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Modified Vacant Spaces
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In a quarter-final match in the Senior trials for USA2, you have to deal with enemy preemption vs. your strong 1.

N-S vul, East deals. As South, you hold:

South
AK10
A4
J
AJ109862
W
N
E
S
P
1
2
X
3
?

1: 16+

DBL: About 7-8 HCP

Pass would not be forcing

Double would be takeout

4 would be forcing

5 would show no slam interest

Your call?

South
AK10
A4
J
AJ109862
W
N
E
S
P
1
2
X
3
?

You are too strong to risk missing game, and you have the wrong shape for a takeout double. Even though there probably is no slam, there is no need to jump to 5. Partner might have a 5-card spade suit, in which case you probably belong in 4.

You bid 4. The bidding continues:

W
N
E
S
P
1
2
X
3
4
P
4NT
P
?

4NT is a slam try in clubs. 4 and 4 would have been natural. 4 would have been RKC in clubs. Thus, this is partner's only slam try.

Your call?

South
AK10
A4
J
AJ109862
W
N
E
S
P
1
2
X
3
4
P
4NT
P
?

Partner says he likes his hand with the 4NT call. However, he is limited by his initial double.

Can there be a slam? Let's give partner perfect working cards of king of clubs and ace of diamonds. He can't have much more, or he wouldn't have initially doubled. Given those cards, you still have a likely spade loser and heart loser unless partner has a singleton heart or a doubleton spade, and you can't count on him for that. Also, partner's cards might not be those perfect cards. While slam is possible, your percentage action is to sign off at 5.

You choose to bid 6, ending the auction.

W
N
E
S
P
1
2
X
3
4
P
4NT
P
6
P
P
P

West leads the 8. Third and fifth leads.

North
9753
J5
A54
Q754
South
AK10
A4
J
AJ109862
W
N
E
S
P
1
2
X
3
4
P
4NT
P
6
P
P
P

What do you play from dummy?

North
9753
J5
A54
Q754
South
AK10
A4
J
AJ109862
W
N
E
S
P
1
2
X
3
4
P
4NT
P
6
P
P
P

It is inconceivable that West would have underled the KQ of hearts, so playing the jack is futile. Playing small shouldn't accomplish anything since East should be able to read the 8 as third best from a 6-card suit, so if East has something like Q9x of hearts he will know that he doesn't have to go up queen. This shows an intrinsic advantage of third and fifth leads vs. fourth best leads. If West had led fourth best, it would be more difficult for East to work out to not spend the queen. Still, players have been known to make mistakes, so you might as well play small. If you play the jack, East can't make a mistake.

You choose to pay the jack of hearts. East covers with the king, and you win the ace. How do you proceed?

North
9753
5
A54
Q754
South
AK10
4
J
AJ109862
W
N
E
S
P
1
2
X
3
4
P
4NT
P
6
P
P
P

Prospects are dim. You have to get the clubs right for starters. In addition, you will need to avoid a spade loser.

You will probably need to take two spade finesses. Since you hold the 6 and 2, you have two late trump entries to dummy. Therefore, rather than committing yourself immediately you might as well cross to the ace of diamonds and lead the queen of clubs. Of course your expert opponent should know not to cover with Kx since you aren't bidding this way with A109xx of clubs, but even the best players have been known to make a mistake. They can't make a mistake if you don't give them a chance. Also, even when East doesn't cover your table feel might help you diagnose the club position.

You cross to the ace of diamonds, West covering your jack with the queen and East playing the 2. When you lead the queen of clubs, East plays the 3. You do not pick up any sense one way or the other as to whether or not he has the king. Which way do you go?

North
9753
5
54
Q754
South
AK10
4
AJ109862
W
N
E
S
P
1
2
X
3
4
P
4NT
P
6
P
P
P

The evidence from the bidding and the opening lead indicates that West has 6 hearts and East has 3 hearts. You can assume that East holds the 3, since if West has that card it won't matter what you do in clubs. That is 6 known cards in the West hand, 4 known cards in the East hand, leaving West with 7 vacant spaces and East with 9 vacant spaces. From this information it appears that East is a 9 to 7 favorite to hold the king of clubs, so the club finesse is the percentage play to avoid a club loser. Since you have the 6 and 2 for late entries to dummy, dummy entries don't figure to be a problem.

It isn't as simple as that. You not only have to avoid a club loser, you have to avoid a spade loser. This means you need East to hold the QJ of spades, so you might as well plan your play on that assumption. Looking at the modified vacant spaces, since you "know" that East has the queen and jack of spades that means there are 7 vacant spaces in each hand. Therefore, if the club play matters and the contract can be made, vacant spaces analysis indicates that either opponent is equally likely to hold the king of clubs.

There is more. Since East is "known" to hold QJ of spades, that means there is a fair chance that West has only 2 spades. West covered the jack of diamonds with the queen, making it likely that he has KQ or Q10. If West were 6-5 in the red suits with a relatively weak heart suit and a decent diamond suit, he might have taken an approach which gets both suits in the auction rather than bidding 2. That tilts the odds in favor of his not having a club void, so the percentage play is to go up ace.

You choose to finesse, naturally playing the 10 so as to retain both club entries to dummy. You are right, as West discards the 2. What next?

North
9753
5
54
754
South
AK10
4
AJ9862
W
N
E
S
P
1
2
X
3
4
P
4NT
P
6
P
P
P

Since you don't need to repeat the finesse, you might as well ruff a diamond. If you can strip the diamonds, you may be able to force the opponents to break the spade suit. Naturally you will ruff with an intermediate club spot, again retaining your small clubs.

You ruff a diamond with the 9, and cash the ace of clubs. Now what?

