Definitions

# Hand evaluation

In contract bridge, various bidding systems have been devised to enable partners to describe their hands to each other so that they may reach the optimum contract. A key initial part of this process is that players evaluate their hands; this evaluation is subject to amendment after each round of bidding. Several methods have been devised to evaluate hands taking account of some or all of strength, shape, fit and "quality" of a suit or the whole hand. This article explains the methods and the situations in which each may best be used.

## Basic Point-Count Method

Most bidding systems use a basic point count system for hand evaluation using a combination of the following:

### High Card Points (HCP)

Based on the McCampbell count of 1915 and publicised/advocated by Milton Work circa 1923 (and called the Milton Work Point Count for many years) this method recognises, in simple arithmetic form, that an ace has a higher trick taking potential than a king which similarly is more powerful than a queen etc. HCP are awarded thus (Cohen & Barrow 1967):

• ace = 4 HCP
• king = 3 HCP
• queen = 2 HCP
• jack = 1 HCP

No pretence is made that 4 jacks are as powerful as 1 ace. Nevertheless, this method has the twin benefits of simplicity and practicality, especially in no trump contracts. Evaluating a hand on this basis takes due account of the fact that there are 10 HCP in each suit and therefore 40 in the complete deck of cards. An average hand contains one quarter of the total i.e. 10 HCP. Most bidding systems are built around the belief that a better than average hand is required to open the bidding; 12 HCP is generally considered the minimum for most opening bids. The combined HCP count between two hands is generally considered to be a good an indication, all else being equal, of the number of tricks likely to be made by the partnership. The rule of thumb (Root 1998 and Klinger 1994) for games and slams in NT is:

• 25 HCP = 3 NT
• 33 HCP = 6 NT
• 37 HCP = 7 NT

A further justification for 37 HCP being suitable for a grand slam is that it is the lowest number that guarantees the partnership holding all the aces; similarly 33 HCP is the lowest number that guarantees only one ace can be missing (Klinger 1994), so a small slam cannot be defeated immediately.

Although this method of hand evaluation has many benefits (especially in notrump bidding), it is often not sufficient of itself, for deciding the level of the contact, mostly so for unbalanced hands. Expert players utilise the HCP count as starting point in the evaluation of their hand, and make adjustments based on hand shape, location of honours, fit with partner, intermediate cards, control cards, unguarded honours, and information on partner's suit length and suit strength as it becomes available during the bidding. As a result, an expert player might refer to a hand as: "a good 16" or "a control-rich 15 point hand", etc.

Although mostly effective for evaluating the combined trick-taking potential of two balanced hands played in notrump, even in this area of applicability the HCP is not infallible. In his book "The Secrets of Winning Bridge", Rubens gives the following example:

Both east hands are exactly the same, and both west hands have the same shape, the same HCP count, and the same high cards. The only difference between both west hands is that two low red cards and one low black card have been swapped (between the heart suit and the diamond suit, and between the spade suit and the club suit, respectively).

With a total of 34 HCP in the combined hands, based on the above mentioned HCP-requirement for slam, most partnerships would end in a small slam (12 tricks) contract. Yet, the leftmost layout produces 13 tricks in notrump, whilst the rightmost layout on a diamond lead would fail to produce more than 10 tricks in notrump. The difference in trick-taking potential between both holdings is due to the presence of duplication: in the rightmost layout the combined 20 HCP in spades and diamonds result only in five tricks. As such duplication can often not be detected during the bidding itself, HCP (and any hand evaluation method for that matter) can only produce statistical estimates for the trick taking potential of the combined hands.

### Distributional points

As it became clear that HCP were not sufficient for evaluating shapely hands, efforts were made to devise an equally simple arithmetic method for taking account of the shape of a hand.

