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Cryptological Techniques in Bidding and Defence

Part I

by Peter Winkler, Murray Hill, NJ, USA


This article and its sequels will show you how to

  1. bid your slam controls without telling the Opponents what to lead;
  2. make opening leads that are informative only to partner;
  3. bid intelligently to three no-trumps without revealing your weak suit;
  4. conceal your strength (or lack of it) from the opponents, but not from partner, during a competitive auction;
  5. employ defensive signals that partner can understand but declarer cannot.

If you thought these things were impossible without cheating, you are not alone. Only the fifth has appeared in print prior to 1981; it was discovered independently by Benjamin (Bridge Magazine, April '77), Winkler (Bridge World, April '80) and probably others, and ironically is the most difficult of the five for a nonexpert to use. The rest were hinted at in a short story in the January '81 Bridge World but are otherwise unavailable, as far as the author knows; (1), (3) and (4) require the establishment of an 'active key', a totally new concept.

Most of the techniques in this article are not at all esoteric, an be done by bidding and card play, and (b) partnerships may not have private agreements.

Nothing in the laws, however, forces you to reveal to the opponents what can be deduced from looking at your own cards. If you hold three aces, and partner gives the one ace reply to an ace-asking convention, you are under no obligation to tell the opponents which ace your partner holds. Of course, that information is not likely to be of much use to them anyway - unless it is later used to encrypt some thing valuable.

Consider, if you will, the following grossly simplified analogue of the communication situation in bridge. A deck of three cards (say, the king, queen and knave of spades) is shuffled and dealt to three players, whom we call A, B and C. Player A wishes to communicate a single bit of information in secret to B, e.g. the answer to some yes-or-no question; but C is listening.

If A and B already share some bit of information -- known as the 'key' -- which C does not possess, then the objective is easily accomplished. Even if they do not, however, they may be able to manufacture their own key from the deal of the cards.

Suppose, for example, that C happens to reveal the fact that he has been dealt the knave, Then A can say to B something like: "The answer is 'yes' if I hold the king, 'no' if I hold the queen." Since B but not C knows which card A holds, the communication is private. This is an example of the use of a 'passive key', so-called because it was provided free by the opponent (C).

If C is not so obliging, A and B may still be able to establish an 'active key' as follows. Suppose A holds the king and guesses that B holds the queen. He announces, "I hold either the king or queen." If B indeed holds the queen he says, "So do I" and the key is established. Otherwise B says, "Whoops -- I have the knave"; the key is 'blown' and no attempt is made to transmit the message.

In bridge, of course, the message itself concerns the deal of the cards; and both the message and the key-guessing must be transmitted via bids and plays. Since there are barely enough bids available for sufficient communication to arrive at a good contract, bids cannot be squandered solely for the purpose of establishing a key. Hence key-establishment is attempted only when the process simultaneously passes information valuable in the selection of a contract.

One of the simplest active-key conventions is the key-card raise, In it the response of three no-trumps to partner's major-suit opening is a forcing raise which guarantees the ace or king of trumps. (Some other response or sequence of responses is used for other forcing raises.) This is useful in itself, since trump quality is often crucial in slam bidding, but is also an attempt to establish a key for encrypted cue-bidding.

If the opener has no interest in a slam he merely bids game; otherwise his actions are affected by his trump holding. If he holds the trump king, he cue-bids normally and the rest of the auction is standard.

If opener has slam interest and holds the trump ace his first cue-bid is negative, i.e. denies control of the bid suit. Subsequent cue-bidding is standard.

In the unlikely event that opener has neither top trump and is still interested in a slam (responder has denied having both the ace and king) he can bid four no-trumps (key-card Blackwood) or make an asking bid at the five-level.

To see the point of all this, suppose you are witness to an auction like the following one at matchpoint pairs:

WestNorthEast South
1S No3NT (a)No
4D (b)No 4S No
(a) A forcing raise with the ace or king of trumps
(b) Either the trump king with a diamond control, or the trump ace without a diamond control.

You ho1d:

S 98
H K63
D K864
C J764

What is your lead?

The problem is unsolvable, of course. You lead a red suit and if you guess wrongly, a very poor score is your due. The East-West hands could be:-

S AQ764
H Q5
D J9
C AQ82
[  ] S K532
H AK984
D Q5
C K3

or they could as easily be:-

S KQ764
H J5
D AQ72
C Q3
[  ] S A532
H Q4
D J3
C AK984

Looked at from the point of view of East and West, this was a successful encryption in three respects: a key was established, the subsequent auction did not unravel the key, and the protected information (red suit controls) was valuable. Even so, if the leader guesses correctly nothing will have been gained. This is typical of encryption techniques: they are helpless against good guessers.

Note, however, that with either of the above deals the ace-or-king of trumps guarantee made the auction much easier on the opening bidder. Standard methods make location of the top trumps difficult without Blackwood.

A more comprehensive and detailed system of key-card raises, for both major and minor suits, will be presented in Part II of this series, along with some uses for encryption by suit-rotation. In Part III some encryption techniques for contested auctions will be explored - here the objective is quite different. Part IV deals with opening leads and defence, where a passive key is paramount.


Editor's note:

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