Bridge Column

                 Double-Dummy Problem


                      ♠ 3
                      ♥ AK7
                      ♦ KJ1065
                      ♣ KJ86

         West                        East

        ♠ A92                       ♠ Q5
        ♥ J10654                    ♥ 9832
        ♦ A72                       ♦ 983
        ♣ 102                       ♣ A974


                      ♠ KJ108764
                      ♥ Q
                      ♦ Q4
                      ♣ Q53

	South is to play the contract of 4♠ with the
opening lead of the ♣10.  In a “double-dummy” problem,
the reader is allowed to look at all four hands and 
find a solution which requires optimal play by both 
sides, declarer and defenders.  In this case, you are
to decide whether you would prefer to declare or defend,
which essentially means:  do you think that the best
line of play by declarer will necessarily result in
fulfilling the contract, or do the opponents have 
defensive plays that must inevitably result in defeat
of the same?  

	When you believe you have arrived at a solution,
it is advisable to look more deeply.  Check and see if 
the opposing side has a counter-play that may have to 
send you back to the drawing board.  If you get stuck,
start reading below, where you will find the answer 
revealed in a Socratic-like fashion in increasing stages.


	On the surface, it looks as though the contract
should make fairly easily.  Suppose East wins the ace 
of clubs and returns another.  Declarer wins in dummy, 
leads a spade and finesses the 10.  West wins the ace 
(if he ducks instead, declarer plays the king of spades
next to smother the queen), but can do declarer no harm,
who eventually will lose only the three outstanding aces.
So what can the defenders do to make declarer’s life 
more difficult?

	For the defense to have any chance, East must
duck the ace of clubs at trick #1.  (As an aside, this
is a good play to remember generally, when you suspect 
that partner may have led from a doubleton, and you 
have no side entry).  Ducking the ace maintains a link
with West, who, upon gaining the lead with either of
his aces, will play a 2nd club.   East will then win 
the ace and give his partner a club ruff for the setting 
trick.  Can declarer do anything to avoid the ruff?

	Declarer can avoid the ruff if he can get rid 
of his clubs.  If dummy had another fast entry, one 
could play off the queen of hearts, then discard two 
clubs on the ace-king in dummy.  As it is, if he cashes
the queen of hearts and then tries to reach dummy with
a diamond, West will seize the ace and play a second 
club as before, so that won’t work  Will it help declarer 
to overtake the queen of hearts in dummy and discard 
one club on the remaining heart honor?

	This will reduce declarer to one club, the same
length as West, but the weak trump spots will prove to be
an Achilles’ heel.  After playing two hearts, declarer
can lead a spade and finesse the 10.  West will win the
ace, and before leading a 2nd club to his partner, will
likely show good technique by cashing the ace of diamonds
before the mice can get at it.  Now in with the ace of 
clubs, East will play a 3rd club, which will then sink 
declarer:  if he ruffs low, West will overruff with the
9 for the setting trick; if declarer ruffs instead with
the jack, he will survive for the moment, but West will 
simply discard, and the 9 of spades will be promoted in
the process and eventually score.  So discarding just 
one club simply won’t work.  Is declarer therefore doomed,
or does he have a way of getting around the trump promotion?

	Try instead the effect of overtaking the queen 
of hearts with the king, discarding a club on the ace, 
then playing dummy’s low heart and....   discarding the 
last club from the closed hand!  This “loser-on-loser” 
play trades a club loser for a heart loser.  If East wins 
and plays a 2nd club now, declarer can afford to ruff low,
because West still has a club in his hand, and the trump 
promotion will be avoided.  Declarer will still have a 
slow entry to dummy via the diamonds to make the trump 
lead to the 10, and West will not be able to get to his
partner for another club play.  So it appears to be correct
to choose playing the hand over defending after all.     
.....or is it?   (better look again)

	Suppose the defender who wins the third heart 
(on which declarer discarded a club) continues by playing
a 4th round of hearts.  Declarer must ruff in his hand, 
as he has to preserve the spade in dummy for a trump 
lead through East.  Now when he leads a diamond to reach
dummy, West will grab his ace and play...   his last heart! 
East will cooperate by ruffing with the queen of spades 
(this play of a high trump to create a trump promotion 
in the opposite hand is called an “uppercut”; see our 
previous column entitled “Missed Opportunity”).  Once 
again, the 9 of spades will ultimately provide the setting

	If you elected to defend—but only because you
foresaw all of the above—take a long, sweeping bow.