#### Length points (or Long-card points)

At its simplest it is considered that long suits have a value beyond the HCP held: this can be turned into numbers on the following scale recommended by the EBU (Landy 1998) and "one of the most popular in the USA" (Root 1998):

• 5-card suit = 1 point
• 6 card suit = 2 points
• 7 card suit = 3 points ... etc

A hand comprising a 5-card suit and a 6-card suit gains points for both, i.e., 1 + 2 making 3 points in total. Other combinations are dealt with in a similar way. These distribution points (sometimes called length points) are added to the HCP to give the total point value of the hand. Confusion can arise because the term "points" can be used to mean either HCP, or HCP plus length points. This method, of valuing both high cards and long suits, is suitable for use at the opening bid stage before a trump suit has been agreed. In the USA this method of combining HCP and long-card points is known as the point-count system (Root 1998).

#### Shortage points (includes a definition of "support points")

Once a trump suit has been agreed, or at least a partial fit has been uncovered, it is argued by many (Klinger 1994, Landy 1998 and Root 1998) that ruffing potential as represented by short suits becomes more significant than long suits. Thus distribution points are added for shortage rather than length, according to this scale (Root 1998):

• void = 3 points
• singleton = 2 points
• doubleton = 1 point

or to this scale (Klinger 1994):

• void = 5 points
• singleton = 3 points
• doubleton = 1 point

This method of distributional point count was introduced in North America by William Anderson of Toronto and adopted/developed by Charles Goren in the 1940s. As with length points, these "shortage points" are added to HCP to give total points also known as "support points" because this measure is only used when a fit has been found. It is important to note that support points for shortness should only be counted when holding at least 3-card support for partner's bid suit.

To summarize: length points are used for opening bids, and shortage points are used after a trump fit has been agreed.

## Supplementary Methods

The point-count method alone does not solve all evaluation problems and needs supplementation in certain circumstamces:

### Control count

The control count is a supplementary point count method that is mainly used in combination with HCP to determine the trick-taking potential (in particular the slam potential) of fitting hands. The use of control count as adjustment to the HCP count stems from the fact that for suit contracts aces and kings tend to be undervalued in the standard HCP metric. Aces (and also kings) allow declarer better control over the hands and can effectively prevent the opponents from retaining or gaining the lead.

To express the 'control value' in one single parameter, the control count values aces as two controls, and kings as one control whilst lower honours do not add to the control count. This control count can be used as "tie-breakers" for hands evaluated as marginal by their HCP count.

Hands with the same shape and the same HCP can have markedly different slampotential depending on whether the hands are 'control rich' or not. An example illustrates the point:
Both west hands are the same, and both east hands have the same shape and the same number of HCP (16). Yet, the layout on the left represents a solid slam (12 tricks) in spades, whilst the layout to the right will fail to produce 12 tricks. The difference between both east hands becomes apparent when conducting a control count: east in the left layout has two aces and two kings for a total of 6 controls, whilst east on the right hand side has 1 ace and two kings for a total of 4 controls.

To determine whether a hand is 'control rich' or not, one needs to know the expected number of controls in balanced hands with specific HCP value. George Rosenkranz has published such control expectation tables in the December 1974 issue of The Bridge World. These tables are reproduced in The Official Encyclopedia of Bridge under the header "expected number of controls in balanced hands". The table can be summarised by linking HCP to the control count for hands that are 'control-neutral' (neither control-rich nor control-weak):

 HCP Controls 5 1 7-8 2 10 3 12-13 4 15 5 17-18 6 20 7

This table can be used as tie-breaker for estimating the slam-going potential of hands like the above two east hands. Whilst the leftmost east hand counts 16 HCP, in terms of controls (6) it is equivalent to a hand typically 1 or 2 HCP stronger. The rightmost east hand however, whilst also counting 16 HCP, is in terms of controls (4) equivalent to a minimum opening hand (12 to 13 HCP).

If west opens the bidding with 1 spade, both east hands should obviously aim for at least game. Despite the superfit that is apparent following west's opening, solely in terms of HCP count, both east hands (16 HCP) are marginal in terms of slam potential. Yet, on the leftmost layout the control-rich east should explore slam and would be willing to bypass the 4-level in order to investigate slam possibilities, whilst on the rightmost layout the control-weak east should be much more cautious and be prepared to stop in game when further bidding reveals west lacking a control in diamonds.

