Hand evaluation

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, the 4-3-2-1 count for honours was not established by computer analysis but was derived from the game Auction Pitch. Although 'Robertson's Rule' for bidding 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. "
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, and now known simply as the high-card point 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:

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:
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.
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 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, 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 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.
;For unguarded honours
Goren and others recommend deducting one HCP for a singleton king, queen, or jack.
;Alternative scale
Marty Bergen claims 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 would be counted as 10 HCP. Since the hard and soft values are equal, there is no adjustment. On the other hand, to take an extreme example, a hand with four aces and four tens 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 Bridge by David Burnstine, Michael T. Gottlieb, Oswald Jacoby and Howard Schenken. The Four Aces' book 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 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 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 Anderson of Toronto and popularized 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 are added to HCP to give total points.

Combination Count

This method 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.