Adjoint positions

It is usually possible to modify a squeeze ending by moving a squeeze card from one hand to the other, while retaining the arrangement of menaces. Often, some adjustment of entries will also be required. In such cases, we will call the resulting position(s) adjoints of the original position.

Automatic adjoints

The most familiar example is the pairing of the automatic simple squeeze and its adjoint, the twin-entry simple squeeze:

Automatic simple squeeze:

 

spade symbol A J
heart symbol --
diamond symbol 2
club symbol --

 

 

 

spade symbol K Q
heart symbol A
diamond symbol --
club symbol --

 

spade symbol 2
heart symbol K
diamond symbol --
club symbol A

 

Twin-entry simple squeeze:

 

spade symbol K 9 3
heart symbol --
diamond symbol --
club symbol A

 

 

 

spade symbol Q J 10
heart symbol A
diamond symbol --
club symbol --

 

spade symbol A 2
heart symbol K
diamond symbol 2
club symbol --

 

In the first position, North has an idle card (the diamond 2) which is discarded on the club A. In the second position, the idle card and the squeeze card have been exchanged between the two hands, while retaining the arrangement of menaces (a one-card heart menace in the South hand, and a long spade menace in the North hand); in order for the second position to work, we have had to augment the spade threat by adding an entry to the South hand.

This type of transformation can be applied to any squeeze in which there is an automatic discard on the squeeze card: exchange the squeeze card for that automatic discard, and (if necessary) add an extra entry to the hand which originally held the squeeze card. In more complex positions, the extra entry might lie in any of several suits, leading to entire families of positions adjoint to a given position. For instance, the following set of four repeating triple ruffing squeezes includes a basic position together with three members of an adjoint family:

Squeeze card in North:

 

spade symbol A
heart symbol Q 2
diamond symbol A 9 2
club symbol A

 

spade symbol K Q
heart symbol A K
diamond symbol Q J 10
club symbol --  

 

 

spade symbol J 3 2
heart symbol --
diamond symbol K 3
club symbol 3 2

 

Extra entry in ruffing threat:

 

spade symbol A
heart symbol A 10 2
diamond symbol A 9 2
club symbol 2

 

spade symbol K Q
heart symbol K Q J
diamond symbol Q J 10
club symbol --  

 

 

spade symbol J 3 2
heart symbol 3
diamond symbol K 3
club symbol A 3

 

Extra entry in blocked threat:

 

spade symbol A K
heart symbol Q 2
diamond symbol A 9 2
club symbol 2

 

spade symbol Q J 10
heart symbol A K
diamond symbol Q J 10
club symbol --  

 

 

spade symbol 9 4 3 2
heart symbol --
diamond symbol K 3
club symbol A 3

 

Extra entry in third threat:

 

spade symbol A
heart symbol Q 2
diamond symbol A Q 7 2
club symbol 2

 

spade symbol K Q J
heart symbol K Q
diamond symbol Q J 10
club symbol --  

 

 

spade symbol J 3 2
heart symbol --
diamond symbol K 4 3
club symbol A 3

 

When the squeeze card (the club A, clubs being trumps) lies in the North hand, that hand requires two further entries, one in each of the non-ruffing threats. When the squeeze card is moved to the South hand, then the North hand needs a third entry, which can lie in any of the three threats.

Positional adjoints

When a squeeze ending involves the discard of a menace on the play of the squeeze card, a more extensive modification is required, and many positional squeezes do not admit adjoints. However, if there is at least one menace in the same hand as the squeeze card, the following recipe may produce an adjoint squeeze or family of squeezes:

  1. Move the squeeze card to the opposite hand.
  2. Recess a menace in the hand which originally held the squeeze card.
  3. Add any necessary entry to the hand which originally held the squeeze card.

For an example of this process, consider the following adjoint family of recessed double squeezes produced from the standard positional double squeeze:

Squeeze card in North:

 

spade symbol 3
heart symbol K
diamond symbol --
club symbol A

 

spade symbol Q 10
heart symbol A
diamond symbol --
club symbol --

 

spade symbol K J
heart symbol --
diamond symbol A
club symbol --

 

spade symbol A 2
heart symbol --
diamond symbol K
club symbol --

 

Extra entry in lone threat:

 

spade symbol 3
heart symbol A K 9
diamond symbol --
club symbol 2

 

spade symbol K J
heart symbol Q J 10
diamond symbol --
club symbol --  

 

spade symbol Q 10
heart symbol --
diamond symbol A
club symbol 4 3

 

spade symbol A 2
heart symbol 3
diamond symbol K
club symbol A

 

Extra entry in double threat:

 

spade symbol K 4
heart symbol A J
diamond symbol --
club symbol 2

 

spade symbol J 9 7
heart symbol K Q
diamond symbol --
club symbol --  

 

spade symbol Q 10 8
heart symbol --
diamond symbol A
club symbol 3

 

spade symbol A 3 2
heart symbol --
diamond symbol K
club symbol A

 

Extra entry in third threat:

 

spade symbol 3
heart symbol A J
diamond symbol A
club symbol 2

 

spade symbol K J
heart symbol K Q
diamond symbol --
club symbol 4  

 

spade symbol Q 10
heart symbol --
diamond symbol K Q
club symbol 3

 

spade symbol A 2
heart symbol --
diamond symbol J 2
club symbol A

 

In each adjoint position, the squeeze card (club A) has been moved from the North hand to the South hand; consequently, the lone threat in hearts has been recessed, and in addition an extra entry to the North hand has been added. (To make the pattern clear, I have retained the club A in the last position, even though it is not a squeeze card; neither defender is under pressure when the club A is cashed - indeed, in the diagrammed ending, both defenders follow suit when the club A is cashed, and each defender is squeezed in turn when the last winner in the suit guarded by the other defender is cashed.)