The Important Factors

Have you ever wondered why North-South on one deal can take eight tricks, while they on another, similar one, only take seven; or, on a third one, also similar deal, take nine tricks? If you have, you may have come to the conclusion that there are two main factors – distribution and honors. Every bridge player was once taught to value his or her honors and distribution. Every one. Then the Law of Total Tricks came along and said "the most important thing is how many trumps you have". OK, in fairness, it also said you shouldn't forget the old way of valuing your cards, but it stressed the number of trumps ahead of honors and distribution. We consider that a serious error. And to some extent that false claim has led to people forgetting the old, important, art of valuing your hand. Our aim is to get things back to normal again by stressing what really is important. We hope that both you, the players, and the game of bridge will benefit from it.

It's easy to demonstrate that extra trumps don't automatically mean extra tricks. We will do it by showing you one deal and modifying it gradually. We start with 16 total trumps and end with 22 total trumps. If you expect the total tricks to vary accordingly, you are in for a big surprise. Just watch!



Deal No. 1.

S K Q 3
H 7 6 5 3
D 7 5 4
C A 9 6
S 8 7 4 2 Table S 5
H K Q 2 H A J 10 9 4
D A 9 5 D K Q J 3
C 8 6 4 C 10 7 5
S A J 10 9 6
H 8
D 10 8 2
C K Q J 3

Both sides can take nine tricks without problems. 16 total trumps, but 18 total tricks. This is a +2 deal (two more tricks than trumps).



Deal No. 2

S K Q 3 2
H 7 6 5
D 7 5 4
C A 9 6
S 8 7 4 Table S 5
H K Q 3 2 H A J 10 9 4
D A 9 5 D K Q J 3
C 8 6 4 C 10 7 5
S A J 10 9 6
H 8
D 10 8 2
C K Q J 3

Here, North has given West one heart in exchange for one spade. That means both sides gain a trump, but neither side gains a trick. 18 trumps and 18 tricks – just what the Law says it should be. This is a 0 deal (trumps equals tricks).



Deal No. 3

S K Q 4 3 2
H 7 6
D 7 5 4
C A 9 6
S 8 7 Table S 5
H K Q 5 3 2 H A J 10 9 4
D A 9 5 D K Q J 3
C 8 6 4 C 10 7 5
S A J 10 9 6
H 8
D 10 8 2
C K Q J 3

Once more we have moved a heart to West and a spade to North. That means one more trump for both sides. Now, there are 20 total trumps, but the total tricks remain the same: 18. This is a -2 deal (there are two tricks fewer than trumps).



Deal No. 4

S K Q 7 4 3 2
H 7
D 7 5 4
C A 9 6
S 8 Table S 5
H K Q 6 5 3 2 H A J 10 9 4
D A 9 5 D K Q J 3
C 8 6 4 C 10 7 5
S A J 10 9 6
H 8
D 10 8 2
C K Q J 3

We have done the same swap for the third time (a spade to North, a heart to West), but just like in the previous examples those two extra trumps don't affect the total number of tricks. With 22 total trumps we have the same 18 tricks. This is a -4 deal.
   Let's do it one more time!



Deal No. 5

S K Q 8 7 4 3 2
H
D 7 5 4
C A 9 6
S Table S 5
H K Q 7 6 5 3 2 H A J 10 9 4
D A 9 5 D K Q J 3
C 8 6 4 C 10 7 5
S A J 10 9 6
H 8
D 10 8 2
C K Q J 3

Finally! This time moving one spade to North and one heart to West resulted in one more trick for each side. Still, with 24 total trumps and 20 total tricks, it is a -4 deal, just like the previous one. Not exactly what the Law predicts.

So why did this swap result in two more total tricks while the previous swaps didn't change anything?