 	My thanks to Bud Biswas for forwarding this 
intriguing deal to my good friend Jeff Lehman, who 
passed it along to me.  Bud informs me that he found
the problem in a book written by Dr. Andrew Diosy,
a Hungarian doctor who is living (or used to live) in

	Many double-dummy problems are less practical
than this one, because they often are of a more puzzle-
like nature, with peculiar card layouts and solutions
involving plays that would be unrealistic to find at 
the table.  This deal, though, is more instructive in
that it contains possible plays that occur with some 
frequency, and which are often missed by the average 
player.  Note particularly:  (1) the duck of the ace 
of clubs at the first trick; (2) the loser-on-loser 
play to avoid the ruff and sever communication between
the defenders, (3) the possible trump promotion by 
leading a suit through declarer’s hand in which both
declarer and LHO are void, and (4) the uppercut.  The
trump position especially is one to study and remember:


              A9x                 Qx


Just one last point:  suppose that, even before any 
trumps were played at all, East had the opportunity 
to lead a side suit in which both South and West were
 void.  If South were to ruff with the 10 or jack, 
West must resist the impulse to overruff with the ace 
and discard instead, in order to promote his 9.

Bridge Column

                  Department of Defense (IV)

                     by Stephen Rzewski

                           North (dummy)


            West (you)                                            


          bidding:   N     E     S     W
                    1♦     P    1♥     P
                    2♥     (all pass)

	Recently, a defensive problem involving a particular card
combination came my way, which you will see from time to time, so 
it is worth confining to memory.

	You start the defense with the ace and king of clubs, partner
playing low-high and declarer contributing the jack on the second round.
You switch to a diamond.  Partner shows up with the ace and queen, so 
he wins two more tricks and exits with a third diamond, declaring 
winning the jack.  A heart is played to dummy’s ace, partner following 
with the queen.  A second heart goes to declarer’s king, who then throws
you in with a third heart, partner discarding clubs on the last two tricks.
What do you now play, looking at:

                                  ♦ ---
                                  ♣ ---

                  ♥ ---
                  ♦ ---
                  ♣ 63

	Declarer appears to have three spades and two trumps left in his
hand.  You will have to break the spade suit, as a club play now will 
give declarer a ruff-and-sluff.  If partner has the king of spades, you 
will always get one more trick, so the relevant case is when partner has 
the queen and declarer the king.  

	You might get away with leading the deuce, if partner has the 
8-spot and puts in that card if declarer calls for a low card from dummy. 
However, if it turns out that declarer has the 8, he will either win the
trick cheaply with that card, or if partner puts up the queen, declarer 
will then have a finessing position over your jack with dummy’s A-10.   

	Suppose you lead the 9, trying to get partner to withhold the 
queen unless dummy’s 10 is played.  If you do that, and declarer turns 
out to have good spots (8-7), the play will go: 10, queen, king, and he
will now be able to run those spot cards through you and pick up your jack.

	The play that covers all the bases is to start with the JACK. 
This renders declarer helpless.  If he plays dummy’s ace, followed by 
the 10, you will always score the 9, provided that partner covers the 
10 with the queen.  The full deal:


                 ♠J92                        ♠Q53
                 ♥J103                       ♥Q
                 ♦874                        ♦AQ65
                 ♣AK63                       ♣109875


Bridge Column

                     THE GREEDY OVERTRICK

                      by Stephen Rzewski

          neither vul
          dlr:  North





              bidding:   N     E     S     W
                        1♣    2♠    3♥     P
                        4♥   (all pass)

                      opening lead:  ♠2

	One of the most important areas of matchpoint play that can
help generate winning games is the matter of overtricks.  This is 
especially true when it becomes apparent that a normal contract has 
been reached which figures to make easily.  Declarer may easily become
complacent and inattentive and miss an opportunity to make a precious
overtrick, which could turn an average result into a top.  Likewise, 
a defender can similarly lose concentration and allow declarer an 
extra trick to which he is not entitled, converting an average into 
a bottom.  One such play on a 26-board session can easily affect one’s
score by about two percentage points, a considerable gain at matchpoints.

