Lesson 4Q Main

Combining Your Chances

by Richard Pavlicek

As declarer you will usually find that there are at least two chances to make your contract. Sometimes you will have to choose between them; that is, you must decide which is the better chance and play for it. Other times you will be able to try both, and that is the subject of this lesson.

Plan Ahead

When looking for a way to make your contract, try to find at least two chances then:

Look for a line of play that will allow you to take advantage of both chances.

1. 8 5 4 Trick Lead 2nd 3rd 4th
Q 10 3 1. W K 2 9 3
A K 5 3 2. W A 5 6 4
J 5 2 3. W 8 J Q 2
J 9 3 Table K 10 7 6 2 4. S A 8 3 4
9 8 J 4 5. S 5 9 Q J
Q 10 9 6 J 8 6. N A! 8 2 6
A K 10 8 Q 9 7 6 7. N K! J 4 9
A Q 8. N 3 2 7 10
A K 7 6 5 2 9. W Q 5 6 6
7 4 2 10. S 7 10 10 7
4 South 4 3 11. N 4 7 Q 3
Claim the rest

The defense begins with three rounds of clubs and you ruff. It is not difficult to see there are two chances to make your contract: either a successful spade finesse or a 3-3 diamond break. It is your goal then to develop a plan that will take advantage of both of these chances.

The correct play is to draw trumps in two rounds. When trumps break 2-2, next lead the A-K and another diamond. If all follow, the 5 will be good (dummy still has a trump entry). As the cards lie, you will learn that the diamonds do not break and you can still try the spade finesse.

It is important to see that trying the spade finesse first would be an error. It would also be wrong to duck a diamond early; East might win and lead a spade to force you to commit yourself before you know how the diamonds break.

Lesson 4Q Main Top Combining Your Chances

Knock Out the Ace

If you have chances in two suits, it is often important which of these suits you play first. If you lack the ace in one of these suits, it is almost always right to play that suit first. Save the suit in which you already hold the ace until later.

If you plan to try chances in two suits, first lead the suit in which you do not hold the ace.

I found a play that gave me two chances.

Terrific. Now you’ll go down two instead of just one.

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

You have eight top tricks and your two chances are to find the A or the K with East. If you plan ahead you will discover that it is very important which of these chances you try first.

Assume you try the heart finesse first. If it loses, West will return a club to knock out your last stopper. If you then cross to dummy and lead a spade, East can win the ace and return his last club to set you.

The correct order is to lead spades first (the suit you lack the ace). If the K lost to the ace, you would still be able to try the heart finesse — except in the extremely unlikely event that West returned a spade and the opponents were able to cash five spade tricks.

As the cards lie you won’t need the heart finesse. The K is your ninth trick.

Lesson 4Q Main Top Combining Your Chances

Two Finesses

Sometimes your contract will depend on one of two finesses. The order in which you take the finesses often matters. Ideally, you should first try the finesse that, if it loses, will still allow you a chance to try the second finesse.

If the loss of either initial finesse would result in the defeat of your contract, you must decide which of the two finesses to risk. You can combine your chances partially by following this strategy:

If you cannot try both finesses, first cash the top cards in the suit in which the outstanding honor is more likely to drop.

3. K J 4 Trick Lead 2nd 3rd 4th
A 7 1. W 6 3 K A
7 4 3 2. S 6 4 A 2
A K J 9 4 3. N 7 3 K 5
10 8 6 5 Table Q 9 7 2 4. S Q 8 4 8
5 4 8 3 2 5. S 3 5 A! 2
Q 10 8 6 K J 9 2 6. N K! Q 7 6
8 6 5 Q 2 Win the rest
A 3
K Q J 10 9 6
A 5
6 South 10 7 3

You have 11 top tricks and there are two chances to make your contract: the club finesse or the spade finesse. Unfortunately, the diamond opening lead has forced out your ace, and either losing finesse would allow the opponents to cash the setting trick in diamonds.

Since you cannot try both finesses, you should first try to drop one of the missing honors. Which card is more likely to drop, the Q or the Q? Obviously, the Q because you have three more clubs than spades. Therefore, after drawing trumps, you should cash the A-K and — bingo — you make an overtrick.

Note that if the Q did not drop, you would still have the spade finesse available to make your contract. The proper technique would be to cross to the A and run all your trumps first.

Lesson 4Q Main Top Combining Your Chances

Avoidance Plays

The strategy of losing the lead to the proper defender should be considered in deciding which chance to try first. Ideally, you would like to keep the “dangerous defender” off lead altogether; but in practice you must often choose between letting him on lead early or later.

If you may lose the lead in two suits, consider which suit might permit an avoidance play and when it would be useful.

