Zar Points By Zar Petkov
Ever wondered how experts bid "aggressive” games that "somehow,"magically” turn out to be cold? It’s simple: they just use their expert judgment, which advanced and intermediate players just don’t have yet.
Zar Points supply the tool for advanced and intermediate players to obtain this expert-level "aggressive” judgment and never miss a game again—be it a "somehow-magical” or just a "regular, plain” contract, while also stopping in a part-score when no game is in sight. The Zar-Points theory is a result of exhaustive research of thousands of "aggressive” contracts bid by world-class experts like Hamman, Wolff, Soloway, Meckwell, Lauria, Versace, DeFalco, Zia, Helgemo, Chagas, Sabine Auken andKaren McCallum, proven through over a million boards played at Double-Dummy.
The initial hand evaluation is where it all starts, and the question is how you can better capture the three main components of the hand’s playing potential: the shape, the controls, and the "standard” Milton Work 4-3-2-1 HCP. The reevaluation as the bidding progresses covers the placement of the honors and the suit-lengths in light of partner’s and opponent's bidding.
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 how these values were determined by solving series of over-determined systems of equations on hundreds of thousands of boards – these values are not a matter of "personal opinion".
Calculating distribution points is not news in Bridge: Charles Goren introduced Goren Points more than a half-century ago. It counts 3 points for every void, 2 points for every singleton, and 1 point for every doubleton. Of course, indirectly it also holds implicit valuation for the long suits, since the sum of all four suit lengths is 13, so with a 5-5 two-suiter you get 3 Goren points (either 2+1 for a singleton and a doubleton or 3 for a void). With Bergen Points you add your HCP to the sum of your longest two suit lengths and use the Rule of 20 as a guideline for opening, while with Goren you need to count 13 HCP to open.
If we denote your longest suit as a, your second longest suit as b, your third longest suit as c, and your shortest suit as d, Bergen Points are HCP+(a+b), which is a step forward on the way to better capturing the distribution. Zar Points go much farther than that: we add the three suit differences (a-b)+(b-c)+(c-d) which boils down to (a-d) after a simple transformation. Thus, the distribution part of Zar Points is (a+b)+(a-d), and the total number of initial Zar Points is HCP +Controls+(a+b)+(a-d). You need 26 to open.
The flat 4-3-3-3 distribution has the minimum amount of Distributional Zar Points, (4+3)+(4- 3)=8 points, while the 7-6-0-0 has (7+6) + (7- 0) = 20, for example. If you increase the length of the longest suit, the valuation also increases, of course: 9-4-0-0 has (9+4) + (9-0) = 22, and the wildest 13-0-0-0 hand gets the max of (13+0) + (13-0) = 26. The wilder the distribution the less HCP and Controls you need to open, and the more Controls you have, the less HCP you need. Here are some opening examples:
10 HCP: 
x 
Kxxxx 
Kxxx 
Axx
Zar Points calculation: HCP CTRLs (a+b) (a-d) TOTAL 10 + 4 + 9 + 4 = 27
9 HCP: KQxxx KJxxx xxx void
Zar Points calculation: HCP CTRLs (a+b) (a-d) TOTAL 9 + 2 + 10 + 5 = 26
8 HCP: Axxx A10xxx xxxx void
Zar Points calculation: HCP CTRLs (a+b) (a-d) TOTAL 8 + 4 + 9 + 5 = 26
7 HCP: Kxxxxx Axxxx xx void
Zar Points calculation: HCP CTRLs (a+b) (a-d) TOTAL 7 + 3 + 11 + 6 = 27
An important difference to note is that while 5-4- 2-2, 5-4-3-1 and 5-4-4-0 distributions all have the same value in Bergen, in Zar they get 12, 13, and 14 points respectively, all coming from adding the three differences in lengths.
If Zar Points seem a bit aggressive to you, let’s have a look at a couple of opening hands from the First Open European Championship in Menton, France.
