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In a semi-final match in the Senior trials, you face an interesting balancing decision.

E-W vul, South deals. As East, you hold

East
QJ1062
J86
J6
A84
W
N
E
S
1NT
P
P
?

If you choose to bid, available are:

2: Overcall in one of the majors. Partner will normally make a pass or correct call.

2: 5 spades and a 4- or 5-card minor. If partner wants to play in your minor, he will bid 2NT asking you to bid your minor.

Your call?

East
QJ1062
J86
J6
A84
W
N
E
S
1NT
P
P
?

If you choose to act, it makes a lot of sense to bid 2 rather than 2. Partner will play you for 5 spades. If he has 2 or more spades he will likely pass 2 rather than get to a 9-trick contract. However, if he has a singleton spade, he will bid 2NT asking for your minor. You don't have one, but you can pass 2NT and at least not be in a 5-1 spade fit.

Do the odds favor balancing? It might not seem so, particularly vulnerable. However maybe it is right to bid. Partner has some high cards since North didn't move towards game. Partner was unable to act over 1NT, which is an indication that he isn't distributional, so you probably won't hit him with the feared singleton spade. Suppose partner has about 10 HCP and is relatively balanced, which is about what he figures to have. If he had opened 1NT with a 9-11 range, you certainly would get to 2 rather than pass out 1NT, since taking 8 tricks in spades looks more likely than taking 7 tricks in notrump. Since you need to take 7 tricks on defense against 1NT to get a plus score, perhaps it is right to bid 2. There is a danger that you will go for a number, but that danger is very small. South can't double, since he has shown his hand. North might be strong enough to double, but with you having the spade intermediates he probably will just defend even if he has 4 spades and 7 HCP.

If you weren't vulnerable, the odds would clearly favor balancing, particularly since it is unlikely that partner will be finding a spade lead vs. 1NT. Vulnerable, it is far from clear.

You choose to pass, ending the auction.

W
N
E
S
1NT
P
P
P

Partner leads the 10.

North
983
9543
84
KQ53
East
QJ1062
J86
J6
A84
W
N
E
S
1NT
P
P
P

Your agreements on honor leads vs. notrump are Rusinow from 4 or more. With a 3-card holding, you lead top of a sequence. Thus, partner's 10 lead would be consistent with J109x or 109x, but not J10x.

Declarer plays the king from dummy. What do you play?

North
983
9543
84
KQ53
East
QJ1062
J86
J6
A84
W
N
E
S
1NT
P
P
P

If the lead is from 109x, you need to duck in order to prevent declarer from getting 3 club tricks. Even if this is the case, it might be necessary to shift to a spade quickly.

If partner has J109x of clubs, winning the first trick will let your side take 3 club tricks. If you duck, declarer can hold you to 2 club tricks.

While partner could have either holding, it is more likely that he has J109x. If he has only 3 clubs, he might have found another lead. Furthermore, if he has only 3 clubs he is likely to have 3 spades, in which case you will have an entry to your spades.

You win the ace of clubs, declarer playing the 6. What do you play next?

North
983
9543
84
Q53
East
QJ1062
J86
J6
84
W
N
E
S
1NT
P
P
P

The spade shift is obvious. If declarer has Kx of spades, it is now or never for the spade suit. There is no reason not to lead an honest queen.

You lead the queen of spades. Declarer plays the 5, and partner the 4 (UDCA). Now what?

North
98
9543
84
Q53
East
J1062
J86
J6
84
W
N
E
S
1NT
P
P
P

It may seem obvious to continue spades. But maybe not. Suppose partner has Kxx of spades. A spade continuation will get your side 4 spade tricks and 1 club trick. You will need 2 more tricks to defeat 1NT. If partner has 2 red-suit tricks, either declarer has 7 winners after knocking out one of partner's high cards in which case it won't matter, or partner will get in twice and will have time to establish your spade tricks. Thus, there is no race to set up your 7 tricks before declarer sets up his tricks.

Continuing spades could cost. Declarer will know from your failure to balance that you probably don't have the ace of spades, so if you continue spades he will duck again from an initial holding of Kxx and that will be very bad. Also, it may be vital to untangle the club position now.

If you do switch back to clubs, you must lead the 4. Partner might have started with J1072, and declarer with 96 doubleton. If you mistakenly lead the 8, dummy's 5 will control the fourth round of the suit.

You lead the 4. Declarer wins the jack, partner playing the 2. Declarer leads a club to dummy, partner following. Declarer now cashes the 13th club. What do you discard?

North
98
9543
84
5
East
J1062
J86
J6
W
N
E
S
1NT
P
P
P

You almost certainly need partner to have Kxx of spades, so you want to hold all your spades as your long spade might be the setting trick. Your jack of hearts could come in handy. It is hard to see any value in keeping both diamonds.

You discard the 6. Declarer discards the 2, and partner the 7. Declarer now leads a diamond to jack, king, and ace. Partner cashes the queen of diamonds. What do you discard?

