Lesson 6A Main

Counting by Declarer

by Richard Pavlicek

The average player considers only the cards that he can see his own hand and the dummy. To be a skillful declarer it is necessary to consider the enemy hands as well; or more specifically, the suit distribution and location of high cards. This lesson explains the proper counting techniques and the ways to derive information.

Counting Techniques

How do you keep track of cards? You should try to remember which high cards were played, but do not count every card. Instead, associate each suit with a pattern.

The lie of any suit or the shape of any hand must conform to one of 39 patterns. Listed below, in order, are the 20 most common patterns:

1. 4-4-3-2	11. 7-3-2-1
2. 5-3-3-2	12. 6-4-3-0
3. 5-4-3-1	13. 5-4-4-0
4. 5-4-2-2	14. 5-5-3-0
5. 4-3-3-3	15. 6-5-1-1
6. 6-3-2-2	16. 6-5-2-0
7. 6-4-2-1	17. 7-2-2-2
8. 6-3-3-1	18. 7-4-1-1
9. 5-5-2-1	19. 7-4-2-0
10. 4-4-4-1	20. 7-3-3-0

Examples 1 and 2 show how to count the cards by patterns:

1.	4 3 2
	A K Q 6 5

All follow to the ace, but East shows out on the king. Instantly you should recall the 5-4-3-1 pattern as the initial lie. Thus you will always have one more card than West unless you or he discards this suit.

2.	3 2
	A K Q 5 4

Assume this is your trump suit. East gets a ruff early in the play, and West shows out on the second round. The original lie was 5-5-2-1, but you now have one more trump than East because he ruffed once.

Lesson 6A Main

Top Counting by Declarer

Clues from the Bidding

The bidding often provides useful information about the enemy hands. If one opponent has bid (excluding weak bids) or doubled, he is likely to have most of the missing high cards. If an has opponent bid a suit, you should be aware of his length in that suit. If an opponent has bid notrump, he should have a balanced hand. If the bidding was fierce, you can expect wild distribution.

It is also noteworthy that a lack of enemy bidding can be informative. In this event you should expect the enemy hand patterns to be tame and the missing high cards to be split between their two hands.

Remember the bidding — or at least who bid what.

3.	J 10 8 7		West	North	East	South
None vul	J 3				2	2
	K 10 4 3		Pass	4	Pass	Pass
	A K 8		Pass
4 2		3
9 6 2		A K 8 7 5 4
A 5		J 8 7 2
Q 10 7 6 5 4		J 2
	A K Q 9 6 5
	Q 10
Lead: 2	Q 9 6
4 South	9 3

East wins the first two heart tricks then shifts to a trump. Your contract depends on finessing correctly for the J.

Draw trumps and ruff dummy’s last club in your hand. You discover that East began with one spade, six hearts (presumed from his bid) and two clubs; hence, he has four diamonds to West’s two. You should also figure West for the A since East would be too strong for 2 with that card.

On these assumptions your contract is assured. Lead the 6 to dummy’s king then finesse the nine on the way back.

Lesson 6A Main

Top Counting by Declarer

Clues from the Lead

The opening lead generally gives information about the length and high-card content in the suit led. Always ask yourself what the lead might be. Is it fourth-best from a four-card or longer suit? Is it “top of nothing” from a short suit? Is it an honor sequence?

Sometimes the opening lead will give information about the player’s entire hand. Why did he choose that suit? Is it an attacking lead (trying to win or establish tricks) or a passive lead (trying to be safe)?

If a defender makes a passive lead, he is likely to be harboring high cards in the other suits.

4.	A K J		Trick	Lead	2nd	3rd	4th
	5 2		1. W	9	A	6	2
	K J 9 4		2. N	J!	5	A!	2
	Q 10 3 2		3. S	10	7	4	6
9 8 5		Q 10 6 4	4. S	3	Q	K	4
K J 8		Q 9 7 6 4	5. N	9	6	8	5
Q 7 2		6 5	6. N	2!	7	10!	J
J 9 6 4		8 7	7. W	8	J!	Q	3
	7 3 2		8. E	4	7	8	K
	A 10 3		9. N	5	9	A	K
	A 10 8 3		10. S	A	4	2	7
3 NT South	A K 5		11. S	K	6	3	8
			12. S	5	9	10!	10
				Win the last trick

West’s lead appears to be top of nothing from a short suit. I would wonder why and conclude that he is more likely than East to have the Q. Therefore, win the A, lead the J (this might tempt East to cover) to your ace, then run the 10.

As you run the diamonds, assume East throws two hearts and West a spade. You hope to win four clubs, but you need more information. Lead the 2 to your 10 and West’s jack. Assume a spade return; jack, queen; then a spade to North as West sheds a heart. Next lead a heart to your ace.

At this point you know West began with three spades, three or four hearts and three diamonds. It must be three hearts because the missing heart is the queen and West would have led a heart originally from K-Q-J-x. Therefore, West has four clubs and the club finesse is indicated.

Lesson 6A Main

Top Counting by Declarer

Reading Enemy Tactics

During the play an opponent will sometimes shift to a suit that forces you to guess, usually as to the location of a certain high card. You can often decide the winning play by asking yourself what holding the defender might lead from. That is, try to decipher his tactics.

