May 22nd, 2005

Weekly bridge column

                                     FIND THE JACK

                                   by Stephen Rzewski

	A jack in a defender’s hand can be a nuisance card for declarer:  high enough 
in rank to frequently win a defensive trick; not typically high enough to be 
reflected in the opponents’ bidding, and therefore often hard to detect.  In the 
following four hands, all taken from real life, declarer had to find a missing jack 
in order to make his contract.  Just as in bridge books, the higher percentage play 
was the one that actually succeeded.  How would you have fared?  Answers will be at 
the end of the quiz.

	#1:  ♠ J          	       North

				      ♠ K10762
                                      ♥ K32
                                      ♦ 875
                                      ♣ Q2


                                      ♠ A853
                                      ♥ AQ
                                      ♦ KQJ2
                                      ♣ J63         

	                bidding:   S        W       N        E

                                  1NT       P       2♥       P
                                  3♠        P       4♠         

	North’s 2♥ call was a transfer bid, promising at least 5 spades.  South’s 
jump was intended to show a hand with maximum values and 4-card support.
	West started by cashing the ace-king of clubs, then shifted to a heart.  You 
win and play the ace of spades, East dropping the queen.  You continue with a low 
spade, West contributing the 9. Should you finesse the 10, or go up with the king?  
How much difference from a probability standpoint do you think there is between the 
two plays:  none, a little, or a lot?

	#2:  ♥ J                        North

                                       ♠ KQ62      
                                       ♥ AK82
                                       ♦ J753
                                       ♣ 5


                                       ♠ AJ1054
                                       ♥ Q54
                                       ♦ A6
                                       ♣ 942                                   

	   	      bidding:   N         E        S        W

                                1♥        2♣       2♠        P
                                4♣        P        4♦        P

	You and your partner were playing a system whereby one opens 4-card majors 
(1♥ when holding 4 of each major).  The 4♣ call was a “splinter” raise of spades, 
promising primary trump support, a singleton or void in clubs, and game-forcing 
values.  South’s 4♦ call was an encouraging cue-bid, promising the ace, and North, 
who obviously has enormous faith in your superb dummy play, took the plunge to slam.

	West led a low club, won by East with the king, who then shifted to the king 
of diamonds.  You win the ace, ruff a club, lead a trump back to your hand, ruff your 
last club, then finish drawing trumps, which turn out to be 3-1, East having a 
singleton.  You have to take four heart tricks in order to discard your diamond 
loser.  So you start with a low one to the king, then low back to your queen. On 
these two tricks, East follows first with the 9, then the 10.  You lead your 
remaining heart, and of course West follows with the last low spot.  Only the jack is 
left.  Once again, do you finesse the 8 or play for the drop by going up with the 
ace.  How much of a probability difference do you think there is between the two 
plays:  none, a little, or a lot?

	#3:  ♣ J                        North

				       ♠ A53
                                       ♥ KQ942
                                       ♦ K104
                                       ♣ Q10


                                       ♠ 42
                                       ♥ AJ106
                                       ♦ QJ7
                                       ♣ AK98

		      bidding:   S        W          N          E
                                1NT       P          2♦         3♠
                                4♥        P          6♥

	East’s pre-empt pushed your back to the wall.  Although North’s transfer bid 
doesn’t promise any particular values and could be based on a weak hand, you were 
afraid to pass with your excellent heart fit.  Partner, probably thinking your hand 
was somewhat better (and also seeing you get the first two hands right), again 
blasted to the pushy slam.

 	West leads a spade.  You call for the ace, then play on trumps, first with 
dummy’s king, then a low one to the jack, trumps turning out to be 2-2.  How do you 
plan the play?

