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In the first session of the Cavendish Pairs, you are dealt a weak hand and it doesn't look like there will be much for you to do.

As West, you hold:

You
109
Q62
1092
87653

Partner deals at unfavorable vulnerability and opens 1, 11-15 HCP, 2+ ; if balanced, 11-13 HCP. If you should choose to respond 1, partner will never raise without 4-card support. Also, partner will always bypass a 4-card spade suit if he is balanced.

Your call?

 

 



West
109
Q62
1092
87653
W
N
E
S
1
P
?


Your hand is so weak that at this vulnerability your primary goal is to avoid going for a number. It would be nice to talk the opponents out of their probably cold game, but there is no good way to do that.

Many players would try 1, thinking it is safer than passing. I don't agree. The problem with 1 is that it is forcing, and the opponents know that.  Your LHO probably has a good hand. If he has heart length he will pass and see what happens. Partner's likely rebid will be 1NT. Now one of the opponents probably has a double, and you are in trouble. If partner has 4 hearts he will raise and you will have found a 7-card fit, but you will be at the 2-level and still may get caught if one of the opponents has a takeout double which his partner can convert.

It takes a parlay for you to get in trouble if you pass. You don't mind playing a silly 1 contract undoubled. Down 4 or even down 5 is no tragedy. It is the 800's or higher you fear. For you to get into trouble, several things have to happen. First, North has to have a takeout double rather than some other call. Second, South has to have a diamond stack good enough to pass the double. If this happens, you can redouble, and partner will bid a 4-card heart suit if he has one. Otherwise, you will eventually land in 2. Since partner won't have 4 hearts and probably won't have long diamonds considering that South passed the double, it is likely that he has some club support and that 2 is your best home.

One argument players give for bidding 1 is that it makes things more difficult for the opponents. That isn't so clear. Reopening auctions aren't as well-defined as other auctions, so passing may be the call which makes it more difficult for the opponents to locate their strength and bid game.

You pass. Your side is done with the auction, which concludes:

West
109
Q62
1092
87653
W
N
E
S
1
P
P
X
P
1
P
2
P
2
P
4
P
P
P


Your lead. You lead third and fifth, top of an honor sequence.




West
109
Q62
1092
87653
W
N
E
S
1
P
P
X
P
1
P
2
P
2
P
4
P
P
P


The auction indicates that South is at least 4-4 in the majors, and if he is 5-4 there is probably no chance for the defense. North appears to have 4 spades from his 4 call, and he is likely to have 3 hearts since he chose to make a takeout double. Against that layout, it doesn't look like a trump lead can accomplish much. The hearts are splitting 3-3. It is better to lead from the 109x. This could establish a trick or two in the diamond suit, and is probably safer than a trump lead anyway.

You lead the 10.

West
109
Q62
1092
87653
North
A743
AK5
AK63
94
W
N
E
S
 
1
P
P
X
P
1
P
2
P
2
P
4
P
P
P


The ace of diamonds wins in dummy. Partner plays the 4, and declarer the 5. Suit preference signals at trick 1. 10, 9, 8 (by priority) are suit-preference high, 2, 3, 4 (by priority) are suit preference low, 6, 5, 7 (by priority) are encouraging.

At trick 2 declarer leads the ace of spades from dummy. Partner plays the 6, and declarer the 2. Does it matter which spade you play, or do you just randomly play the spade nearest your thumb?




West
109
Q62
92
87653
North
A743
AK5
K63
94
W
N
E
S
 
1
P
P
X
P
1
P
2
P
2
P
4
P
P
P


There are two possible holdings partner might have where declarer has a choice of plays. One is Q6x (perhaps Q86). The other is KJ6.

If partner has Q6x, declarer has 3 plays. He can play the king, hoping you have Q9 (or Q10, depending on which you play). He can finesse the 8, hoping you have stiff 9 (or stiff 10). Or he can finesse the jack, hoping you have 109 doubleton. Clearly finessing the jack is the anti-percentage play since you could play either the 9 or the 10 from 109 doubleton, so he should go wrong regardless of which card you play.

If partner has Q86, the deep finesse isn't available for declarer. Still, by the same restricted choice argument he should go wrong whichever honor you play.

If partner has KJ6, things get interesting. It may seem random which card you play, but in fact it isn't random. Playing the wrong card would be an error which would give declarer an advantage.

Suppose you started with J9 doubleton. From your point of view, declarer might have Q10xx, in which case it would be bad to play the jack -- that would eliminate declarer's guess. You would be forced to play the 9. This means that you will always be playing the 9 from the equally likely holdings of K9 doubleton and J9 doubleton. Thus, if your strategy ever involves playing the 9 from 109 doubleton declarer will be seeing the 9 more often when you don't have the king than when you do have the king, hence he will be able to go up queen and be right.

