Zar Points (ZP) is a statistically derived method for evaluating contract bridge hands developed by Zar Petkov. The statistical research Petkov conducted in the areas of hand evaluation and bidding is useful to bridge players, regardless of their bidding or hand evaluation system. The research showed that the Milton Work point count method, even when adjusted for distribution, is not sufficiently accurate in evaluating all hands. As a result, players often make incorrect or sub-optimal bids. Zar Points are designed to take many additional factors into consideration by assigning points to each factor based on statistical weight. While most of these factors are already implicitly taken into account by experienced players, Zar Points provides a quantitative method that allows them to be incorporated into bidding.
Zar Points (ZP) are based on high card points, distributional points and adjustments for suit fits.
Zar distribution points are the sum of the lengths of the two longest suits plus the difference between the longest suit and the shortest suit.
With an 8-card trump fit, add points for:
For bidding systems that allow one partner to know the shape of the other's hand, an additional misfit adjustment exists. To calculate the misfit modifier, find the difference in length between spade suits in each hand. Perform a similar calculation for the other three suits and sum the differences. Call this number M4.
When the partners do not have an 8-card trump fit, the misfit modifier subtracts from the total ZP. When the partners have a trump fit longer than eight, the misfit modifier adds in place of the trump-support modifier if it is larger.
The misfit modifier (M4) can be estimated if one partner knows the difference in lengths between the two most different suits (M2). This works because M2 is almost always approximately 75 percent of M4, meaning that M4 can be estimated by increasing M2 by 1/3. Keep in mind that this estimate will slightly under-value the hand in the case of "freak" distribution (where M4 is greater than 14) because M2 is only 60 percent of M4 for such wild distribution. Fortunately this only occurs 0.8 percent of the time.
To improve the accuracy of the point count, standard "judgment" adjustments can be used, such as:
Zar Points are designed with rubbers scoring in mind. When playing for matchpoints, it is desirable to bid any game or small slam that has a 50 percent chance of making. In order to do this, slight adjustments to the ZP required per level need to be made. The result is that intermediate values are slightly off from the 5 point scale suggested above.
When playing using IMPs, a game should be bid with a 38 percent chance when vulnerable, but only bid a 46 percent game when not vulnerable. This adjustment shifts the ZP required for game and slam one point down when vulnerable or not vulnerable.
Once adjustments have been made, an opening hand requires 26 ZP and a responding hand needs 16 ZP; a major suit game requires 52 ZP, a small slam requires 62 ZP and a grand slam requires 67.
Bidding levels are five points apart yielding:
This scale does not need to be memorized. In order to arrive at the expected number of tricks, one need only subtract 2 ZPs and divide by 5. For example, with 52 ZPs, subtracting 2 gives 50, and dividing 50 by 5 gives 10 - the number of tricks expected to be taken.
Some players use ZP for suit bidding only. Others use them for bidding no-trump as well. Zar recommends the following scheme. Notice that not having an 8 card fit increases the ZP required for a given level by 5.
The simplest way to use Zar Points (in respect of opening hands) is to divide everything by two and open, as Charles Goren taught, with 13 points. Thus we effectively use the same high card point scale devised by the Four Aces in the 1930s with A=3, K=2, Q=1, J=½. We then add the length of the longest suit and finally, we add half the difference in the length of the second and fourth longest suits.
The foregoing normalizes Zar Points to numbers more commonly used in Standard American bidding. Alternatively, see the section below: Obtaining the conversion.
In order to get the HCP equivalent discussed above, Zar points need to be scaled. To scale the values of the honors from a 13 points scale to a 10 point scale, the ZP are multiplied by 10/13 and rounded to the nearest half. This results in slightly under valuing Aces and Jacks, but is much more accurate than the traditional count.
To scale the shape points to the traditional scale, we can subtract 8 (to set the lowest value at 0) and divide by two (to scale the highest value correctly). Algebraically, if 'a' is the length of the longest suit, 'b' the second longest, and 'd' the shortest:
Petkov has proposed a core bidding method, similar to the Precision Club derivatives Symmetric Relay and MOSCITO, that makes extensive use of limit bids, relays, and the shape defining properties of Zar Points to rapidly describe a hand. Below is a summary of the basics, omitting some of the finer points and the research details supporting the decisions. To make this a full system, a partnership would need to agree on what conventions to use. Most of the ideas from other systems can carry over. Partnerships interested in using this system should familiarize themselves with the reasons behind this basic bidding pattern before selecting specific conventions.
Opening bids are divided into three intervals: just enough to open (26-30 Zars), one extra bidding level (31-35 Zars), and two or more extra bidding levels (36+ Zars). Because distribution can dramatically affect the playability of a hand, each of these Zar Points ranges can cover a wide number of traditional high card points. The opening level could represent between 3 and 19 HCP. The middle level could represent between 7 and 22 HCP. The maximum level could represent between 11 and 30 HCP. These ranges are inclusive. These three ranges are statistically derived: 60 percent of opening hands will fall in the lowest range, 30 percent will fall in the middle range, and 10 percent will fall in the top range.
Because of the very descriptive nature of each of the opening bids, the responder is in control of the bidding unless the opener bid 1♣. Also, the responder will be able after the re-bid by the opener to estimate the misfit modifier, allowing an accurate determination of where to play the hand.