The answer is simple. The last swap removed one loser for North-South and one loser for East-West. In diagrams 1, 2, 3 and 4, the extra trumps didn't stop the opponents from cashing the first four tricks. It is also worth noting that in diagram 5, the extra tricks don't come from the extra trumps – they come from the fact that the defending side now only can take the first three tricks. For both sides, the extra tricks came from a reduction of losers. A singleton in the opponents' suit meant one loser there, while a void meant no losers. The explanation is in the distribution, NOT in the number of trumps.

We started with 16 total trumps and moved up to 24 total trumps. What do you think will happen if we move the last trumps too?
   Yes, you're right. Any swap will add a trick – if, and only if the swap removes a loser. So if South gives his heart to West or East and gets a diamond in return, nothing happens since neither side got rid of a loser, but if South gets a club East-West gain a trick, as they now only lose two club tricks.



And the same can be said for swaps within the partnership. If we from deal No. 5 move a diamond to North and a club to South, the result is one more trick to North-South, since the swap removed one of their losers. If we instead give North a diamond and South a heart, nothing happens. The gain in diamonds (two loser instead of three) is balanced by the loss in hearts (two losers instead of one).
   And the gain may be even higher: Go back to deal No. 4 and swap a heart and a diamond between North and South. The result is a gain of two tricks. Instead of one heart loser and three diamond losers, North-South are left with only two diamond losers.
   Also note that neither swap did any harm to the other side, so the net effect was that the total number of tricks changed.



What about going from 16 to 14 total trumps, by removing one trump from each hand from Deal No. 1. Will that matter? Let's see!

Deal No. 6.

S K Q
H 7 6 5 3 2
D 7 5 4
C A 9 6
S 8 7 4 3 2 Table S 5
H K Q H A J 10 9 4
D A 9 5 D K Q J 3
C 8 6 4 C 10 7 5
S A J 10 9 6
H 8
D 10 8 2
C K Q J 3

At the table it is quite likely that the declarer only takes eight tricks if the contract is played with a major suit as trumps, but since the Law assumes best play by both declarer and the defenders, the same 18 total tricks are there (if the defense shortens declarer, he can draw at most one round of trumps, then ruff his last minor suit winner in dummy). Suddenly, we have a +4 deal!

Let's make a new change from deal No 1, but this time we move two minor suit cards, not two trumps. We keep the total trumps at 16, but suddenly the total tricks go up...



Deal No. 7
S K Q 3
H 7 6 5 3
D 7 5
C A 9 6 4
S 8 7 4 2 Table S 5
H K Q 2 H A J 10 9 4
D A 9 5 4 D K Q J 3
C 8 6 C 10 7 5
S A J 10 9 6
H 8
D 10 8 2
C K Q J 3

A club to North and a diamond to West. The total trumps are still 16, but now the total tricks are 20 – ten for North-South, ten for East-West.
   Do you object? You shouldn't! Yes, on a trump lead, the declarers in spades or hearts, respectively, will be held to nine tricks (no ruffs in the short hand), but who says the trump suit should be spades or hearts?

The Law of Total Tricks refers to what happens if each side plays in its "best trump suit", and here clubs play one trick better than spades for North-South, and diamonds play one trick better than hearts for East-West. So, the effect of our moving two minor suit cards was that (a) two tricks were added to the trick total, one for each side, and (b) both sides got a new "best trump suit". Now, these 16 total trumps take 20 total tricks; we have a +4 deal.

The reason why this swap gained one trick for North-South and one trick for East-West should be familiar to you by now. It is because both sides got rid of a loser. The fact that neither side gained a trump is insignificant.

This last swap shows another error in concentrating on the number of trumps: When one side (or both) have two or three trump suits of the same length, it is a not uncommon occurence that one of those suits will take more tricks than the other(s). Suppose you try to apply the Law of Total Tricks and know that the opponents have eight spades, the suit they are bidding. Can you be sure that they are competing in their best suit? If they have another trump suit (of the same length or longer), which will take one or two more tricks, any attempt to use the total tricks formula to guide you will result in failure.


Copyright © 2016, Mike Lawrence & Anders Wirgren