Join Bridge Winners
Change of Heart
(Page of 13)

In a round-robin match in the Open Trials, you face a difficult responding problem.

E-W vul, South deals. As North, you hold:

North
AK3
A103
J982
1093
W
N
E
S
1
P
?

1: 11-15, 2+ diamonds. If balanced, 13-15 (since 1NT would be 10-12).

Meanings of some actions would be:

2: Inverted. Forcing to 3. Denies a 4-card major. Partner will assume you have 5+ diamonds, since he might have a doubleton. Partner's rebids will tend to be stopper-showing, since your side can't have an 8-card major-suit fit. Jumps by partner would be splinters.

2NT: Natural invite. 3 of a minor rebid by partner would be non-forcing.

3NT: The end of the auction unless partner is very distributional.

Your call?

North
AK3
A103
J982
1093
W
N
E
S
1
P
?

The hand looks too strong for 2NT. Partner will be evaluating in the context of his assumed 13-15 if he is balanced, and you could easily miss a good game.

3NT is possible. The problem is that you have no club stopper. If partner is short in clubs, you probably don't want to be playing notrump.

Perhaps the inverted minor raise is best. Partner will be bidding stoppers, so if there is a club problem you will probably be able to diagnose that. It is true that partner will think you have 5+ diamonds, but that isn't likely to matter. The question is whether or not 3NT is a reasonable contract, and this is the way to find out.

You bid 2: The bidding continues:

W
N
E
S
1
P
2
P
2
P
?

2: Inverted

Your call?

North
AK3
A103
J982
1093
W
N
E
S
1
P
2
P
2
P
?

Partner has a heart stopper, but he might not have a club stopper. It is clear to bid 2. If partner has a club stopper he will certainly bid 2NT, and you can get to 3NT from his side, which is probably best. If he doesn't bid 2NT, you can reconsider.

You bid 2. The bidding continues:

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

Your call?

North
AK3
A103
J982
1093
W
N
E
S
1
P
2
P
2
P
2
P
3
P
?

You now know that partner doesn't have a club stopper. If he had one, he would have bid 2NT. Even with a partial stopper he might have tried 3. It looks like 3NT is out.

Where can you play? You might have a 4-3 major-suit fit, but even if you do that doesn't look promising. 5 has to be asking for too much since you had a marginal game drive in the first place.

It looks like a good time for a change of heart. Even though you were planning on getting to game, circumstances have changed. No game looks promising. While partner doesn't have to have 4 diamonds, he is likely to have that particularly since he probably has only a doubleton club. 3 could easily be the par contract.

You pass, ending the auction.

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

You get to pick up partner's hand and see how you did with your imaginative sequence.

West leads the 7. Third and fifth leads. Standard carding.

North
AK3
A103
J982
1093
South
J87
KQJ5
AQ3
642
W
N
E
S
1
P
2
P
2
P
2
P
3
P
P
P

How do you handle trick 1?

North
AK3
A103
J982
1093
South
J87
KQJ5
AQ3
642
W
N
E
S
1
P
2
P
2
P
2
P
3
P
P
P

You are going to want to win this trick in dummy in order to make a diamond play. You would rather not see a club shift if the diamond finesse loses. West should find the shift if he was listening to the bidding, but you never know.

If you win the 10, West will know exactly what is going on. If you win the ace of hearts and play small from your hand, again West should be able to work out the position.

Best is to win the ace of hearts and play the jack from your hand. This would be consistent with KQJ tripleton in your hand. If West thinks this is the case, he might not see the urgency for a club shift.

You choose to win with the 10, East playing the 2. What do you do at trick 2?

North
AK3
A3
J982
1093
South
J87
KQJ
AQ3
642
W
N
E
S
1
P
2
P
2
P
2
P
3
P
P
P

Clearly you will play on diamonds. The question is how you should attack the suit.

You need 3 diamond tricks. That will get you 9 tricks (2 spades, 4 hearts, 3 diamonds). If the suit is 3-3, you have those tricks regardless of how you play the suit. It is the 4-2 splits you must be concerned about.

Low to the queen will work fine when king-doubleton is onside. Otherwise, it will fail. Note that there is a danger of 4 rounds of clubs. For example, suppose West has Kxxx of diamonds. He will duck if you lead a diamond to the queen. If you then cash the ace of diamonds and play another diamond, he can tap you.

Leading the jack is better. This gains when East has K10xx of diamonds. If East has Kxxx, he probably won't cover, since for all he knows his partner has a stiff ace or queen. Even when East has 10x this will succeed, since West will be winning the second round of diamonds, not the third round.

You choose to lead a low diamond to the queen. West wins the king of diamonds, and plays ace of clubs, queen of clubs, and a club to East's king. East comes back with the 4 which you win with dummy's ace to unblock the suit. West plays the 6. Now you lead a diamond to your ace, planning on then playing a third round of diamonds.

If the opponents play only small diamonds, will you play for the drop or take the finesse for the 10?

North
AK3
3
J9
South
J87
KQ
3
W
N
E
S
1
P
2
P
2
P
2
P
3
P
P
P

As far as percentages go, it is pretty much a tossup. West appears to have started with a doubleton heart, increasing the chances that he started with 4 diamonds.

There is a clue in the defense. If the diamonds are 4-2, the defense could have arranged to lead a fourth round of clubs. This would get them a trump trick wherever you ruffed. Since they didn't adopt this defense, that is an indication that the diamonds are 3-3.

In fact, East shows out on the second round of diamonds, discarding the 8 of hearts. How do you continue?

