The power of distribution

The most important factor when you try to estimate how many tricks your side can take is distribution. Actually, when Jean-René Vernes published his famous article The Law of Total Tricks in The Bridge World in 1969, he wrote these wise words:

...We know, from long experience, that the prime factor is distribution... The discovery of an exact scale, fixing the relative value of the various honors, was a great step forward. But we do not have, today, a scale to tell us how high to bid by virtue of our distribution.

The Law of Total Tricks was developed with this in mind. Vernes' answer to the important question "How do we value distribution?" was "by counting the two sides' trumps". But as we have shown in our book and on this site, that wasn't the way to go. Knowing how many trumps the two sides have does not tell us how well our trumps will work for us. Therefore, our answer "look at the short suits!" is the correct one. If you haven't been convinced yet, you will be eventually.

To show the power of distribution, we will start by looking at a simple example:

Diagram No. 1.

S A K 8 7 Table S Q J 10 9
H A K 2 H 8 7 6
D A 8 7 D K 3 2
C 4 3 2 C A 7 6

East-West have 28 HCP, which all are working, a solid eight-card trump suit in spades, and still they can't make 4S unless they can engineer some sort of endplay. We have all been told that 26 points is enough for game in a major – and here 28 points isn't. Yes, they can make 3 notrump, but for the moment, let's concentrate on the 4-4 fit.

The main reason East-West only take nine tricks in spades is that they have the worst possible distribution, which is reflected in the highest possible SST: 6. Our formula says 28-30 WP should produce three more tricks than the SST suggests, but here 28 WP is not enough, due to the side having too many aces. Since an average trick is won by 3 WP, it means that if too many of your tricks are won with aces, you "waste" 4 WP per trick instead of 3, therefore you make bad use of your points. If you click on the link "Working Points" in the left frame, you can read more on this "paradox". And if we change East-West's honors, so that their 28 WP is a mix of aces, kings and queens, they will take one more trick than in this first example:

Diagram No. 2.

S A K 8 7 Table S Q J 10 9
H A K Q H 8 7 6
D A 8 7 D K Q 3
C 4 3 2 C 8 7 6

Once more East-West have 28 WP, but now they take ten tricks because instead of wasting 4 WP to win win one trick (the club ace), they use 4 WP to win two tricks (the heart queen and the diamond queen). Since all East-West's tricks outside of trumps are won with honors, it must surely be one trick better to have six such honors than five.

Diagram No. 3.

S A K 8 7 Table S Q J 10 9
H A K Q H 8 7 6
D A 8 7 6 D K Q 3
C 3 2 C 8 7 6

From the previous diagram (No. 2) we have given West a diamond instead of a club, a change which is worth exactly one trick to them. That is reflected in the SST, which goes from 6 to 5. And the tricks go up from 10 to 11. If we move one more club, we add one more trick to the total:

Diagram No. 4.

S A K 8 7 Table S Q J 10 9
H A K Q 4 H 8 7 6
D A 8 7 6 D K Q 3
C 2 C 8 7 6

Now, the SST is 4, and the difference between diagram No. 3 and No. 4 is exactly one trick: East-West take 12 tricks, one more than in diagram No. 3.

Diagram No. 5.

S A K 8 7 Table S Q J 10 9
H A K Q 4 3 H 8 7 6
D A 8 7 6 D K Q 3
C C 8 7 6

With the SST going from 4 to 3, we add another trick. Cutting your SST by one without reducing your WP at the same time, is equivalent to adding another 3 WP without changing your SST.

When Charles Goren popularized Milton Work's method of valuing honors, he made it easier for ordinary people to value their cards. Our guess is that Milton Work chose the values (4 for an ace, 3 for a king, etc) for simplicity, but experience has shown that it was pretty accurate. But when Goren also introduced a scale for distribution (3 for a void, 2 for a singleton and 1 for a doubleton) and combined it with point count he made an error – because the two scales are not compatible. According to Goren a doubleton is equal to a jack; a singleton is equal to a queen and a void is equal to a king. As these examples show, that is way too little.

Copyright © 2016, Mike Lawrence & Anders Wirgren