Hand evaluation

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This article concerns Contract Bridge and uses terminology associated with the game. See Contract bridge glossary for an explanation of unfamiliar words or phrases.

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.

Contents

[edit] The Point-Count System

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

[edit] 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 ie 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 in notrump bidding, it is not sufficient, of itself, for deciding the level of a suit contact.

[edit] 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.

[edit] 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).

[edit] 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.

[edit] Rule of 20 and Rule of 19

A subtly different method of evaluating opening hands is to combine HCP and shape as follows:

[edit] 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 than 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.

[edit] Rule of 19

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

[edit] 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 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.

[edit] The Value of a Fit

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: 6S, 1H, 5D, 1C) 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 (1S - 3D). 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.

[edit] 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. 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 total is deducted from a systemically agreed base number (24). The net figure is the level of the next bid or final contract. Losing tricks are defined as follows:

[edit] Basic method

Valuing simplicity, this 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 can have more than 3 losing tricks

[edit] Example

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 his 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 maximum number of losers in the two hands). 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 1H:

  • 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 3H (8+7=15 which deducted from 24 = 9 tricks).
  • With 9 losers and a fit, responder bids 2H.
  • With only 5 losers and a fit, a slam is likely so responder may bid straight to 6H if preemptive bidding seems appropriate or take a slower forcing approach.

[edit] Refining the scale

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.

[edit] 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 (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). The trick taking potential of two partnering hands equals 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.

This solves the fundamental problem inherent to LTC that a Grand-slam layout like KQxx KQx KQx KQx opposite Axxx Axx Axx Axx is valued as 4 + 8 = 12 losers or worth 24 - 12 = 12 tricks. In NLTC the combined hands also count 12 losers (24 half-losers), but that total in NLTC corresponds to 25 - 12 = 13 tricks.

Also on hands on which LTC overstates the number of tricks, for instance: AQxxx KQ KQJx xx opposite KJxxx xx xx KQJx (5 + 7 = 12 losers, i.e. 24 - 12 = 12 predicted tricks), NLTC does much better as it counts 13/2 + 17/2 = 15 losers, corresponding to the right prediction of 25 - 15 = 10 tricks.

[edit] Second round bids

Whichever method is being used, the bidding need not stop after the opening bid and the rebid. Assuming opener bids 1H and partner responds 2H; opener will know from this bid that partner has 9 losers (using basic LTC), if opener has 5 losers rather than the systemically assumed 7, then the calculation changes to (5 + 9 = 12 deducted from 24 = 10) and game becomes apparent!

[edit] Important note

All LTC methods are only valid if an 8-card trump fit is evident and, even then, care is required to avoid counting double values in the same suite eg KQxx (1 loser) opposite a singleton x (1 loser).

[edit] 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"

[edit] Playing Tricks and Quick Tricks

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.

[edit] Quick Tricks (Honor Tricks in the Culbertson system)

These are calculated suit by suit as follows:

  • 2.0 quick tricks = AK of the same suit
  • 1.5 quick tricks = AQ in the same suit
  • 1.0 quick trick = A or KQ in the same suit
  • 0.5 quick tricks = Kx

This method is used when replying to very strong suit opening bids such as the Acol 2C where 1.5 quick tricks are needed to make a positive response (Klinger 1994).

[edit] 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)

[edit] 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:

[edit] 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.

[edit] 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

[edit] 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.

[edit] 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.

[edit] 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

[edit] 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.

[edit] References

[edit] Further reading

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