IX.    PARITY PAIRS   


A disclosed pair in a defender's hand is formed by two suits of known parity. The relative parity of the two suits is either equal or opposite.


An unlike disclosed pair is formed by two suits of opposite relative parity.

  • An unlike disclosed pair includes the single suit since both odd and even are represented. 


A like disclosed pair is formed by two suits of equal relative parity.

  • The single suit must be one of the other two suits since the parity of the single suit is unique. 

  • The parity of the single suit is opposite the parity of the like pair. 


The HI/LO signal identifies the high or low ranked member of a pair as the single suit. To employ the HI/LO signal, a defender plays a HI or LO spot from one of the suits of the disclosed pair.  


Consider an example where East, the signaling defender, holds an unlike disclosed pair- clubs and hearts:

CHIX10.gif (16443 bytes)

West leads a low heart, and declarer wins with his singleton ace. A club to the ace fells East's king. The first two tricks indicate that East started with even hearts and odd clubs.


Consider the opening example from West's viewpoint:

CHIX11.gif (12288 bytes)

Declarer wins the opening heart lead with the stiff ace. East has four (even) hearts. Declarer guesses trumps, playing the ace, dropping the club king. East has one (odd) club and an unlike disclosed pair: even hearts and odd clubs -the single suit candidates.

Declarer plays a heart from dummy, discarding a diamond. East follows HI in the disclosed heart suit to indicate that the high ranked candidate (hearts) is the even single suit. West wins with the king.   

Even hearts

Odd Prism

Odd hearts

Index one
6-4-2-1 pattern
4=1=2=6 or 2=1=4=6
distribution

West to play, needing  two tricks in this position:
CHIX12.gif (12490 bytes)

Declarer's distribution is 4=1=2=6, not 2=1=4=6. With two spades and four diamonds declarer would trump diamonds in dummy rather than play hearts.

Declarer started with two diamonds and the king is now alone. West cashes the diamond ace, snatching the king, exits safely, and awaits a spade trick.

The full deal:

CHIX13.gif (22188 bytes)


South and East trade pointed fours. Play proceeds similarly, declarer passing a heart to West at trick three. East has an unlike disclosed pair: even hearts and odd clubs. East plays LO on the heart to signal an odd club single suit.  

Odd clubs

Odd Prism

Even clubs

Index six

6-3-3-1 pattern
3=1=3=6 distribution.

Declarer's diamond king is not alone. If West plays the ace, declarer scores the king and eleven tricks total. Rather, West exits with a heart and the defense is entitled to two more tricks.

The full deal:

CHIX14.gif (22076 bytes)



Next, a problem in which West, the signaling defender, holds a like disclosed pair (clubs and spades.)

CHIX20.gif (17588 bytes)

West leads a spade. East wins with the ace and returns the queen, covered by South and ruffed by West who started with one (odd) spade.

Dummy's king captures the diamond jack exit. Declarer discards a spade on the club ace. West started with five (odd) clubs.  And West is about to follow to clubs.

The single suit candidates are hearts and diamonds. West plays a HI club-  My even single suit is hearts.

The heart two is led from dummy and East must rise with the ace or play low in this position:

CHIX22.gif (9757 bytes)

East's need not consider the prism. The focus stays on West, who started with a two in hearts. One heart was used to trump a spade. If East wins with the heart ace and plays a spade, West will have no heart with which to trump.

Rather East plays low, setting the contract when West holds the king, and giving declarer a losing option when West has the queen.

    The full deal:

CHIX23.gif (21016 bytes)


Consider a variation of the deal where play proceeds similarly. West holds,

s-lg.gif (923 bytes) 4 h-lg.gif (916 bytes) Q 7 5 d-lg.gif (910 bytes) J 10 9 2 c-lg.gif (940 bytes) K J 9 5 2

and leads the spade four, trumps a spade, and errs, exiting with the diamond jack rather than a trump. Declarer wins in dummy with the king and discards a spade on the club ace. West plays LO.

The heart two is led from dummy and East must rise with the ace or play low in this position:

CHIX22.gif (9757 bytes) West holds a like disclosed pair, odd spades and odd clubs and an even single suit. The single suit candidates are hearts and diamonds. West's LO club indicates an even diamond single suit.

West started with a four in diamonds, 1=3=4=5 distribution, including three hearts.

So East plays the heart ace and leads a spade for a trump promotion. A duck would allow declarer, holding the heart king-jack, to play the king and, next, crash defender's ace and queen.



Consider this no trump deal which features an unlike disclosed pair and a Pointed Prism:

CHIX30.gif (16933 bytes) West, at partner's behest (Dbl), leads a top of nothing diamond eight to declarer's jack. The spade king is next. East, not sure of the diamond position, ducks and awaits information. Declarer crosses to the heart jack and West signals an even heart holding. A spade off dummy is won by East's ace.

West shows out and so started with one (odd) spade. West has an unlike disclosed pair: odd spades and even hearts- the single suit candidates.

West discards a LO heart from a member of an unlike disclosed pair, signaling an even heart single suit.

East to lead in this position:

CHIX31.gif (10333 bytes)

Even hearts

Pointed Prism

Odd clubs

index  three
4-4-3-2 pattern
4=4=2=3 distribution

Declarer's diamond ace is now alone. West exits with a diamond and the contract is defeated when the defense gets the spade ace, the club ace and three diamonds.

The full deal:

CHIX32.gif (20982 bytes)

When there is a disclosed pair and the parity of a third suit becomes known, the parity and identity of the single suit can be deduced. So a first discard in a third suit is a count signal, communicating the parity of the suit discarded.


Consider a variation of the above deal where play proceeds similarly. West holds an unlike disclosed pair: odd spades and even hearts. West discards a HI heart, signaling that the high ranked spade candidate is the odd single suit.

The position:

CHIX31.gif (10333 bytes)

Odd spades

Pointed Prism

Odd diamonds

Index three
4-4-3-2 pattern
4=4=3-2 distribution.

The diamond ace has a companion. A diamond return here leaves declarer with nine tricks: three diamonds, four hearts, and two spades.

However, a club return beats the contract three tricks when this is the layout:

CHIX33.gif (21272 bytes)

At the cost of an undertrick, West can discard the club five from a third suit rather than a HI heart to signal even clubs. With odd spades, even hearts, and even clubs, the odd spade suit must be the single suit. If West signals length with a loud shot, the club eight... calamity. Nine tricks for declarer.


Knowledge of the parity of two suits allows the use of the HI/LO signal to identify the single suit. But often the parity of one suit, not two, is known. What then? In the fullness of time there'll be two.

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