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Cryptological Techniques in Bidding and Defence

Part IV

by Peter Winkler, Murray Hill, NJ, USA


A great deal has been written in recent years about partnership communication in defence, but the purpose of this article is not to recommend any particular system; it is to show you how to encrypt whatever system you presently use. It should be noted, though, that the availability of encryption may make some powerful signals, like the distribution signal of Vinje, even more attractive.

An active key for defensive signalling may be obtained via defensive bidding, e.g. the Rosencrypt convention described in Part III of this article. Most of the time, however, the key is obtained passively from the declarer's bidding or play combined with the exposure of dummy.

A key obtained from the bidding is less reliable than a key obtained from play, but more useful because it allows encryption of the opening lead. Usually, as the play of a hand proceeds, an experienced defender can tell whether it will he more useful to signal honestly to partner or to try to mislead declarer; but it is rare that a defender can make this judgment before seeing the dummy, hence most texts on defence recommend honest leads except in special circumstances, e.g. when partner is known to have no entry. The ability to make an opening lead against three no-trumps that only partner can read outweighs, in the author's opinion, all the other uses of defensive encryption combined.

To use lead encryption a partnership must agree on two different lead styles, say fourth-best ("even style") and third/fifth best ("odd style"). It is recommended, for reasons discussed below, that the two styles employ the same leads from honour combinations,

Suit-length Key

A reliable passive key is obtained when the declarer has indicated his exact length in a side suit during the bidding. If this has occurred in more than one suit, the recommended agreement is that the shorter suit (or lower-ranking, if of equal length) be regarded as the "key suit". The opening leader, with an even number of cards in the key suit, uses the "even style" for his lead; with odd length, he uses the odd style. The leader's partner, remembering that there are always an odd number of odd holdings in a given suit round the table, can interpret the lead as soon as dummy comes down.

Here is a sample hand:

Game all
Dealer South
S AJ105
H J104
D 1062
S K3
H 952
D KJ753
C 1074
[  ] S 8752
H A83
D Q84
C 953
S Q96
H KQ74
D A9
C AJ82
2C 2H

Hearts have become the key suit for the defence since West has an odd number of them, he leads his fifth-best diamond. East, who can count partner for three hearts and hence [probably] five diamonds, rises with the queen and alertly returns the four when declarer duckes. Now South has to guess whether diamonds are four-four in which case he can simply knock out the ace of hearts or are five-three in which case he must rely on the spade finesse.

Suppose, on the other hand, that the heart and club suits are interchanged in the above deal. Now declarer can cash the hearts and determine the distribution of the key suit, enabling him to read the opening lead; the encryption has failed, but the defenders are no yorse off than if they had not attempted an encryption.

The real nightmare for the defenders occurs when the distribution of the led suit is such that declarer can read the lead anyway, and can thus make use of the resulting inferences about the distribution of the key suit. This horrible eventuality, called "turning the key," is fairly rare unless the defenders attempt to encrypt leads from honour combinations (which declarer can often read immediately.) Hence the latter practice is not recommended for general use.

Point-count Key

A handy passive key is available whenever the declarer's bidding limits his high-card count to a narrow range; for those willing to put up with occasional ambiguities, the technique below can be used in all cases when the enemy have bid to three no-trumps without providing suit-length key. Opening leader uses odd style when he has fewer than seven points and even style when he has seven or more, except that if he is so strong that he believes he will not need any co-operation from partner,. when he again reverts to odd style. When dummy comes down the leader's partner will usually be able, when it makes a difference, to determine whether the lead was odd style or even.

Love all
Dealer North
S A6
H J5
D 1073
C AQ9874
S J94
H A962
D K2
C 10643
[  ] S 10852
H Q1074
C J2
S KQ73
H K83
D A9654
1C 1D
2C 3NT

West, with eight points, leads his fourth-best heart. East can read the lead since declarer presumably would have found some other action with seventeen points, but the declarer is in the dark. He can make his contract by overtaking the club king, but if hearts are five~three and clubs three-three he would then go down with eleven top tricks.

Encrypted signalling

Any time the defenders obtain a key but fail to use it for the opening lead (e.g. an honour is led), or obtain a key too late for use on the opening lead, they can use it to encrypt their regular defensive signalling. A suggested method is to make whatever is the defender's normal style the "even style", and for the odd style to turn everything upside-down. Thus a defender who normally uses a high card to encourage uses a low one to encourage when he is playing odd style.

The additional form of passive key available for encrypted signalling is obtained whenever declarer shows out of a suit early in the play. At that point only the defenders know the distribution of the spot cards in that suit (the "key suit") and can use it to encrypt subsequent signals in all the suits. One method is to focus on the odd spots held by the opening leader; if he holds an even number of the four cards 3, 5, 7 and 9 of the key suit, the defenders use even style signalling; otherwise they use odd style.

There are times when, in the absence of encryption, a defender can have a signalling problem even when he can see the declarer's hand. Consider the following situation:

Love all
Dealer East
S 74
H 1085
D 652
C KQJ105
S 1083
H QJ962
D 983
C 92
[  ] S 952
H AK73
C A74
H 4
D AK107
C 863
WestNorthEast South
..1NT [a]Dble.
2H NoNo2S
No3C No3D
No3S No4S
[a] 12-14 points.

West leads the queen of hearts; declarer ruffs the continuation, draws trumps, and plays the three of clubs towards the table. What card do you, West, play?

Playing the deuce is likely to result in partner taking the second round of clubs, and declarer taking the rest of the tricks; but to signal a doubleton by playing the nine alerts declarer to the possibility of dropping the club ace in two rounds, and the double finesse in diamonds again results in eleven tricks. Playing encrypted signalling West, with an odd number of odd spots in the key suit [hearts], shows his doubleton club by playing the two; the declarer still has to guess.


Editor's note:

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