Review and Revised Opening Hand Valuation.

by: Stig Holmquist
25 August, 2002 - revised January 2003

Building a house requires a firm foundation and so does developing a good bidding system or it might crumble like a house of cards. The foundation of all bidding must be hand valuation, which for starters involves evaluating honor cards and distribution. Some players might also count quick tricks, losing tricks, controls and honor combinations but such refined valuations will not be dealt with here.

A variety of honor card valuation methods have been used during the past century, as can be verified by consulting the ACBL Encyclopedia. By far the most common and popular honor card valuation (HCP) for the past half-century has been the Work-Goren scale of 4-3-2-1. It is simple but somewhat inaccurate, because the primary honors, A and K, are undervalued, while the secondary ones, Q and J, are overvalued and no numerical value is given to the ten, T, even though it can be a real asset at times. As a compensation or adjustment Goren advocated adding one pt for all Aís but deducting one pt for no A . In reality he implied adding ¼ pt for each A and deducting ¼ pt for each Q, but probably deemed that impractical.

Thus A+K=7 accounts for 70% of the total in a suit, clearly too low. A couple of old systems value them at 75-77%. Specifically, Bamberger recommended 7-5-3-1 and the 4Aís used 3-2-1-0.5. Each of these scales can be recalculated to a 10 scale by dividing each point value by one tenth of the sum of the set.

There is a 20 years old very complex hand valuation method known as 4 C's (aka K&R) because it was designed by the great E. Kaplan with assistance from Jeff Rubens, the editors of Bridge World and published in the October 1982 issue. The 4Cís stood for ďCaution, Complex Computer CountĒ according to Kaplan, who warned ordinary mortals against using it at the table but rather for post mortem analysis. It is very difficult to find and so hard to apply that computerized implementations on the internet often arrive at somewhat different values. Worse yet, the method often yields unrealistic and at times absurd valuations. In short, donít waste time with it.

Considerable discussion has been conducted on the internet at during the past two years especially by A.Martelli, who has revived the old 4Aís valuation under the acronym BUMRAP.

Specifically, he advocates the scale 4.5-3.0-1.5-0.75-0.25 for A-K-Q-J-T, which can be derived by multiplication of the original scale by 1.5 adding 0.25 for the T, thus maintaining a "biblical" total of 40. Players who are unwilling to count ¼ pt may just add 0.5 for each A and deduct 0.5 for each Q in the regular system.

Secondary honor cards should not be fully valued unless they are guarded by one or two higher honor c8ards or are in a long suit. Unguarded honors must be reduced in value, either by deducting one pt or by halving the value for each missing spot card.

It may be interesting to recall that E.Kaplan at one time suggested that the true value of honor cards is :

4.3-3.1-1.7-0.9 but he deemed this scale impractical for most players. Those with a keen sense for numbers can convert the decimal values to 1/8 pt.

To sum it up, all standard 12 HCP hands are far from equal when comparing 3Aís vs 4Kís vs 4(Q+J)ís.

By this new scale 3Aís=13.5, 4Kís=12 but 4(Q+J)ís=9 if guarded. Using this scale eliminates the counting of quick tricks, which seems to have been abandoned in most recent books for beginners. Also, responder never counts quick tricks.

Next letís look at distributional valuation, of which there has been many systems in the past. Goren made popular the 3-2-1 scale for short suits, but he warned against regarding these as ruffing values for opener.

He specifically stressed that they were hand pattern values. He evidently based his count on the perfectly balanced hand shape 4-3-3-3 (10.5%) and gave one pt for each change of one card. Many experts have replaced his method by F.Karpinís recommendation of counting one point for each card over four in any suit regardless of suit strength. He based his count on the most common hand pattern of 4-4-3-2 (21.6%).

Both authors suggested deducting one point for the 4-3-3-3 type hand when bidding a suit. A comparison of the two methods shows some interesting differences. A tabulation of the 25 most common hand patterns accounts for 99.90% of all 39 possible patterns. It will not include the rare 7-6-0-0 nor the 8-5-0-0 types but it will cover the 6-6-1-0 kind as well as the three most common 8-card holdings :8-2-2-1, 8-3-1-1 and the

8-3-2-0 types. A comparison of the point value for each pattern based on the short and the long suit count shows that in 10 cases they are equal while in 13 cases the short method yields one more point and for two cases ,4-4-4-1 and 5-4-4-0 , the short method gives two more pts. Thus the long suit method results in a more conservative evaluation 60% of the time. Is this good or bad or of no import bearing in mind that as a rule of thumb one counts 3pt=1 trick on average? Most players are likely to decide it is of very little account and only a bridge computer programmer is likely to care.