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

You have six top tricks and will get two more in spades. There are two chances for your ninth trick — diamonds or clubs — and you must give up the lead in either suit to obtain it. (A third chance exists in hearts but it is too slim to consider here.)

It appears that West has a long spade suit. You do not mind losing the lead to him early while you still have a spade stopper; but once your spade stopper is removed, you must seal him off. Which suit gives you the better chance of avoiding West? Clearly, clubs because you can finesse the 10 into East. Therefore, you should play diamonds first.

The proper play is to duck a diamond. Assume East wins and returns a spade to West’s ace, then another spade is led to your king as East shows out. Next lead the 2 and finesse the 10. This loses to the safe hand and you will make your contract if either diamonds or clubs break 3-3.

Be sure to see that you would fail if you played clubs first. You would later have to play diamonds, and you could not prevent West from gaining the lead.

Lesson 4Q Main Top Combining Your Chances

Preserving a Chance

If a defender makes an annoying lead through your honor holding, you will often be forced to commit yourself as to which chance to try for your contract. In some cases, however, you can keep your other chances alive by postponing your crucial play in the suit led.

If a defender leads through your A-Q, sometimes you can preserve chances if you win the ace or duck the trick.

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

You have 10 sure tricks. An analysis shows there are three chances to make the contract: West holds the K, West holds the Q-J, or the enemy clubs split 3-3. Unfortunately, the opening lead may force you to make a critical play early.

If you finesse the Q and it loses, a spade return will knock out your ace. Then you will not be able to take advantage of a 3-3 club break — the opponents can cash the setting trick when they gain the lead.

The correct play is to win the A at trick one. Then you will draw trumps and lead a club to the ten. This loses to the safe hand (East) so your Q cannot be led through. Regardless of the return, you will be able to benefit from dummy’s long club.

Note that if the clubs did not break 3-3, you would still be able to lead a spade toward the queen and succeed if West held the K. Thus you kept all your chances alive by winning the A first.

If the opening lead were a low spade, you could accomplish the same objective by ducking the first trick. But you could not afford to duck the jack.

Lesson 4Q Main Top Combining Your Chances

Hidden Chances

Some chances are not so obvious. A skillful player can often gain an edge by taking advantage of some extra chance, however small. The main point is to look around. Do not be satisfied with your immediate analysis. The more you practice this the more skilled you will become.

If your contract appears to have only one chance, look further. You may discover a slight extra chance or two.

6. K 10 9 8 Trick Lead 2nd 3rd 4th
8 6 3 1. W Q 2 7 9!
K 6 4 2 2. W 10 3 4 A
3 2 3. S 3 2 10 6
5 2 Table 6 4. N 2! Q A 3
A Q J 10 9 7 2 5. S 5 8 K 7
9 8 3 Q J 10 7 6. N 4 10 J 9
Q J 10 8 5 K 7 6 4 7. S 4 5 9 6
A Q J 7 4 3 8. N 6! J A 5
K 5 4 9. S 7 8 8 2
A 5 10. N 3 10 4! J
4 South A 9 W endplayed, lose 1

You have nine sure tricks and it appears that your only chance for a tenth is to find the A onside. In fact there are at least three additional chances a skillful player would spot: (1) West holds four or five diamonds, (2) West has ace-doubleton in hearts or (3) West must win the first round of hearts when ducked.

Of course, it takes accurate play to take advantage of them all. The first key play is to duck the opening lead (to keep East off lead) and win the continuation. Draw one round of trumps, then play the A-K and ruff a diamond. Draw a second round of trumps ending in dummy.

Lead the last diamond and, if East shows out, discard a heart. West would win the trick and be forced to lead a heart, else give you a ruff and discard. As the cards lie East would follow to the diamond so you ruff in hand. Chance 1 did not work.

Lead a trump to dummy and lead a heart, but duck the trick completely. In the actual deal West would have to win, and he is endplayed. Whether he leads a club or a heart, you will make your contract.

Lesson 4Q Main Top Combining Your Chances

1.	8 5 4		Trick	Lead	2nd	3rd	4th
	Q 10 3		1. W	K	2	9	3
	A K 5 3		2. W	A	5	6	4
	J 5 2		3. W	8	J	Q	2
J 9 3		K 10 7 6 2	4. S	A	8	3	4
9 8		J 4	5. S	5	9	Q	J
Q 10 9 6		J 8	6. N	A!	8	2	6
A K 10 8		Q 9 7 6	7. N	K!	J	4	9
	A Q		8. N	3	2	7	10
	A K 7 6 5 2		9. W	Q	5	6	6
	7 4 2		10. S	7	10	10	7
4 South	4 3		11. N	4	7	Q	3
				Claim the rest

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

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

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

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

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