	In today’s deal, which occurred at a recent club game, the 
bidding and contract appear routine, and are likely to be the same at 
all tables.  What would be your general line of play?

	If the trumps are 2-2, twelve tricks will be easy.   If the 
clubs should divide 3-3, one of dummy’s diamonds can be discarded on 
the 13th club, and the diamond finesse can be taken for all thirteen 
tricks.  If the clubs do not split evenly, there are still some possible
ways to finesse the diamonds so as to avoid a loser in that suit.  With 
East pre-empting in spades, however, he figures to have shortness 
somewhere, so some suits will undoubtedly split unevenly.  To begin, 
how should one play the hearts?

	It is better to start the play of trumps with the king rather
than with dummy’s ace.  If the hearts are not 2-2, the length is more 
likely to be with West.  If East should play an honor on the first lead,
the percentage line on the second trump play would be to play West for
honor-third and  finesse dummy’s 9, in accordance with the Law of 
Restricted Choice.  

	Because there may be an endplay possibility on the hand, one 
should use the opportunity of being in dummy at the first trick to ruff 
a spade before touching trumps.  Then at trick #3, play the king of hearts.
Both opponents follow low, and when you lead a second trump to dummy’s ace,
West plays the jack and East shows out, discarding a spade. So you will 
have one sure trump loser.  Now lead dummy’s last spade and ruff in hand,
West following.  With the following cards remaining, how would you now 

                              ♠ ---

                              ♠ ---

	It behooves one to count the hand as you play, as the best 
continuation may depend on the opponents’ distribution.  East should 
have six spades for his weak jump overcall and has followed to one heart;
so he has six cards in the minors.  Suppose you were to test the clubs 
and find them to be 4-2, with length in the East hand.  That would give
him two diamonds.  In that case, your best play to avoid a diamond loser
and score twelve tricks would be to hope that he started with exactly 
K-x doubleton.  You should accordingly lead a low diamond from dummy, 
finesse the jack, and if it holds, play the ace next to drop the king.

	If instead it should turn out that West holds four clubs, that 
would leave East with two, and that hand would therefore have four diamonds.
In that case, your only play for the second overtrick would be to hope that
he started with K10xx.  Holding the AJ9, you should plan on taking two 
diamond finesses through East, first leading the queen, and if that card 
is covered, winning the ace and getting back to dummy to finesse the 9. 
The ace of clubs and a ruff of the 4th club will provide the necessary 
entries. The odds of this play succeeding are small, but are essentially 
on the house, since there is no danger of losing any additional trick if 
the double-finesse fails.  (It is somewhat better to start with the queen 
rather than low to the 9, since a careless East might make a mistake and 
fail to cover the queen with Kxxx).  

	To be in the best position to make your choice of plays, first 
play the king and queen of clubs, then low to the ace on the third round 
so as to end up in dummy (if West should ruff in, he will be obliged to 
play a diamond, since he will have no other suit left, which presents you 
with no danger).  As it turns out, the clubs do split 3-3.  So how should 
you play the diamonds now?

	The answer is:  don’t touch the diamonds at all!  Instead, lead 
a trump to West, resulting in an endplay.  He will be obliged to lead a 
diamond into your tenace holding.  You will now be able to discard a diamond
from dummy on your good 13th club and ruff your last diamond in dummy.  
Making twelve tricks for a well-earned top.  The full deal:

                      ♠1062               ♠KQJ983
                      ♥QJ4                ♥5
                      ♦K1073              ♦854
                      ♣973                ♣J104


Bridge Column

		           FORCED ENTRY

                         by Stephen Rzewski

          dlr:  West
          vul:  both


                West                    East

               ♠4                      ♠AQ653
               ♥AQJ107                 ♥984
               ♦10652                  ♦9874
               ♣AQ5                    ♣2


                             ♠ K102
                             ♥ 63
                             ♦ AQJ
                             ♣ J10864

	          bidding:     W      N      E      S
                              1♥      P     2♥      P
                               P     dbl     P     3♣  
                                 (all pass)

                       opening lead:  ♠ 4

	Today’s hand came up in a club game many years ago.  I was seated
East. The bidding is shown as it occurred.  North’s reopening double is 
questionable without better diamond support, but the opponents fell on their
feet when South found the 9-card club fit.  My partner and I, each with a 
singleton, were obviously cowardly lions that day and should have taken the
push to 3♥--- but in that case I would not have this bridge tale to relate,
one of my all-time favorites.	