As alternative to the Blackwood convention, some partnership utilise the so-called Norman four notrump convention to exchange information on the control count. In the Romex system the responses to the dynamic 1NT opening denote the control count of responder such that the opener gets early information on the potential of the combined hands.

In his book "The Modern Losing Trick Count", Ron Klinger advocates the use of the control count to make adjustments to the LTC hand evaluation method (see below).

### Positive/Negative Values

Certain combinations of cards have higher or lower trick taking potential than the simple point count methods would suggest. Exponents (eg Bep Vriend, Netherlands) of this idea suggest that HCP should be deducted from hands where negative combinations occur. Similarly, additional points might be added where positive combinations occur. This method is particularly useful in making difficult decisions on marginal hands, especially for overcalling and in competitive bidding situations. Examples of this idea are:

• Negative points

The following are of less value than the HCP would suggest:

• Honour doubletons KQ, QJ. Qx, Jx unless in partners suit.
• Honour singletons except A.
• Honours in opponents' suit when deciding to support partner's suit
• Honours in side suits when deciding to overcall
• The club suit when opening ... allows opponents to overcall more easily
• The next suit up when overcalling (unless a very good suit) ... gives opponents information but does not cut into their bidding space.
• Honours in suits bid by LHO.
• Positive points
• The following are of more value than the HCP would suggest:

• Honours in long suits.
• Double/triple honours in long suits (better).
• Honour sequences in long suits (best).
• Honours in partner's suit when deciding to bid in support.
• Honours in own suit when deciding to overcall.
• Suits with a preponderance of intermediate cards (8, 9 10) especially if headed by honours.
• The spade suit when opening ... makes overcalling more difficult.
• The suit immediately below that opened by RHO opponent when considering an overcall ... makes LHO's response more difficult.
• Honours in suits bid by RHO

### Defensive/attacking values

Certain combinations of cards are better used in defence whereas others are of most value in attack (i.e. as declarer). There is an element of overlap with the concept of negative/positive points.

• Defensive values

Hands with defensive values (ie hands on which it is better to defend) fall into three categories:

• Honours are in shortish side suits eg Kxx.
• Honours and/or length in opponents suit.
• Few honours in own suit.
• Attacking values
• Hands with attacking values (ie hands which are better suited to play a contract even as a sacrifice) are:

• Own suit contains honours (the more the better).
• Hands without defensive values

## Methods to help with opening bids and overcalls on marginal hands

### Rule of 20

Add together the number of HCP and the number of cards in the two longest suits. If the resultant number is 20 or higher then an opening bid is suggested (the choice of which bid requires further analysis). As an example a hand containing 11 HCP and this shape 5422 would qualify for an opening bid because the resultant number would be 20 (11 + 5 + 4) whereas 11 HCP and this shape 4432 would not (11 + 4 + 4 = 19). This method gives very similar results to Length points as above except for a hand containing 11 HCP and a 5332 shape which gives 19 on the Rule of 20 (insufficient to open) but 12 total points by adding 1 length point to the 11 HCP (sufficient to open). Experience and further analysis are needed to decide which is appropriate.

### Rule of 19

Identical to the Rule of 20 but some expert players believe that 20 is too limiting a barrier and prefer 19.

### Suit Quality Test (SQT)

The SQT evaluates an individual suit as a precursor to deciding whether, and at what level, certain bids should be made. This method is generally considered useful for making an overcall and for making a preemptive opening bid; it works for long suits ie 5 cards at least, as follows: Add together the number of cards in the suit and the number of high (honour) cards in the suit. For this purpose high cards are considered to be A, K, Q, J and 10 but the J and 10 are only to be counted if at least one of the A, K or Q are present. The resultant number determines the level at which the particular bid should be made (Klinger 1998) according to this scale:

• 7 = a one level bid
• 8 = a two level bid
• 9 = a three level bid ... etc

An alternative way to look at this is that the bid should be to the level of the number of tricks equal to the SQT number. This method was originally proposed as a way of enabling overcalls to be made with relatively few HCP but with little risk. It can also be used to determine whether a hand is suitable for a preemptive bid.