North
9753
5
5
75
South
AK10
4
J862
W
N
E
S
P
1
2
X
3
4
P
4NT
P
6
P
P
P

You are probably going to need both spade honors onside, but meanwhile you can give the opponents a chance to help you out. It won't do any good to exit with a heart, since whichever opponent wins will have an easy diamond exit. Your best chance is to cross to dummy with a trump, ruff a diamond high, and exit with a heart. This costs you a dummy entry for one of your spade finesses, but since the opponents have no choice but to lead spades, you will be able to take your spade finesses. Meanwhile, maybe the defense will make an unexpected mistake.

You choose to exit with a heart. East wins the 10, and leads a spade. Your play?

North
9753
5
75
South
AK10
J862
W
N
E
S
P
1
2
X
3
4
P
4NT
P
6
P
P
P

Going up ace is right only if West has singleton honor or QJ doubleton. It is far more likely that East has both honors. You can't draw any inference from the spade shift, since East can see that you have two entries for two spade finesses.

You try the 10. West wins, and you are down 1. The full hand is

West
QJ8
Q98632
KQ108
North
9753
J5
A54
Q754
East
642
K107
97632
K3
South
AK10
A4
J
AJ109862
W
N
E
S
P
1
2
X
3
4
P
4NT
P
6
P
P
P
D
6 South
NS: 0 EW: 0
8
J
K
A
3
1
0
J
Q
A
2
1
2
0
Q
3
10
2
1
3
0
4
3
9
K
3
4
0
A
3
4
K
3
5
0
4
9
5
10
2
5
1
2
10
J
7

What do you think about the opening lead?

West
QJ8
Q98632
KQ108
North
9753
J5
A54
Q754
East
642
K107
97632
K3
South
AK10
A4
J
AJ109862
W
N
E
S
P
1
2
X
3
4
P
4NT
P
6
P
P
P
D
6 South
NS: 0 EW: 0
8
J
K
A
3
1
0
J
Q
A
2
1
2
0
Q
3
10
2
1
3
0
4
3
9
K
3
4
0
A
3
4
K
3
5
0
4
9
5
10
2
5
1
2
10
J
7

If the goal is to set up a trick quickly, the diamond lead is clear. If the goal is safety, West is correct to lead a heart. With West holding some spade stuff he decided that safety had priority, as the diamond lead might find the jack in dummy and the ace in declarer's hand. It was ironic that it was the heart lead, not the diamond lead, which established a trick, and that if declarer gets the clubs right, he could set up a late spade trick for a discard.

Do you agree with the E-W auction?

West
QJ8
Q98632
KQ108
North
9753
J5
A54
Q754
East
642
K107
97632
K3
South
AK10
A4
J
AJ109862
W
N
E
S
P
1
2
X
3
4
P
4NT
P
6
P
P
P
D
6 South
NS: 0 EW: 0
8
J
K
A
3
1
0
J
Q
A
2
1
2
0
Q
3
10
2
1
3
0
4
3
9
K
3
4
0
A
3
4
K
3
5
0
4
9
5
10
2
5
1
2
10
J
7

Clearly West must bid some number of hearts. How many he should bid is not clear. The favorable vulnerability makes preempting more attractive, and even 3 would be quite reasonable. Even if you go too high, it is often difficult for the opponents to get you after an artificial strong 1 opening.

East's 3 call looks on target. That should be okay. If he bids higher it is too easy for the opponents to double, and N-S might not have a game.

West has enough defense that he doesn't expect 6 to make. If the auction were such that partner might be saving, it would be important for him to make a "shut up partner" double. With East bidding only 3 it is clear that East isn't going to be saving, so West doesn't need to shut him up.

Was North's bidding accurate?

West
QJ8
Q98632
KQ108
North
9753
J5
A54
Q754
East
642
K107
97632
K3
South
AK10
A4
J
AJ109862
W
N
E
S
P
1
2
X
3
4
P
4NT
P
6
P
P
P
D
6 South
NS: 0 EW: 0
8
J
K
A
3
1
0
J
Q
A
2
1
2
0
Q
3
10
2
1
3
0
4
3
9
K
3
4
0
A
3
4
K
3
5
0
4
9
5
10
2
5
1
2
10
J
7

The double of 2 is clear. North has exactly the right strength.

North has a pretty good hand in the context of what he has shown, with the queen of trumps and an ace. He isn't strong enough to drive to slam, but simply bidding 5 doesn't do justice to his hand. The 4NT slam try looks on target.

At the other table, after the same start, East chose to bid 4. South naturally bid 5, and North judged well to pass. West also led the 8, and declarer faced the same club guess. However, since his goal was 11 tricks, not 12, he had different information about the enemy hands. While in 6 it is necessary to assume East has both spade honors, playing in 5 the opposite is true. If East has both spade honors the contract will make regardless of the club play, therefore declarer should assume that West has at least one of the spade honors. If West has one spade honor, there are 6 vacant spaces in the West hand (he has 6 hearts and that spade honor) and 9 vacant spaces in the East hand (he has 3 hearts and and the 3 of clubs), making the club finesse the percentage play. However declarer chose to play for the drop, perhaps influenced by the jump to 4 with only 3-card support. Thus, the board was pushed.

How should 4NT be played when partner has bid 4 over an enemy 3-level preempt? Clearly RKC doesn't make sense, since a 5 response will push the pair into a slam which may be off 2 key cards. Many pairs play 4NT as natural, but this is questionable. It is possible that there are exactly 10 tricks available in both clubs and notrump in which case 4NT is the winning contract, but that isn't likely and may be difficult to diagnose. We believe that having both RKC and a slam try available is more important.

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