The concept of Working Points (WP) is an important part of the formula presented in the Lawrence/Wirgren book "I Fought The Law of Total Tricks".  If we had concentrated solely on distribution, we would have come up with something just as vague and inaccurate as the Law of Total Tricks, but with inclusion of Working Points, hand evaluations become much more clear.  
      Incidentally, these principles are an extension of what we all have learned when we started playing bridge: we should value our honors AND distribution.

What exactly do we mean by Working Points ?   Or, rather, which honors are said to be working ?   If you have, say, 9 HCP in ♠, ♥ and ♦, and you know your partner has at most one club, does that mean you have 9 WP ?  

The correct answer is "maybe."  Quite often, you will indeed have 9 WP, as you may expect, but it is also possible that you have less than that — or even more than that.  To understand why, let's start with a trivial combination like this:

East-West have 3 hearts in both hands, including A, K, and Q.   Each of these honors takes a trick, which means that they are all working.   As you see, one trick is taken ♥A (4 HCP), another by ♥K (3 HCP) and a third by ♥Q (2 HCP).   Thus, a working honor with average 3 HCP will take one trick.   That is why an extra 3 WP translates into one extra trick.

When we remove ♥Q, we remove 2 HCP.  But, since the remaining 7 HCP take 2 tricks, those 7 HCP are working.   If we remember that a trick-taking uses 3 WP, East-West use a little "too much" WP in this example, in taking 2 tricks; their 7 WP don't take 2.33 but 2 tricks.

What about this one ?  How many WP do East-West have ?
The answer depends on where ♥K is.   When North has it, ♥Q is worth nothing; but when South has, it is worth a trick.  
      In the first case, East-West have 4 WP (and take one trick).  In the second case, they have 4+2=6 WP (and take two tricks).   When both honors are working, the 6 HCP we assign them is right on target.

Once again, the value of this combination depends on where a key card is.  In the previous example, it was ♥K.   Now, it is ♥A.  Depending on where ♥A is, East-West take one or two tricks.  When ♥A is offside, it's useful to think of the lower honor as a means of promoting the higher one to a trick, i.e. ♥Q is not working, but ♥K is working.  Here, East-West have either 5 WP or 3 WP.

Compared to the preceding two situations, you note that when ♥A is onside, East-West make excellent use of their honors.  With 5 WP, they take two tricks, which is one third of a trick more than the expected 5/3 = 1.67 tricks.

When we have only one honor in the suit, the reasoning will be the same.  When we have ♥A, we take one trick.   Assigning 4 HCP (or 4 WP) to a Singleton Ace is therefore slightly too much, since it takes only one trick (not 1.33 tricks).  Its correct value would be 3 points.

When we have ♥K, as in this example, we need ♥A to be onside.   If it is, we have 3 WP; if it isn't, 0 WP.   Counting ♥K as 3 HCP or 3 WP will be a way too much half of the time, and exactly right the other half.  King's average value with no accompanying honors in the combined hands is therefore 1.5 points.

When our honor is Q, we need both A and K to be onside for it to take a trick.  That happens roughly 25% of the time.  When it does, the Queen is valued slightly too low (you take one trick with 2 WP, not 0.67); when it doesn't, the queen is overvalued by 2 points.  Since it takes a trick once in 4 times, and nothing in the other cases, the Queen's average value without accompanying honors is 0.75 points.

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Together or separated ?

In the above examples, honors were held in one hand.  
What if they are held separately in two hands ?

If we start with 3 honors, it's clear that nothing changes if the honors are split between the hands.  With A-K-Q in the suit, you will take 3 stricks.  And the same is true for the best two honors:   When you have A and K, they are worth 2 tricks no matter how they are distributed.

When you have ♥A in one hand and ♥Q in the other, the situation is similar to the one where you had ♥AQx opposite three low ♥xxx.  The only difference is that now ♥K will be favorably placed for East-West if North has it.  Then, this combination is worth 6 WP, and two tricks. Otherwise, it is 4 WP and one trick only.

When you have ♥K in one hand and ♥Q in the other, things are worse for your side.  Unless one of the defenders has the Ace singleton or doubleton, and you can figure out which, your two honors will only take one trick.  When that happens, we use the same reasoning as in example 4 above: the lower honor ♥Q is used to promote the higher ♥K.  So when we take one trick, we have 3 WP in the suit.

When we add ♥J, we add almost a full trick.   And now it's clear that we have 6 WP in the suit, equalling 2 tricks.

Even ♥10 makes things rosier than when the defenders have it. .  
If we lead ♥3 toward ♥K, later finessing ♥10, we will take 2 tricks slightly more than half of the time.  But how many WP do we have, when that happens ?

Suppose ♥K is taken by ♥A, and you later take a successful finesse with ♥10.  Then, you win 2 tricks with ♥Q and ♥10.   But, we are wrong to say that we had 2 WP in ♥, given that an average trick is taken by 3 WP.   Instead, we suggest you think along these lines:
      With ♥10 lying over defender's ♥J, West's ♥ holding may be regarded equivalent to ♥Q-J-3, and just like in example 10, we say that the lower honor is used to promote the higher honors.  Therefore, East-West have 6 WP in ♥, even though they only had 5 HCP in the suit.

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Copyright © 2005, Mike Lawrence & Anders Wirgren
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