Come on, Joe. Those tactics aren’t gonna work.

If an opponent voluntarily leads a suit with dummy exposed, do not assume he is helping you. Stick to your original plan.

5.	Q 10 9 3		Trick	Lead	2nd	3rd	4th
	K Q J		1. W	2	J	A	6
	J 4		2. E	2	K!	3	4
	K J 8 4		3. S	4	2	10	6
5 2		7 6	4. N	3	7	K	5
10 5 4 2		A 9 3	5. S	7	4	K	3
Q 9 5 3		A 10 6 2	6. N	Q	9	8	5
A 10 6		Q 9 5 2	7. N	J	A	7	5
	A K J 8 4		8. E	6	8	9	9
	8 7 6		9. N	Q	2	A	10
	K 8 7		10. S	3	6	K!	5
4 South	7 3			Lose 1 more trick

East wins the first trick with the A and shifts to a low diamond, a cunning play. Many declarers would be duped into playing low, and be set at least one trick.

Instead you should ask yourself, “What holding would East lead a diamond from?” It would be terrible from the queen because this would give you a chance to make an impossible contract. But the diamond lead would be attractive from the ace. Hence, you should put up the king just as you would if playing the suit yourself.

A further problem on this deal is to guess the club suit. With no enemy bidding you should play West for the ace (i.e., lead up to the king) since East has already shown up with two aces. If East had three aces, it is likely he would have bid or doubled.

Lesson 6A Main

Top Counting by Declarer

Reading Discards

An opponent’s choice of discards is a valuable source of information. Logically an opponent will discard his losing cards and hold on to his winning cards and stoppers. This will often reveal the distributional pattern or the location of high cards in the suit discarded.

Be especially aware of reluctant discards. When a defender huddles before discarding, he probably ran out of idle cards and was forced to let go a potential stopper.

Early discards are usually idle cards — worthless suits, unnecessary protection to stoppers, or extra cards from a long suit.

6.	A Q 6 5		Trick	Lead	2nd	3rd	4th
	9 3		1. W	4	3	A	7
	J 8 3		2. E	10	Q	6	8
	Q J 5 3		3. S	A	2	3	7
7		J 9 8 4 2	4. S	4	6	J	10
A 8 7 5		Q 10 2	5. N	5	2	K	8
K 9 6 4 2		A 10 5	6. S	3	7	A	4
8 6 2		10 7	7. N	5	8	10!	8
	K 10 3			Cash 3 more winners
	K J 6 4
	Q 7
3 NT South	A K 9 4

East wins the A and returns the 10 as West cagily plays the six trying to make you think he has only a four-card suit. You should not be fooled because East’s play of the 10 indicates a short holding.

You begin by winning the A, Q and K as East throws a spade. Hmm…why did East discard a spade? If he held four spades, he would keep equal length with dummy. If he held three spades and five hearts, he would probably throw a heart. It is logical to assume that East held five spades. Lead the 3 to the ace and finesse the ten on the way back. Note that dummy still has a club entry to reach the Q.

The preceding logic might not hold in an expert game. If East is aware of South’s ability, he might throw a spade from other holdings to mislead declarer. Best advice: Don’t play in that game!

Lesson 6A Main

Top Counting by Declarer

Reading Signals

Enemy signals must be evaluated according to the caliber of the opponent. Weak players usually make only simple attitude signals because that is all they know; these signals are often flagrant and careless, thus providing a blueprint for declarer. Good players make fewer attitude signals because they don’t want to advertise where the high cards are; they rely more on count and suit-preference signals. Could there be a defensive tip here too?

Enemy signals are not always reliable. Believe a signal only if it appears to have a legitimate purpose for the defense.

7.	10 9 7		Trick	Lead	2nd	3rd	4th
	A J 2		1. W	Q	2	8	A
	K J 7 6		2. S	Q	4	A!	3
	6 5 2		3. N	10!	Q	A	2
K J 2		Q	4. S	Q!	2	6	3
9 6 5 4		K 10 8 7 3	5. S	A	8	7	5
10 8 2		9 5 3	6. S	4	10	K	9
Q J 9		K 8 7 3	7. N	J	7	4	J
	A 8 6 5 4 3			Lose 2 more tricks
	Q
	A Q 4
4 South	A 10 4

You win the A and lead the Q to dummy’s ace — a good start since West, if he held the king, might have covered to make your contract easy. You next lead the 10 to your ace.

At this point you have two reasonable options: Lead a second spade hoping the spades are 2-2; or lead four rounds of diamonds (throwing a club) which requires a 3-3 diamond break or the rare case that one player is long in both suits. On a percentage basis the plays are very close.

You can get help from the enemy with a clever strategy. Lead the Q (not the ace) from your hand. Each opponent is likely to give an honest count signal because he will think his partner may need to know when to take the ace. If both opponents play low diamonds, continue the suit expecting a 3-3 break; otherwise lead a spade.

Lesson 6A Main

Top Counting by Declarer

© 1994 Richard Pavlicek