Chapter 16

Dummy Has Q-9-7 At Notrump

Q x
A K x x x
K T x
Q 9 7
K J x x x
x x
A J x x
A 2
South	North
1	2
2NT	3NT

West led a small club.  I was dummy and was not totally attentive.  I had the feeling that the lead was from a three, four, or five card suit.  Partner played the nine and subsequently lost three club tricks.  The lead was from the J-8-x-x, and so the seven followed by the nine would have won two tricks.

Options:

1. Play queen at trick one.  If the lead was the J or T, play the nine next time.

2. Play nine.  On the J/T lead, you put in the queen, and then on the second lead you play the nine.  An honor lead reduces this to the Queen play case.

3. Play seven (on a low-card lead.)  If East plays the J/T, you play the nine on the next lead, else the queen.  A J/T/8 lead reduces this to the nine play case.  If West has the J-8-x-x, or the T-8-x-x, and knew this was the deal and this was our strategy he should lead the J or T. 

There are 256 ways the suit can break.  A few are eliminated because West is not void and can lead a low card.

An assumption is the defenders are as difficult as possible.  Their defense does not help partner.  This is contrary to be honest in a suit we attack and deceptive in a suit they attack.  We can argue about what one would lead holding the J-T and different lengths.  I suspect that everybody leads an honor from J-T-x.  In this problem the lead is small.  Strategy would change if West leads an honor.  Also East must play an equal from J-T-8 if declarer inserts the seven from dummy.  Playing the 8 is a sloppy mistake that East is very apt to make.

The opening lead comes from West at trick one.  The second lead comes from either West or South.

The computer produced this table.  Fine tunings are (1) a suit is more apt to break closer to 4-4, and (2) West is short (two or less.) 

West leads.  Dummy = Q-9-7.  Declarer = A-2.

	West cards in suit
West	0	1	2	3	4	5	6	7	8	Sum	/16	East
Q play												7 play	9 play
K		1	4	6	4	1				16	1	J-T-8	J-T-8
K-J			2	8	12	8	2			32	2	J-8	J-8
K-J-T				1	4	6	4	1		16	1	8	8
K-J-T-8					1	4	6	4	1	16	1	x	x
K-J-8				2	8	12	8	2		32	2	J	J
K-8			1	4	6	4	1			16	1	J-T	J-T
J		2	8	12	8	2				32	2	K-J-8
J-T			1	4	6	4	1			16	1	K-8	K-8
J-T-8				1	4	6	4	1		16	1	K	K
J-8			2	8	12	8	2			32	2	K-J
8		1	4	6	4	1				16	1	K-J-T
x	1	4	6	4	1					16	1	K-J-T-8
8										256	16	9	10

Interpret J as the J or T.  In the column at the left you see K alone which means West has the king with 0 to 4 small cards.  East has J-T-8 with the complementary number of small cards.  Bold says the queen wins in the queen play.  Bold in the East column says the seven play wins.  In this K example, the seven play would win if East made the lazy play of the eight.  If East always played the T from this holding, then seeing the T makes playing the queen on the second lead a 50-50 proposition (restricted choice).  Red in the rightmost column (just bold with a black and white printer) says the nine play wins.

The second row has K-J.  Numbers are doubled because K-J includes K-T.  (Perhaps I should have written KJ/KT.)  No deception is possible, and all plays win.

The third and fourth rows are K-J-T and K-J-T-8.  No doubling of numbers.  All plays win.  Here I think the lead would not be one of the equals (jack or ten). "x" in the East column includes void.

All plays win against K-J-8.

With K-8, the seven forces the jack or ten.  On the next lead, play the nine and lose to the other equal.

Continuing down you see the J-T and J-T-8 cases.  I expect a J or T lead in some of these cases.  What one leads depends on style, length of the suit, interpretation of the auction, how many high cards does West have, and does West expect a major to run.  I expect a long discussion here.  This is the meat of this chapter.

The last row is x which again includes the void case.  How can West lead a void?

The final row does summations and divides by 16.  The queen play wins 8/16; the seven play, assuming full deception, 9/16; and the nine play 10/16.

Suppose you know that West has an exact number of cards in the suit because a birdie told you, and not because you read the lead as fourth highest.  Then you sum numbers in the appropriate column.

With perfect defense, it is adequate to play the nine.  There are factors that can make the seven better.  In the real world, I think it is right to play the seven.

Two-trick wins for North-South

	Queen wins	Nine wins	Seven wins
All lengths	128	160	144
West leads J from J-T	160	160	160
East plays 8 from J-T-8			160
Both of above	160	160	176
Carefully look at card combinations
West has 1 card	1	1	1
West has 2 cards	8	8	8
West has 3 cards	21	28	20
West has 4 cards	35	45	41
West has 5 cards	35	45	44
West has 6 cards	21	26	26
West has 7 cards	7	8	8
West has 8 cards	1	1	1
Sum 1 to 8	129	162	149

You, as West, first lead the suit in the middle of the play of the hand.  Now you have seen dummy.  Assume fooling partner is not a concern, and you want two tricks in the suit rather than the best chance for a fast single trick in the suit.  With J-8-x or T-8-x, you lead a high card.  And as declarer, how do you react to the T lead?  With J-T-x, you should lead small or possibly the T.

West leads.  Dummy = Q-9-8.  Declarer = A-2.  Nine play = finesse twice

	West cards in suit
West	0	1	2	3	4	5	6	7	8	Sum	/32	East
Q play												9 play
K		1	5	10	10	5	1			32	1	J-T
K-J			2	10	20	20	10	2		64	2	J
K-J-T				1	5	10	10	5	1	32	1	x
J		2	10	20	20	10	2			64	2	K-J
J-T			1	5	10	10	5	1		32	1	K
x	1	5	10	10	5	1				32	1	K-J-T
4										256	8	6

Extra credit.  What are the probabilities of the two possible play strategies?

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