Even though the WP+SST method will predict accurately most of the time, we would be lying if we said the method does not has its downsides. There are a few cases where the estimation will be wrong, but if you are aware of them, you will know when to upgrade or downgrade your hand.
(1) Ace versus Queen
Q J 9 4 3 | ||
A 6 2 | ||
8 7 6 | ||
A 2 | ||
6 | 7 5 2 | |
K Q J 8 | 10 4 3 | |
Q J 2 | K 10 9 | |
K Q 9 6 3 | J 10 5 4 | |
A K 10 8 | ||
9 7 5 | ||
A 5 4 3 | ||
8 7 |
In our dicussion on "Working Points", we said that when you take a
trick with an Ace, you in fact use a little too much power in winning a
trick. One trick is taken, on average, by 3 pts, while an Ace is valued at 4 pts.
In this example, North-South take three side-suit tricks with Aces, which means their 12
WP in the side suits don't work optimally. Since 12 / 3 = 4, one would expect 12
WP to produce 4 tricks, but they actually take only take 3.
At the same time, East-West will do very well with their 18 HCP.
They have 4 SST, which suggests 8 tricks —
but they will take 9 tricks. And they do it, because
their side-suit honors work optimally.
They have no Aces, so they don't waste 4
WP to win a single trick; they win tricks with Kings and Queens, using up 3 WP
or 2 WP, respectively.
If we say that the lower red-suit honors ♥J
and J are used to promote the higher honors in those suits
(using the same logic as in "Working Points"), East-West
have only 10 WP in the side suits, but those 10 WP take one more trick
than North-South's 12 WP in their side suits.
A digression: The 18 total trumps on the deal produce 17 total tricks, even though the deal is perfectly pure (which is supposed to lead to extra tricks).
You may have read somewhere that Aces and Kings are better for suit play than Queens and Jacks. To some extent, that is wrong. What the writers mean is that Queens and Jacks in side suits are often useless, and hence they are valued too high. But — and this is an important "but" — when a Queen or a Jack is working, they are always undervalued. And an Ace is always overvalued.
This is nothing strange. If you have three Aces, the three honors will take
three tricks. If you have two Kings and three Queens, those five honors may take
five tricks. If one or more of them don't, it means they weren't working and
therefore should be valued at 0 WP.
So, when you take tricks with the two
Kings and one of the Queens, it means you have 8 WP in those suits — but
these 8 WP will take just as many tricks as the (overvalued) three Aces.
Q 7 2 | K J 10 5 4 | |
A K 2 | 7 6 | |
A K 4 | 9 7 | |
A Q J 6 | K 8 |
The WP+SST formula gets it right.
SST is 5. As for WP, since ♣J
provides a useful discard, we value it at 3 WP. Therefore, East-West have 32 WP,
which, coupled with 5 SST, is equivalent to 12 tricks.
A Q 7 4 | K J 10 5 4 | |
A K 2 | 7 6 5 | |
A K 4 | 9 7 | |
A 7 6 | K 8 2 |
But if you realize that you lost two undervalued trick-taking cards and gained one overvalued trick-taking card, and that the fourth trump didn't do East-West any good, the outcome of the swap is predictable.
WP+SST says "31 HCP and 5 SST = 11 tricks," so we would get this one right too.
Our next two examples show the real reason why Aces are useful.
It is easy to understand once you have grasped the concept of Working Points.
A K 9 8 7 6 | Q J 10 | |
2 | A K Q J | |
4 3 2 | 6 5 4 | |
4 3 2 | 6 5 4 |
Let's now give East ♦A, to see what it will mean:
A K 9 8 7 6 | Q J 10 | |
2 | A K Q J | |
4 3 2 | A 5 4 | |
4 3 2 | 6 5 4 |
No. But it means that the added ♦A gave East-West 9 extra WP, since now both ♥K and ♥Q are working. The big thing about Aces is that they bring life to other honors, not that they take more tricks themselves than their point-count suggests.
(2) Not enough potential
When your side has a very low SST, say 0 or 1, you may overestimate
your tricks, when you neither have lots of trumps nor a long side-suit.
Even if you have only few losers, it doesn't automatically follow that you will have lots of winners.
