Hand evaluation

# Hand evaluation

Discussion

Encyclopedia
In contract bridge
Contract bridge
Contract bridge, usually known simply as bridge, is a trick-taking card game using a standard deck of 52 playing cards played by four players in two competing partnerships with partners sitting opposite each other around a small table...

, various bidding system
Bidding system
A bidding system in contract bridge is the set of agreements and understandings assigned to calls and sequences of calls used by a partnership, and includes a full description of the meaning of each treatment and convention...

s have been devised to enable partners to describe their hands to each other so that they may reach the optimum contract. Key to this process is that players evaluate and re-evaluate the trick-taking potential of their hands as the auction proceeds and additional information about partner's hand (and the opponent's hands) becomes available. Several methods have been devised to evaluate the various features of hands, including their strength, shape or distribution, controls, fit with partner and the quality of a suit or of the whole hand.

The methods range from basic to complex. Regardless of which are used, all require the partners to have the same understandings and agreements about their application and meaning in their bidding system.

## Basic point-count system

Most bidding systems use a basic point-count system for hand evaluation using a combination of high card points and distributional points, as follows.

### High card points

Called the Milton Work Point Count in the Twenties when first publicized and then the Goren Point Count when popularized in the late Forties. and now known simply as the high card point (HCP) count, this basic evaluation method assigns values to the top four honour cards as follows:
• ace = 4 HCP
• king = 3 HCP
• queen = 2 HCP
• jack = 1 HCP

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. The method has the dual benefits of simplicity and practicality, especially in notrump contracts. Most bidding systems are based upon the premise that a better than average hand is required to open the bidding; 12 HCP is generally considered the minimum for most opening bids.

#### Limitations

The combined HCP count between two hands is generally considered to be a good indication, all else being equal, of the number of tricks likely to be made by the partnership. The rule of thumb
Rule of thumb
A rule of thumb is a principle with broad application that is not intended to be strictly accurate or reliable for every situation. It is an easily learned and easily applied procedure for approximately calculating or recalling some value, or for making some determination...

and for games and slams in notrump is that:
• 25 HCP are necessary for game, i.e. 3 NT
• 33 HCP are necessary for a small slam, i.e. 6 NT
• 37 HCP are necessary for a grand slam, i.e. 7 NT

A simple 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 at least three aces.

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. Jeff Rubens
Jeff Rubens
Jeff Rubens is a bridge player and writer; he is the editor of the magazine The Bridge World and the author of several bridge books, including Secrets of Winning Bridge....

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 the 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. In this case, the difference in trick-taking potential is due to duplication in the high card values: in the rightmost layout the combined 20 HCP in spades and diamonds results in only five tricks. Because such duplication can often not be detected during bidding, the high card point method of hand evaluation, when used alone, provides only a preliminary estimate of the trick-taking potential of the combined hands and must be supplemented by other means for improved accuracy, particularly for unbalanced hands.

Accordingly, expert players utilise the high card point count as a starting point in the evaluation of their hands, and make adjustments based on:
• refinements to the HCP valuation for certain holdings,
• the use of additional point values for hand shape or distribution (known as distribution points), and
• bidding techniques to determine the specifics of any control cards held by partner.

Collectively, these more effectively evaluate the combined holdings of a partnership.

#### Refinements

For aces and tens

The 4-3-2-1 high card point evaluation has been found to statistically undervalue aces and tens and alternatives have been devised to increase a hand's HCP value.

To adjust for aces, Goren recommended deducting one HCP for an aceless hand and adding one for holding four aces. Some adjust for tens by adding 1/2 HCP for each. Alternatively, some treat aces and tens as a group and add one HCP if the hand contains three or more aces and tens; Richard Pavlicek
Richard Pavlicek
Richard Pavlicek is an American bridge player, author and columnist.-Career:Pavlicek began to play bridge in 1964 at the age of 18 while stationed in Stuttgart, West Germany, with the U.S. Army. Upon returning to Florida in 1966 he started to play in bridge tournaments in his spare time. Since...

advocates adding one HCP if holding four or more aces and tens.

For unguarded honours
Goren and others recommend deducting one HCP for a singleton king, queen, or jack.

### Distributional points

In order to improve the accuracy of the bidding process, the high card point count is supplemented by the evaluation of unbalanced or shapely hands using additional simple arithmetic methods. Two approaches are common - evaluation of suit length and evaluation of suit shortness.

#### Suit length 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:
• 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 honour 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.

#### Suit shortness points

Once a trump suit has been agreed, or at least a partial fit has been uncovered, it is argued by many, , that ruffing
Ruff (cards)
In trick-taking games, to ruff means to play a trump card to a trick . According to the rules of most games, a player must have no cards left in the suit led in order to ruff. Since the other players are constrained to follow suit if they can, even a low trump can win a trick...

potential as represented by short suits becomes more significant than long suits. Accordingly, in a method devised by William Anderson of Toronto and adapted and developed by Charles Goren, distribution points are added for shortage rather than length.