	#4:  ♦ J                        North

                                        ♠ 75
                                        ♥ Q86
                                        ♦ A108753
                                        ♣ K2

                                        ♠ -----
                                        ♥ K53
                                        ♦ Q62
                                        ♣ AQJ10763

		      bidding:   S         W         N          E

                                1♣        1♠        2♦         4♠
                                5♣        P         P          5♠
                                5NT        P        6♣  

	Not one to be pushed around, you decide, perhaps imprudently, to bid on over 
East’s 5♠.  5NT was intended as asking partner to choose a slam, implying that you 
have diamond support.

	West leads a spade, which you ruff.  Let’s assume you start by drawing 
trumps, which requires three rounds, East having started with a singleton.  What do 
you discard from dummy on the third trump?  How do you then proceed?    

          *          *          *          *          *          *          *


#1.   	The relevant holdings are when East started with the singleton queen or 
doubleton Q-J.  These two cases occur with close to equal frequency, the Q-J 
doubleton occurring slightly (about 9%) more often.  For every 100 times the holding 
of Q-J occurs, the singleton queen will occur about 92 times.  Nevertheless, 
finessing the 10 in the actual case is much more likely to succeed than playing the 
        The reason is that when a player holds Q-J doubleton, he has a choice of 
equal cards and will tend to play them somewhat randomly, sometimes playing the queen 
first, sometimes the jack.  So we will see the queen on the first round only about 
half the time in that case, or 50 of those 100 times.  But when a player holds the 
singleton queen, his choice is “restricted” to only one card, and we will see it 
every one of those 92 times.  That means that when the queen is played on the first 
lead, the odds are more like 92 to 50 that the queen is singleton rather than from 
doubleton Q-J.  That makes the finesse of the 10 almost a two to one favorite over 
playing for the drop.

#2.	Again, finesse the 8; you are an even heavier favorite in this case than in 
the previous one. Believe it or not, this time the “Rule of Restricted Choice” states 
that it is almost three times more likely that East started with 10-9 doubleton than 
J-10-9 tripleton.  If you would like to explore the arguments further, consult 
the “Official Encyclopedia of Bridge” under the heading of “Restricted Choice”.

#3.	Since you have to lose a diamond, you must avoid a spade loser, and the only 
way to accomplish that is to take four club winners and discard both of dummy’s 
remaining spades.  Playing clubs from the top will only win if the jack is in the 
hand with shorter length (Jxx or less), which is against the odds.  The jack is much 
more likely to be in the hand with greater length, and that hand is almost sure to be 
West.  East should have 7 spades for his pre-empt and has followed to two hearts, and 
figures to have no more than 4 diamonds and/or clubs.  Since West is likely to hold 
10 diamonds and/or clubs, there is much more “room” for his hand to hold the jack of 
clubs.  So lead a low club from the South hand, swallow hard, and finesse dummy’s 
10.  If it wins, unblock the queen, lead a trump back to your hand, play the ace-king 
of clubs, discarding dummy’s spades, drive out the ace of diamonds and claim 12 

#4.	This time, you have no option:  there is only one case that will let you 
bring in the diamond suit without loss (and the contract), and that is to find the 
singleton jack in the East hand.  After drawing trumps (hopefully, you pitched a 
heart from dummy on the third club), put the queen of diamonds on the table, and 
cross your fingers.  West will presumably cover with the king, and, if all goes well,
the jack will come crashing down from East.  Now lead dummy’s remaining spade (aren’t 
you glad you kept that card, so as to have a sure way to get back to your hand?), 
ruff in your hand, lead another diamond through West’s remaining 9-x and finesse the 
8 if he follows low.  Naturally, you didn’t pitch a diamond earlier either, as that 
would throw away the greedy overtrick.  What a player you are!  

The full deal:
				      ♠ 75
				      ♥ Q86
				      ♦ A108753
 				      ♣ K2

	                   ♠ AQJ82		   ♠ K109643
                           ♥ A9                    ♥ J10742
                           ♦ K94                   ♦ J
                           ♣ 954                   ♣ 8

	                              ♠ -----
                                      ♥ K53
                                      ♦ Q62
                                      ♣ AQJ10763