Here is a simple case:
A K J 9 | ||
Q 10 8 7 | ||
6 5 4 3 2 | ||
— | ||
6 5 | 4 3 2 | |
4 3 2 | 6 5 | |
A K J 9 | Q 10 8 7 | |
Q 10 8 7 | A K J 9 | |
Q 10 8 7 | ||
A K J 9 | ||
— | ||
6 5 4 3 2 |
If we swap two cards between North ♠ and South , we get:
K J 9 | ||
A Q 10 8 7 | ||
6 5 4 3 2 | ||
— | ||
6 5 | 4 3 2 | |
4 3 2 | 6 5 | |
A K J 9 | Q 10 8 7 | |
Q 10 8 7 | A K J 9 | |
A Q 10 8 7 | ||
K J 9 | ||
— | ||
6 5 4 3 2 |
If we make a final change, the formula will be perfect:
J 9 | ||
A K Q 10 8 7 | ||
6 5 4 3 2 | ||
— | ||
6 5 | 4 3 2 | |
4 3 2 | 6 5 | |
A K J 9 | Q 10 8 7 | |
Q 10 8 7 | A K J 9 | |
A K Q 10 8 7 | ||
J 9 | ||
— | ||
6 5 4 3 2 |
This example is another illustration of the fact that distribution is
the most important factor in estimating your tricks. The SST+WP method looks at
your important honors and your short suits.
But as this example shows, you may also have to look at the distribution of your long suits.
If we are to conclude these examples, we can say that
This may surprise you. After all, didn't Ely Culbertson teach the world of the advantages of playing in the 4-4 fit ? And haven't we all heeded his advice ever since ?
Yes we have, but somewhere along the line, the reasons for playing in the 4-4
fit have got lost. What Culbertson said was that if you play on a 4-4 fit,
instead of in Notrump, you will often gain one trick.
Suppose the suit is solid. Then, it
is worth 4 tricks in Notrump. In a suit contract, you can usually draw trumps
in 3 rounds, later using your remaining trumps separately, to get 5 trump
tricks; and should you be able to ruff more, you may get 6 or even 7 trump
tricks. The issue was 4-4 versus Notrump, not 4-4 versus some other possible
trump suits.
On page 71 in "I Fought The Law of Total Tricks", we give an example of
a 4-4 fit being better than a 5-3 fit. Such deals are not uncommon. But it is
important to realize that extra trick(s) don't come from the 4-4 fit; they
come from the discards on the long side-suit. If we can't use those discards, we
can just as well play on the 5-3 fit. And when the discards are useful, that is
reflected in a higher WP.
In this example, North-South have 24 WP, if hearts are
trumps. Add that to the SST of 4, and we get 10 tricks. But if they play in
spades, there are two heart discards coming, so the WP go up to 30. That means
there is potential for 12 tricks, which there is, but on a club lead, declarer
can only take 11 tricks. The reasons for the missing trick comes in the
following section.
(3) Not enough trumps
This one is going to please the Law friends, because the situation we are going to discuss is one where the Law has a good point.
K 8 2 | ||
6 5 | ||
9 7 6 5 | ||
9 7 6 5 | ||
6 5 4 | 7 3 | |
A Q J 9 | K 10 8 3 | |
K J 10 | A Q 3 | |
K 8 2 | Q J 10 4 | |
A Q J 9 4 | ||
7 4 2 | ||
8 4 2 | ||
A 3 |
The reason why the formula fails here is because one of North-South's short suits (North's doubleton ♥) couldn't be used. The result would have been the same, had North been 4-3-3-3. The effect of only 3 trumps in dummy is that SST for North-South was equal to South's short suits, i.e., 5.
This is a fairly common situation, and when one hand is weak without enough trumps, and without source of tricks in side suits, the estimation will be too high.
6 5 4 | ||
7 | ||
Q 10 9 5 4 2 | ||
A Q 3 | ||
K Q 7 3 | A J 10 9 | |
K Q 9 8 2 | A 10 6 5 | |
A J 8 | K 7 6 | |
10 | 4 2 | |
8 2 | ||
J 4 3 | ||
3 | ||
K J 9 8 7 6 5 |
Now, let's swap one of North's spades for one of South's trumps, and the formula predicts accurately. In that scenario, dummy has still not enough trumps to ruff South's all losers but he has an s entry, which permits him to set up and use dummy's long diamonds. And that brings us to the next section...
(4) Entries
Finally, we mustn't forget an important item: entries.
When a contract depends on the dummy having 3 entries, and he has only 2, for instance,
any estimation is likely to fail. Here is a typical example:
A K Q J 10 | 9 8 7 6 | |
9 2 | J 8 7 6 5 3 | |
J 9 3 | 2 | |
A 8 5 | 9 7 |
But if we move one of the spade honors from the West to East hand (say, let East haves ♠Q876 instead), things will change. Now, declarer wins the first 2 trump leads in hand and plays on hearts. Then, he will indeed take 9 tricks as long as hearts are 3-2.
A related issue is if the contract is played from the right side.
On Page 91
in "I Fought The Law of Total Tricks", we gave an example
of a 2-trick difference depending on if South or North is declarer.
Such deals are not rare.
The Law makes no mentioning of this important fact, but we do.
So even if your estimation is correct, you are not guaranteed of a good result – if one of the
sides (or both) is attempting to play the contract from the wrong side.