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All Four Suits
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In a semi-final match in the Senior trials for USA2, you have to decide how high to bid with a long suit.

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

East
Q72
KQJ10763
4
K2
W
N
E
S
1NT
P
2NT
?

1NT: 14-16

2NT: Puppet Stayman

Your call?

East
Q72
KQJ10763
4
K2
W
N
E
S
1NT
P
2NT
?

Clearly you are going to bid some number of hearts. The question is whether you should bid 3 or 4.

North has announced game-going strength with his 2NT Puppet Stayman call. Of course that doesn't mean the opponents necessarily can make a game, but they will either be bidding a game or doubling you. You aren't going to buy the contract for 3 if you bid it.

You have 6 sure tricks in your own hand. That means that if partner has no help at all 4 will go for 800. If partner has nothing, you aren't going to defeat 3NT (or 4 if they have an 8-card spade fit). So, even if you go for 800 you won't lose too many IMPs. If partner has a trick for you or if the opponents have to give you a trick, -500 will be fine assuming they can make a game.

Is there a danger that you can defeat their best game? Possible, but not likely. You have 11 HCP, and might not even take a trick on defense. That doesn't leave much for partner since North has announced game-going values. If the opponents play 3NT, they will be able to hold up in hearts until your partner is out of hearts, and it will be difficult for you to gain the lead. If they have an 8-card spade fit, that figures to play fine for them. 4 doubled is unlikely to be a phantom save.

A 3 call will get you a heart lead against 3NT, but otherwise it won't do much damage to the opponents. If South has a 5-card spade suit he will bid it, and if that is what North was looking for they will have arrived. If South doesn't have 5 spades he will pass, and now North can bid 3 with a 4-card suit. South will know this is a 4-card suit, since if North had 5 spades he would have started with a transfer. Therefore, the opponents will be able to find out for sure whether or not they have a spade fit.

4 does a lot more damage. South might bid 4 with a 5-card spade suit, but that could be wrong. It will be very difficult for them to locate a 4-4 spade fit. They can no longer play 3NT, so they may have to double you whatever they have.

It looks like gobbling up the extra space with 4 is a good bet.

You choose to bid 3. The bidding continues:

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

Your call?

East
Q72
KQJ10763
4
K2
W
N
E
S
1NT
P
2NT
3
3
P
4
?

Clearly you must pass. 5 could easily go for too much, and you might be able to defeat 4. Worse, the opponents know exactly where they stand, so if you save they should be able to make the right decision. Last round was the time to put them under pressure. Now is too late.

You pass, ending the auction.

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

Partner leads the 9:

North
J108
85
AK865
A73
East
Q72
KQJ10763
4
K2
W
N
E
S
1NT
P
2NT
3
3
P
4
P
P
P

You play suit-preference at trick 1. 10, 9, 8 (by priority) is suit-preference high. 2, 3, 4 (by priority) is suit-preference low. 6, 5, 7 (by priority) is encouraging.

Your play?

North
J108
85
AK865
A73
East
Q72
KQJ10763
4
K2
W
N
E
S
1NT
P
2NT
3
3
P
4
P
P
P

There isn't any need to signal partner anything. He has very little strength, and is unlikely to be in until possibly late in the hand. Any signal you give will probably be more helpful to declarer than partner.

It is probably better to simply overtake partner's 9. If nothing else, this doesn't give declarer the option of which opponent he prefers to win the heart trick if he has a doubleton.

You choose to play the 3. Declarer wins the ace. Declarer now leads the 3 to the 5, jack, and your queen. What do you lead back?

North
108
8
AK865
A73
East
72
KQJ1076
4
K2
W
N
E
S
1NT
P
2NT
3
3
P
4
P
P
P

This is a fascinating problem. Offhand, it appears that all four suits are potential candidates.

It might be right to return a spade. This could be effective if declarer has 3 hearts and needs to ruff a heart in dummy.

It might be right to cash a heart. If declarer has a doubleton heart, this will eliminate the danger of declarer discarding his heart loser.

It might be right to return a diamond. This could work if partner can get in and give you a diamond ruff.

It might be right to return a club. This could both set up a club trick for your side and knock out dummy's entry to the diamonds.

Partner doesn't have much. There are only 17 HCP you can't see, and declarer presumably has 14 of them for his 1NT opener. That leaves partner a maximum of 3 HCP.

In the unlikely event that partner has the king of spades, declarer has everything else. That means you aren't beating the contract, since dummy's diamonds will be good and the most you can expect to take is 2 spades and 1 heart. You have to assume that declarer has the king of spades.

What can you figure out from declarer's line of play? It looks like he is counting on the diamond suit coming home for a lot of tricks if he is willing to concede the queen of spades without a fight. That places the queen of diamonds in declarer's hand. If declarer also has the jack of diamonds you don't have much chance, so you can mentally give partner that card. You can also hope that partner has the queen of clubs, as otherwise it is hard to see how declarer won't have 10 tricks.

What about declarer's distribution? You can assume from the 1NT opening that declarer is 5-3-3-2 in some order. If declarer has a third heart, it seems like he would have led a heart at trick 2 in order to prepare to ruff a heart in dummy and then perhaps take a spade finesse. It looks like declarer's shape is 5-2-3-3. His hand may be something like AKx