The Important Factors
Every bridge player was once taught to value his or her honors and distribution. Everyone. 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 that 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 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 is 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!
 | K Q 3 | |
 | 7 6 5 3 | |
 | 7 5 4 | |
 | A 9 6 | |
| 8 7 4 2
|
| 5
|
| K 9 2
| A J 10 9 4
| |
| A 9 5
| K Q J 3
| |
| 8 6 4
| 10 7 5
| |
| A J 10 9 6 | |
| 8 | |
| 10 8 2 | |
| K Q J 3 |
Both sides take 9 tricks without problems.
16 total trumps, but 18 total tricks.
This is a "+2" deal (two more tricks than trumps).
| K Q 3 2 | |
| 7 6 5 | |
| 7 5 4 | |
| A 9 6 | |
| 8 7 4
|
| 5
|
| K 9 3 2
| A J 10 9 4
| |
| A 9 5
| K Q J 3
| |
| 8 6 4
| 10 7 5
| |
| A J 10 9 6 | |
| 8 | |
| 10 8 2 | |
| K Q J 3 |
Here, North has given West ♥3 in exchange for ♠2. 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 equal tricks).
| K Q 4 3 2 | |
| 7 6 | |
| 7 5 4 | |
| A 9 6 | |
| 8 7
|
| 5
|
| K Q 5 3 2
| A J 10 9 4
| |
| A 9 5
| K Q J 3
| |
| 8 6 4
| 10 7 5
| |
| A J 10 9 6 | |
| 8 | |
| 10 8 2 | |
| K Q J 3 |
Once again, we have moved ♥5 from North to West and got ♠2 in return. That means one more trump for both sides. Now, there are 20 total trumps, but the total trick count remains the same: 18. This is a "–2" deal (there are two tricks fewer than trumps).
| K Q 7 4 3 2 | |
| 7 | |
| 7 5 4 | |
| A 9 6 | |
| 8
|
| 5
|
| K Q 6 5 3 2
| A J 10 9 4
| |
| A 9 5
| K Q J 3
| |
| 8 6 4
| 10 7 5
| |
| A J 10 9 6 | |
| 8 | |
| 10 8 2 | |
| K Q J 3 |
We have done the same swap for a third time (♠4 to North, ♥6 to West), but just as 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 still once more !
| K Q 8 7 4 3 2 | |
| — | |
| 7 5 4 | |
| A 9 6 | |
| —
|
| 5
|
| K Q 7 6 5 3 2
| A J 10 9 4
| |
| A 9 5
| K Q J 3
| |
| 8 6 4
| 10 7 5
| |
| A J 10 9 6 | |
| 8 | |
| 10 8 2 | |
| K Q J 3 |
Finally! This time, moving ♠8 to North and ♥7 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 Deals No. 1, 2, 3 and 4, the extra trumps didn't stop the
opponents from cashing the first 4 tricks.
It is also worth noting that in the
Deal No.5, the extra tricks do not come from the extra trumps — they come from
the fact that the defending side now can take only the first three tricks. For
both sides, the extra tricks came from a reduction of losers.
A singleton in 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 ♥8 to West or East and gets a diamond in return,
nothing will happen, since neither side will get rid of a loser; but if South gets a club instead,
East-West will gain a trick, as they now have only two losers in clubs.
And the same can be said for swaps within the partnership.
Suppose, in Deal No.5, swap ♦2 and ♣6, 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 losers 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 in Deal No.1.
Will that matter ? Let's see!
| K Q | |
| 7 6 5 3 2 | |
| 7 5 4 | |
| A 9 6 | |
| 8 7 4 3 2
|
| 5
|
| K Q
| A J 10 9 4
| |
| A 9 5
| K Q J 3
| |
| 8 6 4
| 10 7 5
| |
| A J 10 9 6 | |
| 8 | |
| 10 8 2 | |
| K Q J 3 |
Deal No. 6
At the table, it is quite likely that the
declarer takes only 8 tricks in contract of Major suits;
but since the Law assumes best play by both declarer and 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 got a "+4" deal!
Let's make another change on Deal No.1, but this time, we move 2 cards in minor suits , not 2 trumps. We keep the total trumps at 16, but suddenly the total tricks are going up...
| K Q 3 | |
| 7 6 5 3 | |
| 7 5 | |
| A 9 6 4 | |
| 8 7 4 2
|
| 5
|
| K 9 2
| A J 10 9 4
| |
| A 9 5 4
| K Q J 3
| |
| 8 6
| 10 7 5
| |
| A J 10 9 6 | |
| 8 | |
| 10 8 2 | |
| K Q J 3 |
Deal No. 7
We move ♣4 from West to North and ♦4, in return.
The total trumps are still 16, but now the total tricks are 20 (10 for
North-South in ♣, and 10 for East-West in ♦).
Do you object ? You
shouldn't !
On a trump lead, both declarers in ♠ and ♥ will be held to 9 tricks (no ruffs in the short hand), but who
says the trump suit should be ♠ or ♥ ?
The Law of Total Tricks refers to what happens when 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 total tricks, one from 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 have got rid of one 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 has (or both have) two or three posible trump suits of equal length,
it is not uncommon that one of those suits will take more tricks than the
other(s).
Suppose you are going to apply the Law of Total Tricks, when you know that the
opponents have 8 spades, which suit they are bidding. Can you be sure that
they are competing in their longest suit ? If they have another trump suit
(of equal length or longer) which will take one or two more tricks, any
attempt to use the total-trick formula to guide you will result in failure.