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Difficult Evaluation
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In a round of 16 match in the Open trials, you face a difficult evaluation problem on a Relay auction.

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

South
A1095
AKQ
J3
AQ94
W
N
E
S
P
1
P
2
P
2
P
2
P
2NT
P
3
P
?

1: Strong, artificial

2: 5+ diamonds, no major, at most 4 clubs, 9+ points

2: Relay

2: No second suit, spades shortest suit (might be 6-3-2-2 with doubleton spade)

2NT: Relay

3: Generic 5-3-3-2, so exactly 2=3=5=3

Avialable to you are:

3: Control ask (A = 2, K = 1). Partner responds in steps as follows: 0-2, 3, 4, 5, 6, etc. After the response, you may sign off or initiate denial cue-bidding, where partner shows his exact location of honors.

3: Also a control ask. The difference is that partner will bid 3NT with 0-3 controls. He will also bid 3NT with 4 controls but less than 13 HCP. Thus, he will go beyond 3NT only if he has 4 controls and 13+ HCP or 5+ controls (which we call a super-positive). If he is going beyond 3NT he shows his number of controls, starting with 4 = 4 controls, etc. We call this bid a weak relay.

3NT: Signoff. This is a very minimal hand, not even worth a weak relay. Partner needs about a queen more than a minimal super-positive to override. Thus, with 4 controls and less than 15 HCP or 5 controls and nothing else partner will pass.

4: Puppet to 4, to be followed with an RKC call.

4: Puppet to 4, to be followed by placing the contract.

Higher bids: Natural slam tries.

Your call?

South
A1095
AKQ
J3
AQ94
W
N
E
S
P
1
P
2
P
2
P
2
P
2NT
P
3
P
?

The hands don't fit well. Still, you have a powerful hand opposite a positive response. You can't afford to sign off with 3NT. If partner has something like Kx xxx AKxxx Kxx he will pass (5 controls but nothing extra), and you want to be in slam opposite that.

On the other hand, the normal control ask of 3 is too risky. Partner's response with 4 controls is 4. That could get you too high. Picture him with something like Kx xxx Axxxx Kxx, and 3NT is quite high enough.

The weak relay of 3 hits the spot. If partner has 5 controls, his barebones hand will be Kx xxx AKxxx Kxx, and all you need is 4 diamond tricks, which you will get if the diamonds are 3-3 or if they are 4-2 with East having the queen. If partner has 4 controls, he won't be bidding higher than 3NT unless he has a queen or two. If his decision is close, he will like having the queen in his long suit. Opposite something like Kx xxx AKQxx xxx, you won't mind being in slam, and he might have a little more (like a black jack) which makes slam very good. If he has only 3 controls, he would need a lot of fillers for slam to be good, so you won't mind stopping.

You choose to bid 3. The bidding continues

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

3: Control ask

3NT: 3 controls

Your bids now mean:

4: Initiates denial cue-bidding. Partner will show where his honors are, starting with his longest suit and going down (ties going to higher-ranking suit). Since you know his exact distribution, you will know the order he is scanning his suits. He keeps skipping steps until he hits a suit he doesn't have a scanned-for card. For example, suppose his hand is: xx xxx AQxxx Kxx. He would be saying: (yes in diamonds, no in hearts), so his bid would be 4.

4: Puppet to 4 for signoff. Your next bid places the contract.

Higher bids: Natural slam tries.

Your call?

South
A1095
AKQ
J3
AQ94
W
N
E
S
P
1
P
2
P
2
P
2
P
2NT
P
3
P
3
P
3NT
P
?

Denial cue-bidding isn't going to accomplish anything. If you want to move to slam, the only sensible approach is a power invite of 4NT. The best you could hope for is something like Qx xxx AKQxx Jxx, and even opposite that slam isn't laydown. Take away any of the queens or jacks, and slam becomes pretty bad. In addition, if partner is minimal 9 tricks might be the limit of the hand. It looks wisest to give up on slam and pass 3NT.

You choose to bid 4NT, ending the auction.

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

West leads the 3. Fourth best leads vs. notrump.

North
K8
J106
A10762
J65
South
A1095
AKQ
J3
AQ94
W
N
E
S
P
1
P
2
P
2
P
2
P
2NT
P
3
P
3
P
3NT
P
4NT
P
P
P

You play small from dummy. East plays the 7, and you win the 9. How do you start?

