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Cryptological Techniques in Bidding and Defence

Part III

by Peter Winkler, Murray Hill, NJ, USA


The area of competitive bidding is currently the most speculative - some might say the most bizarre -- in the arsenal of cryptologic techniques. The potential uses for passing secret information in a contested auction are many, but a key (usually based on the location of the top two trumps) will be difficult to obtain.

The acquisition of a key, when possible, can be thought of as being awarded the privilege of a "free kick" - a player is allowed, at a certain time known to all, to kick his partner under the table or to choose not to. Experience has suggested that the three most useful kinds of messages to send via a 'kick' are:

  1. "Partner, don't believe my last bid;"
  2. "Partner, don't believe my next bid;" and
  3. "Partner, don't bid!"

In what follows we give one sample convention for each of the above message types. The reader is encouraged to supply the details or to work out his own conventions.


When partner has overcalled in a suit and right hand opponent makes a bid, a popular modern treatment is to have a double (or redouble) to show a raise of partner's suit with one of the top two, or one of the top three, trump honours; an ordinary raise thus serves to warn partner about leading the suit. This convention is often called "Rosencranz" in the U.S., after Dr. George Rosencranz of Mexico City.

If used to show just the ace or king in partner's suit, Rosencranz is a 'natural' for establishing a key; partner will usually have the missing top honour. Ideally the overcaller should have some bid available to confirm the key, but the auction may get too high for him; in practice it rarely hurts to presume that the key has been established. The overcaller can cancel the presumption by bidd-ing a new suit at his next opportunity (if his suit is topless then he will usually have a good hand for his non-jump overcall.)

If the overcaller does not cancel, his partner's next interesting bid will be honest when he holds the trump king, phony when he holds the ace. If he doesn't get another chance to bid, the key is saved for the opening lead or for defensive signals (see Part IV).

Here is a sample auction:

WestNorthEast South
1S 2DDble. 3D

Normally three hearts would be a game-try and three spades competitive, and that is how East bids when he holds the spade king; when he holds the ace the meanings of the two bids are switched. Enthusiastic cryptologists will go further and use 'double' to show a good defensive hand with the spade king, or a poor one with the ace; thus three spades, with the spade ace, implies a desire to double the opponents at the four-level. If West's spades were topless or he had a good hand and wanted honest bidding from East, he would have bid three hearts on the second round.

WestNorthEast South
2H 2SDble. 4S

Here a pass or double will have to be treated honestly but four no-trumps is serious only when East holds the heart king. A bid of five clubs or five diamonds suggests a lead in that suit against five spades when East holds the heart king, but a lead in the other minor when he holds the ace. If East passes or doubles, and West chooses to lead a heart he will lead the queen or a small heart rather than the ace or king; if they can successfully hide the location of the top two trumps then they can still use the key for defensive signalling.

Obviously you have to give up some things to use Rosencrypt, but the pleasure of watching the opponents' reactions to your explanations is exquisite.

Controlled psychics Note1

Players who cannot resist opening one spade on S K8643 H 75 D 854 C 952 frequently use some sort of control, e.g. if partner jump--shifts the cheapest rebid exposes the psyche. Clearly if psychics are constrained to contain one of the top trumps - not a bad idea in any case, since lead direction is an important objective - then the responder, with the other top trump, is in a position to receive in secret the message that the opener has psyched.

In practice, however, when the responder jump-shifts, the knowledge that the opener has psyched is not so valuable to the opponents as to warrant the necessary encryption measures. On the other hand, psychic opening bids are frequently followed by double-redouble. Now if the redoubler is the only one to catch the psyche, there may be ethical problems; and in other cases the opener's side is less likely than the defender's to profit from the psyche. This is a good time for the following agree-ment: opener makes his cheapest bid (not pass or double) to show a psyche with the trump king, the next cheapest to show a psyche with the trump ace. Thus, after:

WestNorthEast South
1S Dhle.Redble.?

South rebids two clubs with either
S A8542 H 83 D J942 C 94 or
S KQ1085 H 83 D 4 C AQ942. If North holds the missing high trump he is sitting pretty, as he is the only one who knows whether South has psyched. Otherwise, North has had fair warning and will tread lightly; one of the opponents will know the truth but may have trouble making use of it or communicating it to his partner.

Note1 I hasten to add that these are definitely illegal in Britain, but it is another interesting possibility - Bridge Magazine Editor

Anticipating the Sacrifice

This convention is tailored for a particular situation: you are bidding hearts, the opponents spades, and they seem likely to outbid you when the four--level is reached. Typically your opening heart bid has encountered a spade overcall, some sort of raise by partner, arid a three spade bid on your right. The bids of four clubs or four diamonds by you are useful for pin-pointing strength and helping partner to make a decision over four spades, but three no-trumps is largely wasted.

Consider the following scheme: a bid of three no-trumps commands partner to double four spades unless he has the heart king; four hearts commands partner to double four spades unless he has the heart ace. If he has the card in question, he is invited to pass, double or bid on as usual.

An example may serve to illustrate the point of all this:

WestNorthEast South
1S 3H 3S?

North-South are vulnerable and if:

  1. South holds S 4 H AQ875 D J6 C AJ1076, he bids four clubs inviting his partner's co-operation.
  2. South holds S 43 H AJ875 D KQ65 C A7, he bids three no-trumps enjoining partner from bidding on unless he holds the heart king - in which case he may use his judgment.
  3. South holds S QJ106 H AJ942 D K3 C K2, he bids four hearts, forcing partner, who obviously does not have the ace of hearts, to double four spades. Without this bid South must either be content to double three spades, or risk partner bidding one more; with it, if he catches the opponents, they won't even know who has the long trumps.
  4. South holds S None H KQ98643 D KQJ75 C 83, he bids three no-trumps, forcing partner to double four spades, which he will pull to five hearts. The opponents, not knowing whether they have been honestly doubled, may let South play there.

A similar arrangement is possible when partner has opened with a pre-empt. Here it is preferable to assume the pre-emptor has either the king or queen of his suit. The responder, in any system, should have two kinds of raises available - one which invites the pre-emptor's co-operation, and another which forbids it. If the responder happens to have the trump king or queen, he can also employ raises which say "You may co-operate only if you hold the trump king," or "You may co-operate only if you hold the trump queen." That way the opponents usually cannot tell whether the responder is waiting to double, or just testing the waters.


Editor's note:

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