Axxx AJxxxx x xx (Daily Bulletin 9) This hand has 9 HCP but still both Duboin and Ludewig opened it in the Open Teams. And indeed, the distribution Zar Points are 10+5=15 plus the 4 controls and the 9 HCP=28! Well above the opening minimum of 26.
Qx AKxxx Jxxxx x (Daily Bulletin 11) "Chagas’ light distributional opening bid changed matters.” In fact, the hand has 10+4=14 distributional Zar Points plus the 9 HCP (Qx)+3 controls=27 Zar Points, well into the opening hand range. Nothing special indeed, once you have a proper view on the potential of the hand.
You get 1 upgrade point if all your points are concentrated within three suits (if you have a strong hand of 15+ HCP) or within two suits (if you have a normal opening of 11-14 HCP). Obviously, in light openings you can never get this 1-point upgrade. This actually takes care of the value added by having your honors in combination rather than scattered among the four suits.
One final touch in the Initial Hand Evaluation concerns holding the spade suit, the so called resident suit In borderline cases, when you have 25 Zar Points, you add 1 point for holding the spade suit. ONLY when you are at the border of opening, holding the spade suit gives you the right to add 1 Zar Point and get to the 26-Zar-Points opening.
Here is an example of such an opening coming again from Menton, with the to-be-EuropeanChampion Eric Rodwell in action: AQxx Jx Axxx xxx (Daily Bulletin 13)
"Rodwell opened 1 and as the commentator said "EW were talked out of their game by Rodwell’s light opening bid…" He actually has 11 HCP (depreciates the Jx but gets 1 point back for two-suits concentration of points) plus 4 controls for 15 points, plus the 8+2=10 DP for a total of 25 Zar Points. When you upgrade the hand for holding the "president’s suit" of spades by 1 point, you reach the 26 needed to open.
On top of the aggressive constructive advantage that "light openings" present, there is one more thing to consider: the very fact that you have entered the bidding effectively puts the opponents in a defensive bidding track. After you study the matter a bit further, you come to the following summary of light openings using Zar Points:
1) With 8 HCP you need AT LEAST 5-5, 6-4 or 5-4-4-0 distribution with two aces.
2) With 9 HCP you need AT LEAST 5-4-3-1 distribution with two aces.
3) With 10 HCP you need AT LEAST 5-4 distribution and corresponding controls.
4) With 11 HCP you need EITHER a five-card suit OR 5 controls as a minimum.
Let's have a look at the responding side. Your partner has already opened and it’s your turn to respond. You first do the Initial hand evaluation that has been already been covered, and THEN make certain adjustments—adjustments to partner’s suit and adjustments to the opponent's suit (if they have overcalled). The minimum point count that allows you to act is 16:
1 additional point for the trump honors (including the 10), up to a MAX of 2.
1 additional point for the Invitational-second suit honors (including the 10), up to a MAX of 2. The total allowance here is 2, whether 2, 3, 4 or 5 are held (the rest is 'duplication values').
The last upgrade you make is for "superfit” in both the primary and secondary fits (if you have a secondary fit). You get 3 Zar Points for every card that brings the number of cards above 8, so if your partner has opened 1 (five-cards) and you have four spades you get 3 Zar Points for the fourth trump. So how do you judge the level at which you are ready to play? Here are the Game Calculations:
52 Zar Points for a four-level game or 3NT (based on "Two opening hands make a game”);
57 Zar Points for the five level;
62 Zar Points for a slam at the six level;
67 Zar Points for a GRAND slam.
Plain and simple: 5 points per level. These 5 points may come from an additional king in partner’s suit (3 points from the HCP, 1 from the control, and the premium 1 from the honor in partner’s suit), from an additional outside ace (2 from the controls plus 4 from the HCP), from 2 additional trumps in the superfit, etc. On the website you will see the Zar Bidding Machine which bids in Goren, Bergen, and Zar Points simultaneously, so you will have a chance to play and get a feel for the way things work
.