## Methods to help when a fit has been discovered

Paraphrasing Crowhurst and Kambites (1992), "Experts often sail into an unbeatable slam with only 25 HCP whereas it would never occur to most players to proceed beyond game". This hand is quoted as an example:
♠ K109864
A43
KQ8
♣ 4
with this bidding:
 North South 1♠ 3♦ 4♦ 4♠ ?
their point is that the bidding indicates at least 6/3 in spades and 5/3 in diamonds. If partner has 3 aces (easily discovered), a grand slam (13 tricks: 6, 1, 5, 1) is likely. This grand slam can easily be bid despite the partnership holding around 29 HCP only (12 in hand above plus 17 in the hand bidding the jump shift (1 - 3). At lower levels it is harder to be as precise but Crowhust & Kambites advise "With a good fit bid aggressively but with a misfit be cautious". Some of the methods that follow are designed to use arithmetic in the evaluation of hands that fit with partner's.

### Losing-Trick Count (LTC)

This is an alternative (to HCP) method to be used in situations where shape and fit are of more significance than HCP in determining the optimum level of a suit contract, once a fit has been found. The "losing-tricks" in a hand are added to the systemically assumed losing tricks in partners hand (7 for an opening bid of 1 of a suit) and the resultant number is deducted from 24; the net figure is the number of tricks a partnership can expect to take when playing in the established suit.

The basic method assumes that an ace will never be a loser, nor will a king in a 2+ card suit, nor a queen in a 3+ card suit, thus

• a void = 0 losing tricks.
• a singleton other than an A = 1 losing trick.
• a doubleton AK = 0, Ax, Kx or KQ = 1, xx = 2 losing tricks.
• a three card suit AKQ = 0, AKx, AQx or KQx = 1 losing trick.
• a three card suit Axx, Kxx or Qxx = 2, xxx = 3 losing tricks.
• suits longer than three cards are judged according to the three highest cards since no suit may have more than 3 losing tricks.

A typical opening hand, eg AKxxx Axxx Qx xx, has 7 losers (1+2+2+2=7). To calculate how high to bid, responder adds the number of losers in their hand to the assumed number in opener's hand (7). The total number of losers arrived at by this sum is subtracted from 24. The answer is deemed to be the total number of tricks available to the partnership and this should be the next bid by responder, Thus following an opening bid of 1:

• partner jumps to game with no more than 7 losers in hand and a fit with partner's heart suit (3 if playing 5-card majors) ... 7 + 7 = 14 subtract from 24 = 10 tricks.
• With 8 losers in hand and a fit, responder bids 3 (8+7=15 which deducted from 24 = 9 tricks).
• With 9 losers and a fit, responder bids 2.
• With only 5 losers and a fit, a slam is likely so responder may bid straight to 6 if preemptive bidding seems appropriate or take a slower forcing approach.

### LTC refined

Thinking that this method tends to overvalue unsupported queens and undervalue supported jacks, this scale can be refined (Crowhurst & Kambites 1992) as follows:

• AJ10 = 1 loser.
• Qxx = 3 losers (or possibly 2.5) unless trumps.
• Subtract a loser if there is a known 9-card trump fit.

### New Losing Trick Count (NLTC)

Extending these thoughts, Klinger believes that the basic method undervalues an ace but overvalues a queen and undervalues short honor combinations such as Qx or a singleton king. Also it places no value on cards jack or lower. Recent insights on these issues have led to the New Losing Trick Count (The Bridge World, 2003). For more precision this count utilises the concept of half-losers and, more importantly, distinguishes between 'ace-losers', 'king-losers' and 'queen-losers':

• a missing Ace = three half losers.
• a missing King = two half losers.
• a missing queen = one half loser.