It is to be noted that the same theme applies if you have J10 doubleton. You would always have to play the jack from KJ doubleton, and you would never play the jack from J9 doubleton. Therefore, if your strategy ever involves playing the 10 from J10 doubleton declarer will be seeing the jack more often when you do have the king, which will enable him to be right more often than not when you play the jack.

Putting all this together, since you must play the 9 from J9 doubleton your correct strategy to balance the books is to always play the 10 from 109 doubleton and always play the jack from J10 doubleton. If you follow this strategy, this is what declarer will be seeing:

The 9 from J9 doubleton and K9 doubleton
The 10 from 109 doubleton and K10 doubleton
The jack from J10 doubleton and KJ doubleton

As all of these holdings are equally likely, barring no other information, declarer will be on a straight guess whichever card he sees. Any deviation from this strategy will give declarer an advantage.

You choose to play the 9 of spades. Declarer continues spades. Partner wins his king, cashes his ace of clubs, and leads another club. Declarer wins his king, draws trumps, and claims 10 tricks. The full hand is:


West
109
Q62
1092
87653
North
A743
AK5
AK63
94
East
KJ6
J103
J74
AQ102
South
Q852
9874
Q85
KJ
W
N
E
S
 
1
P
P
X
P
1
P
2
P
2
P
4
P
P
P
D
4 South
NS: 0 EW: 0
10
A
4
5
1
1
0
A
6
2
9
1
2
0
3
K
5
10
2
2
1
A
J
3
4
2
2
2
2
K
5
9
3
3
2
Q
6


Should partner have ducked the king of spades in order to give declarer a guess?




West
109
Q62
1092
87653
North
A743
AK5
AK63
94
East
KJ6
J103
J74
AQ102
South
Q852
9874
Q85
KJ
W
N
E
S
 
1
P
P
X
P
1
P
2
P
2
P
4
P
P
P
D
4 South
NS: 0 EW: 0
10
A
4
5
1
1
0
A
6
2
9
1
2
0
3
K
5
10
2
2
1
A
J
3
4
2
2
2
2
K
5
9
3
3
2
Q
6
  

His defense was probably correct. He doesn't know that you have the 10 of spades, particularly since from 109 doubleton you are supposed to play the 10 as we have seen. Also he did open the bidding, so declarer will probably guess right anyway. If ducking the spade were the only way to defeat the contract he should still try it, but it might be necessary for him to defend as he did. Suppose the distribution of the hand is the same, but you hold the king of clubs. This is not inconsistent with anything. You still might well have passed 1, and declarer hasn't shown any strength at all. If that is the hand, ducking allows declarer to make a no-play contract by winning the queen of spades and running diamonds, discarding a losing club on the long diamond. It is almost always better to go for a legitimate set if you see one.

Suppose that instead of the actual hand West held king-doubleton of spades with one of the honors, giving East two honors and a small spade. East would of course play his small spade on the first round of spades. Does it matter which of his 2 honors he plays on the second round of spades?




West
109
Q62
1092
87653
North
A743
AK5
AK63
94
East
KJ6
J103
J74
AQ102
South
Q852
9874
Q85
KJ
W
N
E
S
 
1
P
P
X
P
1
P
2
P
2
P
4
P
P
P
D
4 South
NS: 0 EW: 0
10
A
4
5
1
1
0
A
6
2
9
1
2
0
3
K
5
10
2
2
1
A
J
3
4
2
2
2
2
K
5
9
3
3
2
Q
6
  


Suppose West has KJ doubleton of spades. He will have played the jack of spades on the first round. Declarer will know that is not from J9 doubleton. Therefore, if East started with 109x it will be necessary for East to play the 9 of spades. If he mistakenly plays the 10, declarer will never misguess.

The rest of the logic follows the same path. East will always play the 9 from both K9x and 109x, and these are equally likely holdings. If East's strategy involves ever playing the 9 from J9x declarer will be seeing the 9 more often when East doesn't have the king, so declarer will go right. Similarly, East will always play the 10 from K10x and never from 109x. If East's strategy involves ever playing the jack from J10x declarer will see the 10 less often when East doesn't have the king, and again will go right. Thus, East's only correct strategy is:

From 109x, always play the 9 on the second round.
From J9x, always play the jack on the second round.
From J10x, always play the 10 on the second round.

Once again, if East follows this strategy declarer gets no information, since the play of any honor will be equally likely to be from the king as from not the king. If East deviates in any manner, declarer can take an advantage.

I find the above combination fascinating. Instead of randomly falsecarding, it is necessary for the defenders to stick to a fixed strategy in order to avoid giving anything away. I wonder if there are other similar card combinations.

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