Zar Points is an advanced, statistically-derived method for evaluating Contract Bridge hands developed by Zar Petkov for use by more experienced players. 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 statistically 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.

Hand Evaluation

To evaluate an opening hand, in addition to standard high card point count, add points for:

• Controls: add two points for each ace and one point 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

When re-evaluating a hand based on earlier bidding, add points for:

• Support: add one point for each honor in partner's suit (up to two)
• 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
• Extra Trump Support: add three points for each trump over the promised length
• Secondary Fit: add three points for any invitational second suit card over 4
• Super-fit: After agreement on trumps, add points for each trump over 8: 3 if your shortest suit is a void, 2 for a singleton, 1 for a doubleton.

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. When the partners do not have an 8 card trump fit, the misfit modifier subtracts from the total Zars. When the partners have a trump fit longer than 8, the misfit modifier adds in place of the super-fit 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) because m2 is approximately 75% of m4 when m4 is below 14. When m4 is above 14, 0.8% of the time, m2 is only 60% of m4. This means that the misfit modifier can be estimated by increasing m2 by 1/3.

26 Zar Points(Zars) are required to open. 16 Zars are required to respond. 52 Zars is 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

Use in Existing Bidding Systems

One way to use Zar Points is to convert them into the more traditional HCPs.

To do this, take the total Zar Points, excluding high card points and controls, then subtract eight, and then divide by two. Add to this result points for high cards and controls using this scheme:

• Each Ace as 4.5pts
• Each King as 3pts
• Each Queen as 1.5pts
• Each Jack as .5pts.

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.

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.

Requirements for Game

• 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 Gam
  • 52+ZP and major suit fit

• Minor Suit Game
  • 57+ZP and minor suit fit
  • Does not meet No Trump requirements
  • Not more than 2 quick tricks in any suit

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

• 1C: 36+ Zars, Any Distribution, or 31-35 balanced
• 1D: 31-35 Zars, Any Distribution, or 26-30 with 6-card minor
• 1H: 26-30 Zars, 4+ cards in H, may have 4 cards in S
• 1S: 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

• 2C: 26-30 Zars, 6H or 6H and 5 in another suit
• 2D: 26-30 Zars, 6S or 6S and 5 in another suit
• 2H: 26-30 Zars, 5-card H suit and 6 cards in a minor
• 2S: 26-30 Zars, 5-card S suit and 6 cards in a minor
• 2NT: 26-30 Zars, At least 5-5 in minors

• 2C: 26-30 Zars, 7-card Club suit
• 2D: 26-30 Zars, 7-card Diamond suit
• 2H: 26-30 Zars, 7-card Heart suit
• 2S: 26-30 Zars, 7-card Spade suit

• 3NT+: 8+ card suits

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 1C. 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 1H or 1S
  • 1S response to 1H 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 1H.
  • 2C is artificial and forcing; shows prospects for game; denies 4 spades if in response to 1H.
  • Direct raise of the suit is pre-emptive and sign-off.
  • All other bids are "natural" and to play.

• Responses to 1NT
  • 2C is a game-forcing relay asking for distribution
    • 2D rebid is 4333 distribution (so 18-22 HCP + Controls). Oriented towards 3NT
    • 2H rebid is 4432 with 3 cards in hearts (implying 2 cards in spades and a 4-4 minors).
    • 2S 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
    • 3C is distribution with 5 diamonds and no singleton
    • 3H is 5431 with 3 hearts (implying 1 spade)
    • 3S is 5431 with 3 spade (implying 1 heart)
  • 2D is a transfer to 2H; Afterward:
    • a rebid of 2NT is invitational to 3NT or 4H with 5+ hearts
    • a rebid of 2S is invitational to 3NT and shows no relevance to either major
  • 2H is a transfer to 2S; a 2NT rebid is invitational with 5+ spades
  • 2S is a transfer to 2NT or 3C; 2NT by opener shows interest in game in clubs
  • 2NT is a transfer to 3C or 3D; 3C 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 2C with 2D (a relay)
  • Rebid of 2H specifies uni-suit (6 hearts)
  • Rebid of 2S specifies 5 card spade side-suit
  • Rebid of 3C specifies a 5 card club side-suit
  • Rebid of 3D specifies a 5 card diamond side-suit

• Respond to 2D with 2H (a relay)
  • Rebid of 2S specifies a uni-suit (6 spades)
  • Rebid of 2NT specifies 5 card heart side-suit
  • Rebid of 3C specifies a 5 card club side-suit
  • Rebid of 3D 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 1C
  • 1D is negative (less than 16), any distribution
  • 1H is positive (16+), at least four cards in hearts
  • 1S 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 1D
  • 1H forcing, natural asks opener to show his hand, any new suit on the next round is forcing
  • 1S 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
  • 2C 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