Zar Points
From Wikipedia, the free encyclopedia
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 high card points
Zar Points (ZP) are based on high card points, distributional points and adjustments for suit fits.
Zar high card points (ZHP) are the sum of the traditional Milton Work or Charles Goren 4-3-2-1 scale and control values for the ace and king.
| 4-3-2-1 value |
Control value |
ZHP | |
|---|---|---|---|
| Ace | 4 | 2 | 6 |
| King | 3 | 1 | 4 |
| Queen | 2 | 2 | |
| Jack | 1 | 1 |
Zar distribution points
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.
Adjustments
Trump fit re-evaluation
With an 8-card trump fit, add points for:
- Extra trump support with a void: for each trump over 8 when the shortest suit is a void, add 2.
- Extra trump support with a singleton: for each trump over 8 when the shortest suit is a singleton, add 1.
- For a secondary 9-card fit, add 1.
- For a secondary 10-card fit, add 2.
Misfit adjustment
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. This only occurs 0.8 percent of the time.
Minor adjustments
To improve the accuracy of the point count, standard "judgment" adjustments can be used, such as:
- Concentration: with 15+ HCP add 1 point if all the HCP are concentrated in three suits; with 11–14 HCP add 1 point if all of the HCP are concentrated in two suits.
- Short honors: subtract one point for short suit honors like KQ or QJ
- Spade suit: With 25 Zars and the suit is spades, 1 point may be added.
- Finesse: subtract or add a point for honors in opponents' suits depending on whether they are on or off side
- Unguarded Honors: discount honors in short suits bid by opponents
- Support: add one point for each honor in partner's suit (up to two)
Strategic adjustments
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. 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 below.
- 44 ZP — 8 tricks
- 48 ZP — 9 tricks
- 52 ZP — 10 tricks
- 56 ZP — 11 tricks
- 61 ZP — 12 tricks
- 67 ZP — 13 tricks
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.
Bidding levels and Zar Point requirements
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:
- Two level – 42 i.e. 26 + 16
- Three level – 47
- Four level – 52
- Five level – 57
- Six level – 62
- Seven level – 67
This scale does not need to be memorized. 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.
- Grand slam
- 67+ ZP with fit or
- 72+ ZP without fit
- First round control in all suits
- Small slam
- 62+ ZP with fit or
- 67+ ZP without fit
- First round control of at least three suits
- Second round control for the suit with no first-round control
- Notrump game
- All suits stopped
- 52+ ZP and any 5-3 fit or 4-4 minor fit
- 57+ ZP without fit
- Major suit game
- 52+ ZP and major suit fit
- Minor suit game
- 57+ ZP and minor suit fit
- Does not meet notrump requirements
- Not more than two quick tricks in any suit
