Zar Points

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Zar Points is an advanced, statistically-derived method for evaluating Contract Bridge hands developed by Zar Petkov for use by players of intermediate or better skill. The statistical research Petkov conducted in the areas of hand evaluation and bidding is useful to any advanced bridge player, regardless of their bidding or hand evaluation system, but the research showed that the Milton Work point count method, even when adjusted for distribution, does not accurately describe 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 accurately.

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[edit] Using Zar Points in existing bidding systems

One way to use Zar Points is to convert them into the more traditional High Card Points (HCP).

Count Honors using the following scheme:

  • Each Ace as 4½ points
  • Each King as 3 points
  • Each Queen as 1½ points
  • Each Jack as ½ point.

Then:

  • Add 1 point for each card in the longest suit beyond four. For example, a 5-card suit counts 1 point, 6-card suit counts 2 points.
  • Add ½ point for each card in the second longest suit beyond the length of the shortest suit. For example, add 1½ points with 5-4-3-1 distribution; add 1 point with 4-4-3-2 distribution.

The result will be a more accurate estimate of hand strength adjusted to the traditional scale. Several experts have used Zar Points in this fashion. Additionally, other adjustments discussed below may be taken into account. Alternatively, the number of Zar Points as counted below can be divided by two; this will preserve the correct ratio between distribution and honors. Dividing by two is potentially more accurate, but no statistical tests have been done to confirm this.

[edit] Hand evaluation using the Zar scale

Using Zar Points (ZP), 26 ZP are required to open and 16 ZP are required to respond. Fifty-two ZP (two opening hands) should result in game at the four level. 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. 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 by 50 by 5 gives 10 – the number of tricks expected to be taken.

[edit] Basic hand evaluation

To evaluate an opening hand, use standard 4-3-2-1 high card points and add points for:

  • Controls: add 2 for each ace and 1 for each king
  • Length: add the lengths of the two longest suits
  • Shape: add the difference between the length of the longest suit and the shortest suit

[edit] Hand re-evaluation

With an eight 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.
  • Secondary nine-card Fit: Add 1 for a nine card secondary suit.
  • Secondary ten-card Fit: Add 2 for a ten card secondary suit.

[edit] The 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 8, 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.

[edit] 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 of 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)

[edit] More elaborate requirements for game

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
  • No trump 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 No Trump requirements
    • Not more than two quick tricks in any suit

[edit] 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. 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.

  • 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.

[edit] 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:


\frac{(a+b) + (a-d) - 8}{2} = (a-4) + 0.5(b-d)

[edit] New bidding systems

Petkov has proposed the guts of 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.


[edit] Opening bids

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 hands will fall in the lowest range, 30 percent will fall in the middle range, and 10 percent will fall in the top range.

  • 1♣: 36+ Zars, Any Distribution, or 31-35 balanced
  • 1♦: 31-35 Zars, Any Distribution, or 26-30 with 6-card minor
  • 1♥: 26-30 Zars, 4+ cards in H, may have 4 cards in S
  • 1♠: 26-30 Zars, 4+ cards in S, may have 4 cards in H (and 5 in S)
  • 1NT: 26-30 Zars, No 6-card suit, no 4-card major, no 5-5 minors
  • 2♣: 26-30 Zars, 6H or 6H and 5 in another suit
  • 2♦: 26-30 Zars, 6S or 6S and 5 in another suit
  • 2♥: 26-30 Zars, 5-card H suit and 6 cards in a minor
  • 2♠: 26-30 Zars, 5-card S suit and 6 cards in a minor
  • 2NT: 26-30 Zars, At least 5-5 in minors
  • 3♣: 26-30 Zars, 7-card Club suit
  • 3♦: 26-30 Zars, 7-card Diamond suit
  • 3♥: 26-30 Zars, 7-card Heart suit
  • 3♠: 26-30 Zars, 7-card Spade suit
  • 3NT+: 8+ card suits

[edit] Responding to opening bids

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.

  • Responses to 1♥ or 1♠
    • 1♠ response to 1♥ is round forcing and asking to the opener to better describe his hand. It shows 4+ spades. If opener rebids the heart suit, he has exactly 5 hearts.
    • 1NT is "to play", it discourages game and denies 4 spades if in response to 1♥.
    • 2♣ is artificial and forcing; shows prospects for game; denies 4 spades if in response to 1♥.
    • Direct raise of the suit is preemptive and sign-off.
    • All other bids are "natural" and to play.
  • Responses to 1NT
    • 2♣ is a game-forcing relay asking for distribution
      • 2♦ rebid is 4333 distribution (so 18-22 HCP + Controls). Oriented towards 3NT
      • 2♥ rebid is 4432 with 3 cards in hearts (implying 2 cards in spades and a 4-4 minors).
      • 2♠ rebid is 4432 with 3 cards in spades (implying 2 cards in hearts and a 4-4 minors).
      • 2NT is distribution with 5 clubs and no singleton
      • 3♣ is distribution with 5 diamonds and no singleton
      • 3♥ is 5431 with 3 hearts (implying 1 spade)
      • 3♠ is 5431 with 3 spade (implying 1 heart)
    • 2♦ is a transfer to 2♥; Afterward:
      • a rebid of 2NT is invitational to 3NT or 4H with 5+ hearts
      • a rebid of 2♠ is invitational to 3NT and shows no relevance to either major
    • 2♥ is a transfer to 2♠; a 2NT rebid is invitational with 5+ spades
    • 2♠ is a transfer to 2NT or 3♣; 2NT by opener shows interest in game in clubs
    • 2NT is a transfer to 3♣ or 3♦; 3♣ by opener shows interest in game in diamonds
    • All level three responses are game forcing and show a 4441 distribution with a singleton in the bid suit
  • Respond to 2♣ with 2♦ (a relay)
    • Rebid of 2♥ specifies uni-suit (6 hearts)
    • Rebid of 2♠ specifies 5 card spade side-suit
    • Rebid of 3♣ specifies a 5 card club side-suit
    • Rebid of 3♦ specifies a 5 card diamond side-suit
  • Respond to 2♦ with 2♥ (a relay)
    • Rebid of 2♠ specifies a uni-suit (6 spades)
    • Rebid of 2NT specifies 5 card heart side-suit
    • Rebid of 3♣ specifies a 5 card club side-suit
    • Rebid of 3♦ specifies a 5 card diamond side-suit
  • Other responses above 1NT
    • 2NT asks for side top honor
    • New suit is round forcing oriented toward fit and then side top honor
    • Other bids are "to play" unless partnership has agreed otherwise
  • Responses to 1♣
    • 1♦ is negative (less than 16), any distribution
    • 1♥ is positive (16+), at least four cards in hearts
    • 1♠ is positive (16+), at least four cards in spades
    • 1NT 16-20, balanced hand, etc.
    • Other bids are similar to Precision Club or related systems of the partnership's choosing
  • Responses to 1♦
    • 1♥ forcing, natural asks opener to show his hand, any new suit on the next round is forcing
    • 1♠ forcing, natural asks opener to show his hand, any new suit on the next round is forcing
    • 1NT negative, responder is ready to pass next bid of opener
    • 2♣ artificial, forcing, 21+, game prospects, no 4 card major, will support a major bid with 3 cards on next round
    • Other responses are up to the partnership

[edit] External links