A typical opening bid is assumed to have 15 or fewer half losers (i.e. half a loser more than in the basic LTC method). NLTC differs from LTC also in the fact that it utilises a value of 25 (instead of 24) in determining the trick taking potential of two partnering hands. Hence, in NLTC the expected number of tricks equates to 25 minus the sum of the losers in the two hands (ie half the sum of the half losers of both hands). So, 15 half-losers opposite 15 half-losers leads to 25-(15+15)/2 = 10 tricks.

The NLTC solves the problem that the basic LTC method undervalues aces and overvalues queens.

### Law of Total Tricks, Total Trumps Principle

For shapely hands where a trump fit has been agreed, the combined length of the trump suit can be more significant than points or HCP in deciding on the level of the final contract. It is of most value in competitive bidding situations where the HCP are divided roughly equally between the partnerships.

• The Law of Total Tricks states that "On every hand of bridge, the total number of tricks available is equal to, or very close to, the total number of cards in each side's longest suit". Total tricks is defined as the sum of the number of tricks available to each side if they could choose trumps.
• The Total Trumps Principle is derived from the Law of Total Tricks and argues that this is more often than not a winning strategy, "Bid to the contract equal to the number of trumps you and your partner hold (and no higher) in a competitive auction".
• In 2002, Anders Wirgren called the accuracy of the "law" into question, saying it works on only 35-40% of deals. However, Larry Cohen remains convinced it is a useful guideline, especially when adjustments are used properly. Mendelson (1998) finds that it is "accurate to within one trick on the vast majority of hands"

## Methods to help with strong hands

Hands with relatively solid long suits have a trick taking potential not easily measured by the basic pointcount methods (eg a hand containing 13 spades will take all 13 tricks if spades are trumps, but will only score 19 on the point count method, 10 HCP + 9 length point). For such hands, playing tricks is deemed more suitable. Responding to such hands is best made considering quick tricks.

### Quick Tricks (Honor Tricks in the Culbertson system)

These are calculated suit by suit as follows:

• 2 quick tricks = AK of the same suit
• 1½ quick tricks = AQ in the same suit
• 1 quick trick = A or KQ in the same suit
• ½ quick tricks = Kx

This method is used when replying to very strong suit opening bids such as the Acol 2 where 1½ quick tricks are needed to make a positive response (Klinger 1994).

### Playing Tricks

For relatively strong hands containing long suits (eg an Acol 2 opener), playing tricks are defined as the number of tricks expected, with no help from partner, given that the longest suit is trumps. Thus for long suits the ace, king and queen are counted together with all cards in excess of 3 in the suit; for short suits only clear winner combinations are counted:

• A = 1, AK = 2, AKQ = 3
• KQ = 1, KQJ = 2

An Acol strong 2 of a suit opening bid is made on 8 playing tricks (Landy 1998)

### Zar Points

This is an advanced, statistically derived method for evaluating Contract Bridge hands developed by Zar Petkov for use by more experienced players. It attempts to account for many of the factors outlined above in a numerical way. Details of the method and an allied bidding system can be found in the main article: Zar Points.

### Visualisation

Key differentiator between the bidding effectiveness of experts versus laymen is the use of hand visualisation during all stages of bidding.

In his book The Secrets of Winning Bridge, Jeff Rubens advises to focus on just a few hands that partner might be holding, and more particularly on perfect minimum hands compatible with the bidding. This means that in order to reach an informed decision in, for example, deciding whether a hand is worth an invitation to game or slam, a player should 'visualise' the most balanced distribution with the minimum HCP partner might have with the high cards selected such that these fit precisely with your own hand. He advises that "your hand is worth an invitation to game (or slam) if this perfect minimum holding for partner will make it a laydown".

Rubens gives the following example: QJ2 A32 KQJ54 A3

Partner opens 1. A minimum hand compatible with the bidding would have no more than 12 HCP, and be relatively balanced (i.e. 5332). The hand would be perfect if partner's points were solely located in spades and diamond. So a perfect minimum would be: AK543 654 A2 542

Such a perfect minimum would give a solid slam in spades, relying on hcp would not indicate a slam possibility. This is the advantage of the 'visualisation' method.