North
98
9543
8
East
J1062
J86
W
N
E
S
1NT
P
P
P

You no longer need all your spades to defeat the contract. You might as well throw a spade, since your guarded jack of hearts might be important. It won't matter, but your proper discard is the current count 6.

You discard the 6. Partner leads the king of spades. Declarer wins the ace, cashes AK of hearts, and the defense has the rest. The full hand is

West
K74
Q102
AQ107
1092
North
983
9543
84
KQ53
East
QJ1062
J86
J6
A84
South
A5
AK7
K9532
J76
W
N
E
S
1NT
P
P
P
D
1NT South
NS: 0 EW: 0
10
K
A
6
2
0
1
Q
5
4
3
2
0
2
4
J
2
3
3
1
2
7
9
Q
8
1
2
2
5
6
2
7
1
3
2
4
J
K
A
0
3
3
Q
8
6
3
0
3
4
K
8
2
A
3
4
4
K
2
6
3
3
5
4
A
10
4
8
3
6
4
10

How was West's defense?

West
K74
Q102
AQ107
1092
North
983
9543
84
KQ53
East
QJ1062
J86
J6
A84
South
A5
AK7
K9532
J76
W
N
E
S
1NT
P
P
P
D
1NT South
NS: 0 EW: 0
10
K
A
6
2
0
1
Q
5
4
3
2
0
2
4
J
2
3
3
1
2
7
9
Q
8
1
2
2
5
6
2
7
1
3
2
4
J
K
A
0
3
3
Q
8
6
3
0
3
4
K
8
2
A
3
4
4
K
2
6
3
3
5
4
A
10
4
8
3
6
4
10

West's opening lead looks right. This doesn't looks like a race to take 7 tricks before declarer takes 7 tricks. Any other lead is likely to be costly.

West's diamond discard looks right. He can't afford to pitch from either major.

West's cash of the queen of diamonds could have been costly. If declarer's hand had been Axx AK K9xxx Jxx, this would have given declarer time to establish a long diamond trick. Better would have been to lead the king of spades. If that holds, West could trust partner's jack of diamonds play (along with perhaps a suit-preference signal on the king of spades) and shift to a heart in time to defeat the contract.

How about declarer's line of play?

West
K74
Q102
AQ107
1092
North
983
9543
84
KQ53
East
QJ1062
J86
J6
A84
South
A5
AK7
K9532
J76
W
N
E
S
1NT
P
P
P
D
1NT South
NS: 0 EW: 0
10
K
A
6
2
0
1
Q
5
4
3
2
0
2
4
J
2
3
3
1
2
7
9
Q
8
1
2
2
5
6
2
7
1
3
2
4
J
K
A
0
3
3
Q
8
6
3
0
3
4
K
8
2
A
3
4
4
K
2
6
3
3
5
4
A
10
4
8
3
6
4
10

Declarer made a fine play at trick 1. Since declarer owned the jack of clubs he could read the club position. In addition, he could see that East might have a problem if the king were played from dummy. If declarer had played small from dummy, East would have known to duck the first two rounds of clubs.

After the club return, declarer could have made the hand by going after hearts rather than diamonds for his seventh trick. This would succeed if hearts were 3-3, or if an opponent had two honors doubleton. In a vacuum, finding the ace of diamonds onside is more likely than finding a favorable heart lie, although it is close since if the hearts are 5-1 declarer will find that out in time and be able to revert back to diamonds. However, bridge isn't played in a vacuum. A close analysis of the hand would show that going after hearts is vastly superior.

What is the spade position? The spades have to be 5-3. If the spades were 4-4, it is inconceivable that East wouldn't have continued spades. The reason East shifted back to clubs had to be because he thought either the spades wouldn't run or continuing spades wasn't necessary. If East started with 4 spades he would think a spade continuation is necessary, since declarer could have Kxx of spades.

The inference on the spade suit and assumed inference from the opening lead places West with 3-3 in the black suits. If West had a 5-card red suit, West would have led that in preference to a club from 109x. Therefore West is 4-3 in the red suits. As he is about equally likely to be 4-3 either way, that makes the chances of a 3-3 heart split about 50-50 as opposed to the 36% in a vacuum. Add in the two honors doubleton in the East hand, and this alone makes going after hearts superior.

There is more. East sold out to 1NT. If East had the ace of diamonds, he might have been inclined to get to 2. That increases the odds against the ace of diamonds being onside, making going after hearts overwhelmingly percentage.

It turns out that the mundane defense of continuing spades was necessary to ensure a set. The actual layout is an argument that East's entire defense was wrong. It is far from clear.

The treatment of Rusinow from 4 or more cards backfired on this hand, since it was declarer who knew what was going on while East was in the dark. More often than not it is the other way around, where the defender needs to know which is the case and/or declarer is the one facing a guess in the suit.

At the other table, the lead was the standard 10, which was ducked to declarer's jack. This eventually resulted in a 2-trick set.

Perhaps the most interesting aspect of this hand was declarer's choice of which red suit to attack. It is important to realize how percentages can change as new information is added and the action of the other players is taken into account. Declarer's failure to do this cost him the contract.

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