North
K8
J106
A10762
J6
South
A1095
AKQ
J3
AQ4
W
N
E
S
P
1
P
2
P
2
P
2
P
2NT
P
3
P
3
P
3NT
P
4NT
P
P
P

You can definitely take 2 spades, 3 hearts, 1 diamond, and 3 clubs. The diamond suit could produce another trick if the KQ are onside or if the suit splits 3-3. The spade suit could produce another trick if the same hand has the QJ of spades and you guess which hand, or if one opponent has honor-doubleton or tripleton and you play spades through that opponent. The club suit could produce another trick if East has the king of clubs, which isn't likely but it is possible that West's lead was from 1083 in which case East might not have put up the king.

Unfortunately, there doesn't appear to be a convenient way to combine all chances. Assuming West has the king of clubs, you will have to give up a club trick in order to get your third club winner. If you go for a 3-3 diamond split, you will have to duck two rounds of diamonds, and if the suit turns out to be 4-2 you will no longer be able to take advantage of a favorable spade layout since you will have lost a club trick and 2 diamond tricks.

If you go after diamonds, what is the best approach? Leading the jack may cause problems. West will surely cover whether he has one honor or both, and then what do you do? If you win and then lead up to the 10, this could give the opponents a lot of diamond tricks. If you duck and then later finesse, the honors may be split and you will have lost two diamond tricks and not have a chance to go after spades. It is better to lead a small diamond to the 10. If West has both honors, you are home. Otherwise you will have lost only one diamond trick, and your other options will still be open.

If you go after spades, what is the best approach? West appears to have long clubs, so he is probably shorter in spades. Playing a spade to the 8 will get you 3 spade tricks if West has honor-doubleton or tripleton.

Which should you try first? A diamond to the 10 looks best. This will let you retain your king of spades for a later entry if needed. If you play a spade to the 8 and East wins and returns a spade, things could get sticky.

It might look like there is a danger that East will continue diamonds and set up some diamond tricks for the defense. Realistically, this isn't likely. Picture East holding KQ98 of diamonds. From his point of view you started with Jxx, and a diamond return would be disastrous. East would have to have started with 5 diamonds to know a diamond return is safe.

Suppose you lead a diamond to the 10, losing to the queen, and East returns a heart. Would you try diamonds or spades in search of your tenth trick?

North
K8
J10
A762
J6
South
A1095
KQ
J
AQ4
W
N
E
S
P
1
P
2
P
2
P
2
P
2NT
P
3
P
3
P
3NT
P
4NT
P
P
P

If you try diamonds, you need a 3-3 diamond split. The odds on that are about 36%, perhaps a bit better since West doesn't have both honors.

If you try spades, that will succeed when West has both honors -- on the order of 25% (ignoring that West has long clubs). Of the roughly 50% of times when the spade honors are split, West will have a doubleton or tripleton about half the time. That is another 25% of winning chances, for a total of around 50%. It is clear that the chances of an extra spade trick will be better than the chances of an extra diamond trick.

In fact, you choose to lead a spade to the 8 at trick 2. East wins the jack, and returns a heart. Which honor do you win with?

North
K
J106
A10762
J6
South
A109
AKQ
J3
AQ4
W
N
E
S
P
1
P
2
P
2
P
2
P
2NT
P
3
P
3
P
3NT
P
4NT
P
P
P

It probably isn't going to matter, but the best technique is to win the king. If you win the ace you might as well be showing the opponents the king, since without the king you would surely play small. When you win the king, either opponent might think his partner has the ace.

You win the king of hearts. What do you do next?

North
K
J10
A10762
J6
South
A109
AQ
J3
AQ4
W
N
E
S
P
1
P
2
P
2
P
2
P
2NT
P
3
P
3
P
3NT
P
4NT
P
P
P

You need to make your diamond play now, while the king of spades is there in dummy. If you fail to do so, you might not be able to take advantage of West having both diamond honors. There is no rush to unblock the spades or make a club play, as you have several hand entries.

You choose to lead a spade to the king, both opponents following small. Now what?

North
J10
A10762
J6
South
A10
AQ
J3
AQ4
W
N
E
S
P
1
P
2
P
2
P
2
P
2NT
P
3
P
3
P
3NT
P
4NT
P
P
P

As long as you are in dummy you might as well lead a club. You are going to have to set up a club trick at some point, and it is possible that East has the king of clubs.

You lead the jack of clubs. East discards a heart. You play small. West wins the king, and returns a heart. What do you try now?

