III.    SIMPLE PRISMS

 {8-6-6-6} {7-5-7-7} {8-4-6-8} {9-5-7-5}

simple prism is a set of four odd or four even numbers  that total twenty-six. The numbers represent the total spades-hearts-diamonds-clubs in the two closed hands.

An Even Prism is a prism in which all four numbers are even-  {6-6-6-8}.

Prosecution Exhibit I from the Prologue features an Even Prism.

 The spade five is led, and the dummy is tabled. To calculate the prism, West considers her own hand and the dummy, adds the cards in each suit, and subtracts each total from thirteen. Here, an Even Prism results:{6-6-8-6}.

Now, examine Exhibit I's two closed hands:

 In both hands, the single suit is the spade suit. And the relative parity of the two holdings is equal.

Switch minor suit fives in the closed hands and examine the resulting relationships:

 Both hands have the same single suit, this time hearts. Again, the relative parity of the single suits is equal.

Switch any number of cards in the South and East hands, examine the results, and relationships crystallize: same single suit and equal parity.

Even Prisms:

• The two concealed single suits are the same suit.

• The relative parity of the two single suits is equal.

An Odd Prism is a prism in which all four numbers are odd-  {7-7-5-7}.

Odd Prisms:

• The two concealed single suits are the same suit.

• The relative parity of the single suits is opposite.

Consider this deal featuring an Odd Prism:

 West leads the diamond nine. East reckons this to be from a doubleton and holds up to prevent a late entry to dummy. Declarer draws trump in three rounds; and plays the heart king. East wins with the ace.

The order of West's spot plays- 8-2-5, a prism signal, sends the message I am even only in diamonds.

East has calculated the Odd Prism {9-7-5-5}.

 Odd Prism: The closed hands have the same single suit with opposite relative parity.

 West...Even diamonds Odd Prism Declarer...Odd diamonds

East receives the refracted message Declarer is odd only in diamonds.

 East knows partner led a doubleton diamond. Declarer started with three diamonds.  Declarer's hand pattern index is three: 6-3-2-2 or 6-4-3-0.

The two possible distributions are 6=2=3=2 and 6=0=3=4. And declarer's has just led the heart king. He has no heart void. Declarer's start: 6=2=3=2.

East wins with the heart ace and is on lead in this position:

 If East returns a heart, declarer wins with the queen and plays a club to dummy. East must hold up. Declarer trumps a heart, stripping East of his exit card, and ends him with a club out. Four spades bid and made.

But, East knows that declarer started with 6=2=3=2 distribution. So in the diagrammed position East gets out with a small club rather than a heart, saving for later both the club ace and the heart exit -one down.

The full deal:

Switch the minor suit fours in the South and West hands and the message changes.

 North-South again reach a doomed four spades and play proceeds similarly. West leads a singleton diamond  and East misjudges and allows dummy's king to win. Declarer plays three rounds of trump.

This time West's prism signal in trump, 8-5-2, sends the message I am even in clubs.

 West...Even clubs Odd Prism Declarer...Odd clubs

East receives the message Declarer is odd only in clubs.

The singleton opening lead and subsequent play reveal that declarer's holds one club. So declarer's hand pattern index is one: 6-4-2-1.

The only distribution which East must consider upon capturing declarer's heart king is 6=2=4=1.

The position:

 East's low club exit, correct before, now costs a trick. So East cashes the club ace, exits with a heart, and awaits three diamond tricks. Diamond ruffs? Who needs 'em?

The full deal:

The four hands of a bridge deal are structurally interdependent. The two hands in view, a defender's and the dummy, determine a prism.

In turn, the prism determines relationships between features of the two closed hands -the single suits and their relative parity.

The two Simple Prisms determine direct relationships. There are six more prisms. The relationships that these six determine are not as simple nor as direct.