Hand evaluation

Bidding systems devised for contract bridge

In contract bridge, various bidding systems have been devised to enable partners to describe their hands 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. Hand evaluation methods assess various features of a hand, including: its high card strength, shape or suit , , fit with partner, quality of suits and quality of the whole hand. The methods range from basic to complex, requiring partners to have the same understandings and agreements about their application in their bidding 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.

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.

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. When intending to raise an agreed trump suit, add high card points and shortness points. When making a bid in notrump with intent to play, value high card points only.

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

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 above represents a solid slam (12 tricks) in spades, whilst the layout below will fail to produce 12 tricks. The difference between the East hands becomes apparent when conducting a control count: in the top layout East has two aces and two kings for a total of six controls, whilst in the bottom layout has one ace and two kings for a total of four controls. HCPExpectedControls517–8210312–13415517–186207 The interpretation of the significance of the control count is based upon a publication by George Rosenkranz in the December 1974 issue of The Bridge World. 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 top East hand counts 16 HCP, in terms of controls (6) it is equivalent to a hand typically 1–2 HCP stronger, whereas the bottom 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 top 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 bottom 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, the Norman four notrump convention, the Roman Key Card Blackwood convention and cuebids. 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).

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

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". NorthSouth1344? 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.

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. Bridge: TNT and Competitive Bidding (1981) was probably the first major book on this topic. In the introduction the authors acknowledge Jean René Vernes as the first writer to delve into the TNT (Total Number of Tricks) Theory. This book and these authors are little known in North America. What a shame! They touch several aspects of TNT that are rarely mentioned by others. Chapter Four on Total Distribution is worth the price (if you can locate a used copy of this out of print book). Page 19 carries a key table that may not be printed elsewhere. 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 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"

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.

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.