Half Points

In Short

A queen, jack, or ten is more valuable when it is protected by a higher honor. To make a long story short (and leave out a few minor modifications), I suggest subtracting a half-point for every unprotected queen and jack, and adding a half-point for any protected 10.

Introduction

Everyone agrees that the Work point count (ace=4, king=3, queen=2, jack=1) is not perfect. Unfortunately, any improvements require fractions. My system requires only halves, which are very manageable.

A Quack is a Queen or Jack.

-1/2 for Unsupported Quacks

Compare

Kxx  Qxx     to     KQx  xxx

The first combination has little chance for a second trick. The second comination is a finesse for the second trick. So the second is much better. But both count as 5 HCP in the 4-3-2-1 point count system.

Of course, counting HCP is probabilistic, not perfect. But this is a problem with an easy solution. Quacks simply are not as valuable when they are not protected by a higher honor.

Compare:

AJx  Qxx     or     AQx  Jxx     or     Axx  QJx     to     AQJ  xxx

The first three all have an unsupported quack and have little chance for a third trick. The final combination is a finesse for the third trick.

Sometimes the problem is not quite so bad. Compare

Axx  Qxx     to     AQx  xxx

In both combinations, there is one sure trick and a finesse for the second. But when the queen is with the ace, you might get two tricks without losing a trick. In the first combination, the opponents can always get the second trick. Sometimes this is critical.

Qxx  Jxx     vs.     QJx  xxx

The first combination is 50% for a trick if you have to attack the suit. The second is 75%.

For the sake of honesty in advertising,

AKx  Qxx     vs.     AKQ  xxx

The unsupported queen is fine if partner has AK, and the supported jack is fine if partner has AKQ and someone has a four-card suit.

Axx  Jxx     vs.     AJx  xxx

The unsupported jack has no chance for a second trick, but the supported jack has a 25% chance.

AKx  Jxx     vs.     AKJ  xxx     or     AJx  Kxx     or     Axx  KJx

The supported jack is 50% for another trick. The unsupported jack is just a chance for a third trick.

To reflect the fact that an unsupported quack is usually worth less then a supported quack, I suggest subtracting 1/2 point from your point count for every unsupported quack. For example, Qxx is 1 1/2 points, and QJx is 2 1/2 points because the queen is unsupported but the Jack is supported by the Queen.

Also, it should be noted that unsupported honors are not quite as bad when the opponents are leading the suit. You would rather have KQx opposite xxx if the opponents are leading the suit, but if you have Kxx opposite Qxx, the opponents have to twice lead from the hand without the ace to get all of their tricks. At the extreme, if the opponents are going to lead the suit, Qxx opposite Jxx is a sure trick, while it is possible to not win a trick with QJx opposite xxx.

+1/2 for Supported Tens

Tens are often important, but they are given no credit in the traditional point count. An unsupported Ten is not much use, but a supported 10 is. For example,

AKx  10xx     vs.     AK10  xxx

The first combination is just two tricks, but in the second, the 10 is 25% for another trick.

KJx  xxx     or     KJx  10xx     vs.     KJ10  xxx

Here, even the unsupported 10 is worth a trick in the 25% of the AQ being off-side. But the third combination is by far the best, with a 50% chance for two tricks whenever the queen is onside.

The presence of a 10 usually balances the problem of an unsupported quack.

AQx  Jxx     vs.     AQJ  xxx     or     AQ10  Jxx     or     AQx  J10x

The last three combinations are all 50% for making three tricks.

Kxx  Qxx     vs.     KQx  xxx     or     K10x  Qxx

The last two combinations are now both 50% for a second trick.

Qxx  Jxx     vs.     QJx  xxx     vs.     Q10x  Jxx

Here the 10 is more valuable than protecting the queen. The first combination is only 75% for a trick, the second combination guarantees a trick.

Sometimes a supported 10 is not so valuable.

Axx  Qxx     vs.     AQx  xxx     vs.     Axx  Q10x.