The rule of thumb that trick taking potential equals 1/3 of the point count is most accurate for balanced hands and NT bidding, but it fails badly for very distributional hands ,especially those with very long suits such as 13-0-0-0 , which would count only as 10+9=19 pts, implying it can take only 6 tricks. So why not devise a suit length valuation method that will arrive at more realistic values?

This can be done by adopting a progressive point count for length in a bid suit , since the more cards a suit has the more valuable they become. Specifically, one would count the fifth card =1, the 6th=2, the 7th=3, and 3 for each additional card but deduct 1 for the flat 4-3-3-3 type hand, when bidding a suit. Thus the cumulative value of a long suit will be: 1-3-6-9-12-etc. Since 9-card or longer suits occur only once per 100 sessions, one should consider valuation of them by the LTC method.

The value of a long suit must also depend to some degree on its honor cards but not on their HCP count. Rather, the number of the three top honor cards (AKQ)in the suit should be counted .A slight modification might be considered in the case of just one honor card by applying a "reverse " adjusted LTC count, i.e. A=1.5, K=1 and Q=0.5. Also, count QJT=K and JT=Q. A computer program might consider a more detailed LTC scale. Now a 13-0-0-0 type hand would count as 10+24+3=37 pts.

The most common unbalanced or distributional hand pattern is the 5-4-3-1 type, which occurs in one out of eight deals on average per player. It rates as 2 DP by the short suit count but only as 1 DP by the long suit count method.

Letís compare two such hands with the same honor cards and 11 HCP like: Akxxx-Axxx-xxx-x vs A-AKx-xxxx-xxxxx and ask if they are of equal value. Both might rate an opening bid in the 5-card suit if it is in spades, especially if one follows Bergenís rule of 20. Both hands potentially have 7 losers by the LTC method. But surely, the strong 5-card suit makes a better hand . Based on the above proposed valuation for honor cards and distribution count, the first hand would count as 12+1+2=15 pts, while the second counts as only 12+1=13pts. For comparison it might be mentioned that Edgar.Kaplan would have valued the first as 14.1 pts and the second as only 11.5 pts according to an internet algorithm for the K&R method.

ACBL does not stipulate how to count HCP or any other form of hand valuation and thus each player is free to adjust the standard method without changing the convention card.

There remains to decide if shape or hand pattern should be evaluated by counting both length and shortness or neither for opening bids. Goren counted only shortness,while today most authorities count only length. But there are a few notable exceptions. Alvin.Roth counts 1 pt for a good 6-card suit and 2pts for a good 7-card suit. Alan Truscott counts "assets" for both length and shortness by adding 1 pt for any suit longer than 4 cards and 1 pt for a singleton and 2 pts for a void. Eddie Kantar seems to count no distributional points as opener - neither do any of the strong 1C opening systems. In England it is common to use a combination count based on Karpin and Truscott. Until a computer simulation with statistical treatment has been performed, to establish which method is best, each partnership must agree on a method best suited for them. It may well turn out that no method is best for all situations. E.g. hands with two long suits (5-5 to 7-6) may need special treatment. Also, a good case can be made for counting one point for a void, so as to differentiate a hand with a long suit and a void from one without a void, such as 5-4-4-0 vs 5-4-3-1 or 5-4-2-2 , 5-5-3-0 vs 5-5-2-1 and 6-4-3-0 vs 6-4-2-1. A balanced opening hand would count only HCPís.

In summary, I propose to change the HCP count based on the scale of: 4.5-3.0-1.5-0.75-0.25 and to count length points as:5th card=1, 6th=2, 7th=3 and 3 for each additional card but supplemented by the number of high honor cards in the suit.

This article has been limited to the opening bid valuation. Responder and revaluation are a separate topic. It is intended to help ordinary  players  but not experts , who have superior judgment . The above hand valuation might serve as an inspiration or challenge to experts to devise a better biding system. Other hand valuation systems can be found on the internet.

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Stig Holmquist is a retired research chemist whose specialty is ceramic materials. He currently still works at University of Connecticut. He dabbles considerably in bridge theory, having some of his ideas written (and written about) in both Bridge World and ACBL Bulletin. 

(for those of you on BBO, he's no relation of Stig from Norway who is a host there)

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