When the supporting hand holds three trumps, shortness is valued, as follows:
• void = 3 points
• singleton = 2 points
• doubleton = 1 point

When the supporting hand holds four or more trumps, thereby having more spare trumps for ruffing, shortness is valued as follows:
• void = 5 points
• singleton = 3 points
• doubleton = 1 point

Shortage points (also known as support points or dummy points) are added to HCP to give total points.

### Summary

When intending to make a bid in a suit and there is no agreed upon trump suit, add high card points and length points to get the total point value of one's hand. With an agreed trump suit, add high card points and shortness points instead. When making a bid in notrump with intent to play, value high card points only.

## Supplementary methods

The basic point-count system does not solve all evaluation problems and in certain circumstances is supplemented by refinements to the HCP count and/or by additional methods.

### Control count

The control count is a supplementary method that is mainly used in combination with HCP count to determine the trick-taking potential of fitting hands, in particular to investigate slam potential. The use of control count addresses the fact that for suit contracts, aces and kings tend to be undervalued in the standard 4-3-2-1 HCP scale; aces and kings allow declarer better control over the hands and can prevent the opponents from retaining or gaining the lead.

The control count is the sum of the controls where aces are valued as two controls, kings as one control and queens and jacks as zero. 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 slam potential depending on the control count.
In the above examples, both West hands are the same, and both East hands have the same shape and HCP (16). Yet, the layout on the left represents a solid slam (12 tricks) in spades, whilst the layout on the right will fail to produce 12 tricks. The difference between the East hands becomes apparent when conducting a control count: in the left layout East has two aces and two kings for a total of six controls, whilst in the right layout has one ace and two kings for a total of four controls.
 HCP ExpectedControls 5 1 7-8 2 10 3 12-13 4 15 5 17-18 6 20 7
The interpretation of the significance of the control count is based upon a publication by George Rosenkranz
George Rosenkranz
George Rosenkranz is a Mexican scientist in steroid research and a professional bridge player. He was born in Hungary, educated in Switzerland and lived in Mexico for 66 years...

in the December 1974 issue of The Bridge World
The Bridge World
The Bridge World , the oldest continuously published magazine about contract bridge, was founded in 1929 by Ely Culbertson. It has since been regarded as the game's principal journal, publicizing technical advances in bidding and the play of the cards, discussions of ethical issues, bridge politics...

. Rosenkranz defined "the expected number of controls in balanced hands" at specific HCP counts as 'control-neutral' in a table similar to the consolidation shown on the left; having more controls is deemed 'control-rich' and having less is 'control-weak'.

The 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 1-2 HCP stronger, whereas the rightmost East hand, also counting 16 HCP, is in terms of controls (4) more equivalent to 12-13 HCP.

If West opens the bidding with 1, both East hands should aim for at least game (4), the partnership having the minimum 26 total points typically required for a game contract in the majors. Despite the spade suit fit, both East hands have marginal slam potential based on their 16 HCP count alone. On the leftmost layout the control-rich East (an upgraded 17-18 HCP) should explore slam and be willing to bypass 4 in doing so, whilst on the rightmost layout the control-weak East (a downgraded 12-13 HCP) should be more cautious and be prepared to stop in 4 should further bidding reveal West lacking a control in diamonds.

Having determined the degree of interest in exploring slam possibilities, the methods and conventions to determine which controls (aces, kings and even queens) are held by the partnership include: the Blackwood convention
Blackwood convention
In the partnership card game contract bridge, the Blackwood convention is a popular bidding convention that was developed by Easley Blackwood. It is used to explore the partnership's possession of aces, kings and in some variants, the queen of trumps, to judge more precisely whether slam is likely...

, the Norman four notrump
Norman four notrump
Norman four notrump is a slam bidding convention in the partnership card game contract bridge designed to help the partnership choose among the five-, six-, and seven-levels for the final contract...

convention, the Roman Key Card Blackwood convention and cuebids.

In his book "The Modern Losing Trick Count", Ron Klinger
Ron Klinger
Ron Klinger is a leading bridge author, writing more than 50 books on the game. He is an Australian Grand Master and a World Bridge Federation International Master.-Biography:...

advocates the use of the control count to make adjustments to the LTC hand evaluation method (see below).

### Negative/positive features

Certain combinations of cards have higher or lower trick taking potential than the simple point count methods would suggest. Exponents (e.g. Bep Vriend
Bep Vriend
Brechiena Vriend is a Dutch contract bridge player. As of April 2011, she ranks number 8th among Women World Grand Masters....