North
J
A10762
6
South
A10
Q
J3
AQ
W
N
E
S
P
1
P
2
P
2
P
2
P
2NT
P
3
P
3
P
3NT
P
4NT
P
P
P

If the diamond honors are split, you will need the queen of spades to be coming down. However, if the diamond honors are in the same hand you have chances by going after diamonds.

Leading the jack might work.  If West covers, you can duck and play him for both honors. If East has both honors as well as the spade guard, you will have him in a spade-diamond squeeze. The main probem occurs when West covers, you duck, and West comes back a diamond. Now you will have to commit yourself, and if you take the diamond finesse you may find that the spades were good all the time. By now West will have enough information to find this defense from any layout where he has one or both diamond honors. Unfortunately, you can't test the spades first, as that blows some of your otherwise favorable positions.

Suppose you lead a small diamond to the 10. If West has both honors he can defeat the contract by splitting, although this might not be apparent. If East has the diamond guard he can break up a squeeze with a diamond return, and by now he will know enough about the hand to find this defense.

You could cash one round of clubs to get another discard from East. But that isn't going to tell you anything, since East can afford to discard a heart.

All things considered, it looks best to lead the jack of diamonds, ducking, and if West covers and leads back a diamond you will just have to get it right.

You choose to lead a small diamond. West plays small. You put in the 10, and it holds. You have 10 tricks. The full hand is:

West
76
983
KQ4
K10832
North
K8
J106
A10762
J65
East
QJ432
7542
985
7
South
A1095
AKQ
J3
AQ94
W
N
E
S
 
P
1
P
2
P
2
P
2
P
2N
P
3
P
3
P
3N
P
4N
P
P
P
D
4NT South
NS: 0 EW: 0
3
5
7
9
3
1
0
5
6
8
J
2
1
1
2
K
3
6
3
2
1
9
7
K
2
1
3
1
J
4
4
K
0
3
2
8
10
5
A
3
4
2
3
4
10
7

Should the defense have done differently?

West
76
983
KQ4
K10832
North
K8
J106
A10762
J65
East
QJ432
7542
985
7
South
A1095
AKQ
J3
AQ94
W
N
E
S
 
P
1
P
2
P
2
P
2
P
2N
P
3
P
3
P
3N
P
4N
P
P
P
D
4NT South
NS: 0 EW: 0
3
5
7
9
3
1
0
5
6
8
J
2
1
1
2
K
3
6
3
2
1
9
7
K
2
1
3
1
J
4
4
K
0
3
2
8
10
5
A
3
4
2
3
4
10
7

West has to choose between an aggessive lead and a passive lead. From his point of view the diamonds lie favorably for declarer. Also, South is trying for slam knowing North's shape and controls. South could have anything, but it doesn't appear that West will be able to defeat 4NT going passively if South is interested in 6NT. It turns out a passive lead would have been better, but that is only because South overbid.

At the point South led the diamond, West should have had a count of the hand. South is known to have 4 clubs, and certainly has 4 spades since he is attacking the spade suit. If South started with 3 diamonds and 2 hearts he would have been attacking diamonds a lot earlier, so South's hand figures to be what it is. West can't know about the jack of diamonds, but if South has it West should see that splitting will block the suit.

Should E-W have been in the auction?

West
76
983
KQ4
K10832
North
K8
J106
A10762
J65
East
QJ432
7542
985
7
South
A1095
AKQ
J3
AQ94
W
N
E
S
 
P
1
P
2
P
2
P
2
P
2N
P
3
P
3
P
3N
P
4N
P
P
P
D
4NT South
NS: 0 EW: 0
3
5
7
9
3
1
0
5
6
8
J
2
1
1
2
K
3
6
3
2
1
9
7
K
2
1
3
1
J
4
4
K
0
3
2
8
10
5
A
3
4
2
3
4
10
7

At favorable vulnerability, there is a lot to be said for opening the East hand a weak 2. Sure, it could backfire, but there is a lot more to be gained than to be lost. Had East opened 2, it is easy to see how N-S might have gotten way overboard.

West might have overcalled 2. Once again, this is trading in on the vulnerability. That vulnerability means an overcall will usually gain more when it works than it will lose when it goes badly.

When playing a relay system, it is vital for the relayer to picture what is known about partner's hand and plan his sequence appropriately. South failed to do so here, and landed in a treacherous contract.

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