of the “missed”
boards are with double-fit when you download the database),
you again end-up in the 99% coverage!
First let’s have a look
at the facts presented by the computer report.
For the Games in minors I ran
2 sets of boards, all played in double-dummy as usual.
The first set comprised 27,776
boards whose Best Contract indication by the Double-Dummy
play was either 5
or 5.
Here again is the very bottom of the report, including
the last board and the final statistics.
Board
#27776
North:
Q654
A7
J5
KT632
South:
---
KJT5
K8642
AJ94
BEST
contract, actually played on double-dummy, is 5CL,
Controls = 7, ControlPoints
= 24
SP_len N = 4, HE_len N = 2, DI_len N = 2, CL_len N = 5
SP_len S = 0, HE_len S = 4, DI_len S = 5, CL_len S = 4
The fitin this contract
is 9-card, N has 5, S has 4
a_N = 5, b_N = 4, c_N = 2, d_N = 2
a_S = 5, b_S = 4, c_S = 4, d_S = 0
N - Zar Points (a+b) + (a-d)
= 12
Controls N = 3, HCP N = 10------------------------>
NZar Points
= 25
S - Zar Points (a+b) + (a-d)
= 14
Controls S = 4, HCP S = 12------------------------>
SZarPoints = 30
Hands
below 54 Zar + FitPointsfor 27776 boards is 1618
Hands below 52 Zar + FitPointsfor 27776 boards is 493
Hands below 50 Zar + FitPointsfor 27776 boards is 100
Hands below 48 Zar + FitPointsfor 27776 boards is 16
So the average Zar Points with
the 3 pt. Fit calculations (rather that the Zar Ruffing
Power calculations which a bit more sophisticated and
depend on both your fit and shortnesses
in the side suits) is 59 Zar Points.As you remember, the 5-level mark was 56,
which is 3 points below the average. So the bottom level
is only 5% below the average! This gives
you an idea about the precision interval Zar Points
work with.
Let’s have a look at
the “missed” boards. When you calculate
the rough 3-points-per-additional-trump, the missed
boards fell 3 times to only 1,600 out of 27,776. If you download the 27,776
boards from the website, you’ll see that 95% of
the “missed” boards are boards with
double-fit which the program does not calculate.
If you add the calculations for double-fit, you
are in the 99% Game Bidding coverage.
Let’s have a look at
the second sample of 5-in-Minor Games. It contains 43,014 totally different
Games:
Board
#43014
North:
JT8642
Q
KT843
9
South:
AQ3
832
A9765
J6
BEST
contract is 5DI, Controls = 5, ControlPoints
= 16