, 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. In lieu of arithmetic addition or subtraction of HCP or distributional points, 'plus' or' minus' valuations may be applied to influence the decision.

Negative features worth less than the HCP suggest:
• Honour doubletons K-Q, Q-J. Q-x, J-x unless in partners suit. Although Samuel Stayman
Samuel Stayman
Samuel M. Stayman was an American bridge player, author and administrator. A graduate of the Amos Tuck School of Business Administration at Dartmouth College, he was also a successful textile executive and portfolio investment manager.He was the eponym of the Stayman convention...

recommended deducting one HCP for K-Q, K-J, Q-J,Q-x,J-x Q-x-x, J-x-x holdoings, this is now considered extreme.
• Honour singletons; some exempt the singleton ace but others consider it inflexible in play.
• Honour combinations not accompanied by a small card.
• Honours in opponents' suit when deciding to support partner's suit.
• Honours in side suits when deciding to overcall.
• The club suit when opening because it allows opponents to overcall more easily.
• The next suit above RHO's suit when overcalling (unless a very good suit) which gives opponents information but does not cut into their bidding space.
• Honours in suits shown by LHO.

Positive points features worth more than the HCP suggest:
• Honours in long suits.
• Two or three honours in long suits (better).
• Honour sequences in long suits (best).
• Honours in partner's suit when deciding to support it.
• Honours in own suit when deciding to overcall.
• Two or three intermediate cards in a suit (8, 9 10) especially if headed by honours.
• The spade suit when opening ... makes overcalling more difficult.
• The next suit below RHO's suit when overcalling reduces the opponents' bidding space.
• Honours in suits shown by RHO.

### Defensive/attacking values

Certain combinations of cards are better defence and others are more valuable in attack (i.e. as declarer). There is some overlap with the concept of negative and positive points.

Defensive values that suggest a hand should defend:
• Honours in shortish side suits, e.g. Kxx.
• Honours and/or length in opponents suit.
• Lack of honours in own suit.

Attacking values that suggest a hand should play a contract as declarer or dummy:
• Honours in own suit (the more the better).
• Lack of defensive values.

### Rule of 20

Add together the number of HCP in the hand, and the number of cards in the two longest suits. If the resultant number is 20 or higher and most of the high cards are in the long suits, then an opening bid is suggested (the choice of which bid requires further analysis). As an example, a hand containing 11 HCP and 5-4-2-2 shape would qualify for an opening bid because the resultant number would be 20 (11 + 5 + 4) whereas 11 HCP and 4-4-3-2 shape 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 5-3-3-2 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 i.e. 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 1994) 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".
 North South 1 3 4 4 ?
For example, holding with the auction shown on the left, they point out 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)

Once a trump fit has been found, this alternative (to HCP) method is used in situations where shape and fit are of more significance than HCP in determining the optimum level of a suit contract. 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 win when playing in the agreed trump 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; no suit may have more than 3 losing tricks.

A typical opening hand, e.g. 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 is subtracted from 24. The answer is 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 the method tended to overvalue unsupported queens and undervalue supported jacks, Eric Crowhurst and Andrew Kambites refined the scale as follows:
• AQ doubleton = ½ loser according to Ron Klinger
Ron Klinger
Ron Klinger is a leading bridge author, writing more than 50 books on the game. He is an Australian Grand Master and a World Bridge Federation International Master.-Biography:...

.
• Kx doubleton = 1½ losers according to others.
• 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
The Bridge World
The Bridge World , the oldest continuously published magazine about contract bridge, was founded in 1929 by Ely Culbertson. It has since been regarded as the game's principal journal, publicizing technical advances in bidding and the play of the cards, discussions of ethical issues, bridge politics...

, 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 (i.e. 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 (e.g. 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
Acol
Acol is the bridge bidding system that, according to The Official Encyclopedia of Bridge, is "standard in British tournament play and widely used in other parts of the world". It is named after the Acol Bridge Club, previously located on Acol Road in London NW6, where the system started to evolve...

2 where 1½ quick tricks are needed to make a positive response (Klinger 1994).

### Playing Tricks

For relatively strong hands containing long suits (e.g. 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
Acol
Acol is the bridge bidding system that, according to The Official Encyclopedia of Bridge, is "standard in British tournament play and widely used in other parts of the world". It is named after the Acol Bridge Club, previously located on Acol Road in London NW6, where the system started to evolve...

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

### Zar Points

This statistically-derived method for evaluating Contract Bridge hands was developed by Zar Petkov. It attempts to account for many of the factors outlined above in a numerical way.

### 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
Jeff Rubens
Jeff Rubens is a bridge player and writer; he is the editor of the magazine The Bridge World and the author of several bridge books, including Secrets of Winning Bridge....

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.