North
AK3
3
J9
South
J87
KQ
3
W
N
E
S
1
P
2
P
2
P
2
P
3
P
P
P

Playing on hearts won't work. West probably has a doubleton heart. He can ruff the third round of hearts, and you still potentially have another trump loser and a spade loser. You must use your entry to take the marked diamond finesse now. You will get out for down 1 if West started with 2-3-5-3 distribution. Even when West has a doubleton heart, you may be able to end-play him if he has the queen of spades. He will always be getting one more trump trick, but you cannot afford to let him score two trump tricks.

You lead a trump to dummy's 9. East discards another heart. You cash the jack of diamonds, East discarding a spade. What do you discard from your hand?

North
AK3
3
J
South
J87
KQ
W
N
E
S
1
P
2
P
2
P
2
P
3
P
P
P

You don't need both hearts. Keeping the jack of spades guarded may be important in case an opponent is down to queen-doubleton.

You discard a heart. What do you do next?

North
AK3
3
South
J87
K
W
N
E
S
1
P
2
P
2
P
2
P
3
P
P
P

You know West has the long trump. If he has the fourth club, you are always down 2. Otherwise, you might have an end-play. Your AK of spades won't run away from you. It can't hurt to play a heart and see what happens.

You lead a heart. East discards a club, and West ruffs. West leads a spade. Do you go up or play small?

North
AK3
South
J87
W
N
E
S
1
P
2
P
2
P
2
P
3
P
P
P

East has discarded his last club, so the opponents are both down to 3 spades. It can't hurt to play small, hoping West has the queen.

You play small. East wins the queen, and you are down 2. The full hand is:

West
652
76
K10764
AQ5
North
AK3
A103
J982
1093
East
Q1094
9842
5
KJ87
South
J87
KQJ5
AQ3
642
W
N
E
S
1
P
2
P
2
P
2
P
3
P
P
P
D
3 South
NS: 0 EW: 0
7
10
2
5
1
1
0
2
5
Q
K
0
1
1
A
3
8
2
0
1
2
Q
9
7
4
0
1
3
5
10
K
6
2
1
4
4
J
6
A
1
2
4
8
8
A
4
3
3
4
3
6
9
9
1
4
4
J
4
Q
7
1
5
4
3
J
K
10
0
5
5
2
3
Q
11

How was the lead and defense?

West
652
76
K10764
AQ5
North
AK3
A103
J982
1093
East
Q1094
9842
5
KJ87
South
J87
KQJ5
AQ3
642
W
N
E
S
1
P
2
P
2
P
2
P
3
P
P
P
D
3 South
NS: 0 EW: 0
7
10
2
5
1
1
0
2
5
Q
K
0
1
1
A
3
8
2
0
1
2
Q
9
7
4
0
1
3
5
10
K
6
2
1
4
4
J
6
A
1
2
4
8
8
A
4
3
3
4
3
6
9
9
1
4
4
J
4
Q
7
1
5
4
3
J
K
10
0
5
5
2
3
Q
11

West wasn't listening to the bidding. If South had the guarded king of clubs, he would have an automatic 2NT call, so a club lead can't cost. There may be a discard of a losing club available. West should lead the ace of clubs.

East had an interesting discarding problem at the end. If his partner has the jack of spades nothing matters, but what if declarer has the jack of spades? His actual defense of discarding his club guarantees down 2. However, if he discards another spade declarer may play West for the queen of spades and go down 3.

All the players have the count on the hand at this point. If East doesn't have the queen of spades then clearly he will discard a spade, since discarding a club is a concession as it is then safe for declarer to play small. Discarding a spade risks letting declarer get out for down 1 if declarer goes with the 4 to 3 odds.

Let's suppose that declarer knows what East's strategy is when East holds the queen of spades:

If East never discards a spade when he holds the queen, declarer will know the end-play has worked when East does discard a spade. Thus, declarer will get out for down 1 3/7 of the time, and be down 2 4/7 of the time.

If East always discards a spade when he holds the queen, the percentage play for declarer will be to play for the drop. He will be down 1 4/7 of the time and down 2 3/7 of the time.

I'm pretty sure that from a game-theoretic point of view the correct strategy is a mixed strategy, which involves discarding a spade some percentage of the time. If that is the case declarer's correct strategy will also be a mixed strategy, playing for the drop some percentage of the time. Note that if declarer takes the finesse when East has come down to Qx of spades, declarer will be down 3. What these optimal mixed strategies are I will leave to the mathematicians.

How was South's auction?

West
652
76
K10764
AQ5
North
AK3
A103
J982
1093
East
Q1094
9842
5
KJ87
South
J87
KQJ5
AQ3
642
W
N
E
S
1
P
2
P
2
P
2
P
3
P
P
P
D
3 South
NS: 0 EW: 0
7
10
2
5
1
1
0
2
5
Q
K
0
1
1
A
3
8
2
0
1
2
Q
9
7
4
0
1
3
5
10
K
6
2
1
4
4
J
6
A
1
2
4
8
8
A
4
3
3
4
3
6
9
9
1
4
4
J
4
Q
7
1
5
4
3
J
K
10
0
5
5
2
3
Q
11

The 1 opening was systematically mandatory, and the 2 call was clear since that is where South's stoppers are. On his third call, South might have bid 3 rather than 3. This would show less than a full club stopper (since no 2NT call), but more than a worthless doubleton. Opposite that, North might try 3NT, which is probably a better contract than 3.

When partner's hand is limited, you are the captain. You don't always have to have what you say you have, and you don't always have to follow through with a game force you may have created. It is your job to do what gets you to the right contract, however you get there.

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