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An Unusual Layout
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At Caltech's bridge club, I faced an interesting lead problem: 

South
KQJ
1082
A63
Q973
W
N
E
S
P
P
1
P
1
P
1NT
P
P
P
 What would you lead?

Not being an expert, I can't claim to know what's right, but I chose a small diamond.  I think a spade is plausible as well, and a heart perhaps better; I could even see an argument for a club.  The full hand was 

West
A976
K9
742
K842
North
843
QJ63
QJ985
5
East
1052
A754
K10
AJ106
South
KQJ
1082
A63
Q973
W
N
E
S
P
P
1
P
1
P
1NT
P
P
P
D
8
1NT East
NS: 0 EW: 0
 Here is the puzzle for you: double dummy, what leads beat the contract, if any?

If you said a heart, you'd be... wrong!  In fact, you must lead one of the top two hearts to beat the contract.  Let's look at the successful defense first.  Suppose the heart ten is lead, and declarer wins the heart king. Now an entry to North's hand is established.  Declarer has six tricks available immediately: one spade, two hearts, and three clubs.  Further, declarer needs more than one tempo to set up a trick. If the defense gets in on a non-heart trick (1), they can enter North's hand through hearts perforce (2), and take five diamond tricks (3-7), for off one.  If Declarer attempts to put the defense in on a heart by cashing the heart ace, south can unblock the heart 8 and endplay declarer in hearts-- now declarer can't help but give up a black suit trick, a heart, and five diamonds.  For example: 

West
A976
K9
742
K842
North
843
QJ63
QJ985
5
East
1052
A754
K10
AJ106
South
KQJ
1082
A63
Q973
W
N
E
S
P
P
1
P
1
P
1NT
P
P
P
D
8
1NT East
NS: 0 EW: 0
10
K
3
4
0
0
1
9
J
A
8
2
0
2
J
Q
K
5
0
0
3
2
3
A
3
2
0
4
2
J
6
4
3
1
4
2
2
Q
5
1
2
4
Q
K
A
4
3
3
4
3
7
J
10
1
4
4
9
5
6
4
1
5
4
8
10
7
7
1
6
4
5
6
9
9
1
7
4
8
7
Q
A
0
7
5
8
6
10
K
2
7
6
E/W -50
13
 Okay, so what if declarer ducks the heart king?

Now there is a canny defense: North must overtake the first heart.  If declarer wins, a heart entry is established perforce, and we are back to the first scenario.  But what if declarer ducks?  The defense would like to cash five diamond tricks, but there's a problem; on cashing the third diamond, North will exhaust the entries to his hand.  If he exits without cashing all of the diamonds, he doesn't get them.  Now we have four scenarios: North takes five, four, three, or two diamond tricks.  In the first and second scenarios, South will be squeezed in the black suits, like so: 

West
A976
K9
742
K842
North
843
QJ63
QJ985
5
East
1052
A754
K10
AJ106
South
KQJ
1082
A63
Q973
W
N
E
S
P
P
1
P
1
P
1NT
P
P
P
D
8
1NT East
NS: 0 EW: 0
10
9
Q
4
1
1
0
Q
K
A
2
3
2
0
3
4
J
10
1
3
0
9
2
6
7
1
4
0
8
5
2
6
1
5
0
5
5
8
7
1
6
0
3
10
J
A
0
6
1
K
3
7
3
0
6
2
2
5
J
7
2
6
3
A
Q
9
6
2
6
4
A
9
4
4
2
6
5
6
Q
K
8
0
6
6
8
J
10
K
2
6
7
E/W +90
13
 In the third scenario, declarer can endplay south, like so: 
West
A976
K9
742
K842
North
843
QJ63
QJ985
5
East
1052
A754
K10
AJ106
South
KQJ
1082
A63
Q973
W
N
E
S
P
P
1
P
1
P
1NT
P
P
P
D
8
1NT East
NS: 0 EW: 0
10
9
Q
4
1
1
0
Q
K
A
2
3
2
0
3
4
J
10
1
3
0
9
2
6
7
1
4
0
3
5
2
K
0
4
1
6
3
5
J
3
5
1
8
7
6
A
2
5
2
10
Q
A
4
0
5
3
9
8
7
K
3
6
3
9
(there are also potential squeezes, and declarer may also be able to just set up the spade nine, if the defense is innacurate).  Thus after winning two diamonds, North must shift to a black suit.  Declarer can cash out for six tricks, but South retains the crucial diamond entry; if declarer ever gives up a trick, the diamonds will run, for off one.  All in all, declarer's best try is to 1) duck the first heart 2) duck the diamond return.  Now when south gets in on the A, they have to find the spade shift.  So, why doesn't the lead of the heart two work?

In this case, declarer can tangle the defense's entry to North's hand.  Win the K on the board, and immediately lead another heart.  If North ducks, so does declarer, and the defense can't enter North.  If North goes up, Declarer wins the A, and leads the 5.  Now the defense is stuck; because South's remaining spot is necessarily larger than the heart six, the unblocking play from before doesn't work.  Thus North must overtake-- but this sets up declarer's 7, the extra trick that was needed!

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