The first combination, is 50% for a second trick. The second combination has a supported 10, but it is not much better. It allows you to guess whether to finesse for the king or the jack, so it's better than the first combination. But without any knowledge you would still have just one 50% finesse.

AQx  xxx     vs.     A10x  Qxx

If you need two tricks and can't afford to lose a trick, the first combination is the best. But if you can afford to lose a trick, the second combination lets you have two chances at your second trick.

Given all this, it seems perfectly reasonable to add the same amount for a supported 10 as you subtract for an unsupported 10. Which is 1/2 point.

What Others Have Said

In the excellent book Hand Evaluation: Points Schmoints, Marty Bergen mentions many factors that influence the evaluation of a hand. However, he does not mention protection by a higher honor.

Marshall Miles says "one must deduct for unsupported honors" and "Lower honors are worth more in combination than by themselves." He also notes that before high card points became popular, a queen by itself was 1/4 of a trick but a queen with a king or ace was 1/2 trick; jacks by themselves are dubious values, but worth something when accompanied by higher honors.

However, Miles also says that opposite a strong no trump, Qxxxxx,Jxx,Kxx,Ax is as good as KQJxx,xxx,xxx,Ax. I believe he is wrong. Essentially, he is correctly noting that honors are more valuable when they are supported in either hand, but he is missing the fact that they are stronger when supported in the same hand.

Miles also says, "the added complication of using fractions would outweigh the slight increase in accuracy". I have not found this to be true. Miles also says to make corrections when there are several overevaluations or underevaluations. This is essentially correct. Counting half points will not make too many changes in your bidding, because they usually cancel each other out, or amount to only a half-point total, or do not change the bid anyway. They just make your bidding slightly more accurate.

To bottom-line this, there has not been a lot of discussion of this. It was obvious when people evaluated the quicktrick potential of a card combination in isolation, but it is not as obvious when using the point count system. Also, most people do not want to get into fractions, even though everyone agrees that accuracy can be increased. The hoi polloi will not count fractions. But a player who wants to be good should make the small sacrifice.

Several other factors influence the value of your hand. I will be concerned with factors that just influence the value of your honors. If you are going to start counting half-points, you can make some other corrections. The following factors are in Bergen's book, though he does not assign a specific correction factor.

The 4-3-3-3 distribution is bad. I subtract a half point for it. I have no idea if this is the correct value. I believe that if your partner is distributional, a flat hand is fine, but when partner is flat too a half point subtraction is conservative.

In terms of high cards and honors, a singleton honor is usually not as valuable as a honor accompanied by a small card. You can't lead towards the honor and hope a higher honor is onside, and you can't take a finesse to the other hand. Or in the case of AKQ, there might not be a fourth card in partner's hand for this to promote, and Jxx in his hand is worthless. Therefore, it is reasonable to adjust for when an honor is not accompanied by a small card. I suggest taking off a 1/2 point.

This adjustment isn't as reliable as the correction for an unsupported quack or the correction for the supported 10. But it is clearly a factor. I suspect that a singleton jack is still worth 1/2 point, at least at NT.

Bergen suggests taking off a full point for a singleton K. According to Miles, Goren subtracts one point for a singleton K, Q, or J or a doubleton QJ; Culbertson subtracts 1 point from opener's hand (at least), and Jacoby deducts a point for no low cards in a suit. Miles says these rules do too much or too little, suggesting to me that half points might be more accurate. QJ doubleton is the worst to evaluate accurately -- opposite Kxx is it full value and opposite xxx is it worthless.

Bottom Line

If you use half points, it will be more accurate. You can make these adjustments without your partner knowing. You can also notice that when you voluntarily a bad game, your partner will usually not have the HCP promised in the bidding. These adjustments are not the end to hand evaluation, but they are simple and they work.

Obviously, they can help you avoid a 40% game and then you get a bottom when everyone else is in the game and it makes. But in general, the corrections I suggest work well. As noted, the main problem is devaluing Qxx when partner turns out to have AKx; this is most likely when partner shows a very strong hand.