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.
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
First published in 1915 by Bryant McCampbell in Auction Tactics (page 26), the 4-3-2-1 count for honours was not established by computer analysis (as is sometimes rumoured) but was derived from the game Auction Pitch. Although 'Robertson's Rule' for bidding (the 7-5-3 count) had been in use for more than a dozen years, McCampbell sought a more "simple scale of relative values. The Pitch Scale is the easiest to remember. (Those ... who have played Auction Pitch will have no difficulty in recognizing and remembering these values.)"
Called the Milton Work Point Count when popularized by him in the early Thirties and then the Goren Point Count when re-popularized by Work's disciple Charles Goren in the Fifties,Francis et al, 2001, page 355: POINT-COUNT. and now known simply as the high-card point (HCP) count, this basic evaluation method assigns numeric 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 balanced 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 for games and slams in notrump is as follows:Root, 1998Klinger, 1994 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 gives the following example:Rubens, 1971, pages 7–8.
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 left layout produces 13 tricks in notrump, whilst the right 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 bottom 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 use HCP 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 recommendedGoren, 1954, page 11. deducting one HCP for a hand without any aces 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 advocates adding one HCP if holding four or more aces and tens.Richard Pavlicek website retrieved August 11, 2011.
For unguarded honours Goren and othersDowney and Pomer, 2005, page 27. recommend deducting one HCP for a singleton king, queen, or jack.
Alternative scale Marty Bergen claimsBergen, 2002, page 8. Bergen does not cite the source of the computer analysis. that with the help of computers, bridge theorists have devised a more accurate valuation of the honors as follows:
ace = 4.5 HCP king = 3 HCP queen = 1.5 HCP jack = 0.75 HCP ten = 0.25
Note that this scale keeps the 40 high card point system intact. The scale may seem cumbersome, but if one considers the ace and ten honors "hard" and the queen and jack honors "soft" it is much easier to accurately count high card points by using the familiar 4-3-2-1 system and then adjusting. One can see that the ace and queen have something in common in that they are both "off" by a half point. The jack and ten are also both "off" by a quarter point. So for example, a hand with one of each honor (A, K, Q, J, 10) would be counted as 10 HCP. Since the hard and soft values are equal (the ace and queen cancel out, and the jack and ten cancel out), there is no adjustment. On the other hand, to take an extreme example, a hand with four aces and four tens (no kings, queens, or jacks) would be counted at 16 HCP at first, but since it holds eight hard values and no soft values, it is adjusted to 19 HCP.
Bergen's “computer” scale appears to be identical to the “high card value of the Four Aces System” found on the front inside cover and on page 5 of the 1935 book, The Four Aces System of Contract BridgeJacoby, 1935, page 5. by (alphabetically) David Burnstine, Michael T. Gottlieb, Oswald Jacoby and Howard Schenken. The Four Aces' book (Jacoby may have written most or all of it) gives the simpler 3-2-1- version of the progression. Dividing Bergen's numbers by 1.5 produces exactly the same numbers published by the Four Aces seven decades earlier: * Bergen ace = 4.5 ÷ 1.5 = 3 Four Aces Count * Bergen king = 3.0 ÷ 1.5 = 2 Four Aces Count * Bergen queen = 1.5 ÷ 1.5 = 1 Four Aces Count * Bergen jack = .75 ÷ 1.5 = ½ Four Aces Count — Q.E.D.
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 numbersEnglish Bridge Union, 1998. 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 potential as represented by short suits becomes more significant than long suits. Accordingly, in a method devised by William AndersonCanadian Bridge Federation, Bridge Canada, April 2012, page 18 of Toronto and popularized by Charles Goren,Francis et al, 2001, page 120: Distributional Count. distribution points are added for shortage rather than length.
When the supporting hand holds three trumps, shortness is valuedDowney and Pomer, 2005, page 35. 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.
Combination Count This methodFrancis et al, 1994, page 111: DISTRIBUTIONAL COUNTS. uses both lengths and shortages in all situations. The hand scores two shortage points for a void and one for a singleton, and this total is added to the usual length count: one point is added for each card in a suit beyond four.
An alternative approach is to create a distributional point count of a hand to be added to HCP simply by adding the combined length of the two longest suits, subtracting the length of the shortest suit, and subtracting a further five. On this basis 4333 hands score -1 and all other shapes score a positive distributional count.
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. 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.
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 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.