	My partner, Harry Kaufmann of North Bennington, VT, led his singleton
spade. I won the ace and returned the 5♠, trying to show by a middle card a
lack of enthusiasm for either a heart or diamond play back.  South made the
right play in spades by putting in the 10, as West ruffed and contemplated 
what to do next.  He knew that if I had the AQ of spades, I couldn’t have 
much else, and with all those kings onside for the opponents, it looked as 
though they were destined to fulfill their contract.  But, in accordance with
the old saw, “Necessity is the Mother of invention”, my partner found an 
ingenious way to set the hand.  Even looking at all four hands, do you see 
how he managed to do so?  
	At trick #3, West led the queen of hearts!  As we were playing 
Bergen raises, the play of the queen was unlikely to cost, since I nearly 
always showed exactly three-card support for my single raise during the 
auction, leaving declarer with two.  Declarer called for dummy’s king.  It 
took me a moment to figure out what my partner was up to, and I signaled 
with the 9, attempting to show the highest of touching cards of a sequence 
and therefore implying the 8.  After winning the heart in dummy, declarer 
came to his hand with a diamond in order to lead a club up to the king.  
But West rose with the ace, and, in a demonstration of faith in my previous 
play, he led his lowest heart, the 7, enabling me to overtake with the 8 so 
that I could provide him with a second spade ruff.  Down one.

Bridge Column

                              MORTON’S FORK




                                 ♣ -----

                 bidding:   S      W      N      E

                           1♥      P     2♦      P
                           2♠      P     3♥      P
                           3♠      P     4♣      P
                           5♥      P     6♥  (all pass)

	             opening lead:  a low club

	Today’s play problem came up at a recent club game.  Suppose 
you find yourself in a heart slam, with a possible auction shown.   
South’s 5♥ call was intended to show a very strong trump suit, and North,
figuring that declarer could not lose more than one minor-suit trick, 
hoped that his spades were good enough to solidify his partner’s second
suit.  How would you plan the play (trumps are 3-1)?

           *          *          *          *          *          *   

	The full deal:	


                 ♠53                           ♠Q104
                 ♥8                            ♥J106
                 ♦A1096                        ♦874
                 ♣Q108762                      ♣KJ95

                                   ♣ -----

	If you draw trumps and drive out the ace of diamonds, the 
contract would seem to depend on finessing against the queen of spades,
as you will always get two discards from dummy’s ace of clubs and extra
diamond honor for your two small spades. There is also a possible squeeze 
-–which does not exist on the actual layout-–if LHO had started with 
length in both diamonds and spades.

        However, there is a significant extra chance if you are careful:
DON’T play dummy’s ace of clubs at trick #1.  Instead, play a low club 
and ruff in your hand (as an aside, it would be good technique to ruff 
with the 7, just in case the trumps are 2-2, in which case that lowly 
deuce might provide you with a needed entry to the dummy at some later 
point).   Now draw three rounds of trumps and lead a LOW diamond from 
hand—-not the jack.  If LHO has the ace of diamonds, he will have a choice
of ways to let you win:  if he plays the ace, you will be able to score
two diamond discards, thus enabling you to throw away all three of your
low spades and avoid the spade finesse altogether.  And if he ducks the 
ace, you will win the trick with one of dummy’s honors, then discard your
diamond loser on the ace of clubs.  Now you will only need to play the 
spade suit in a way to avoid the loss of two tricks there, which is a 
very high-percentage proposition.

	With this combination:



the standard safety play if you can afford the loss of one trick is to 
start with the king, then lead low from the opposite hand up to the J-x; 
however, that can not be done unless there are sufficient entries to both
hands, a luxury you do not have on the actual hand.  In this particular
case, your best play is to lead low to the jack to start.  You will probably
go down when this loses to a singleton queen, but you will make the hand 
whenever the spades are 3-2, or all other 4-1 splits, such as when either 
opponent starts with Q10xx.  If that hand should be RHO, LHO will show out
on the second spade play to dummy’s king, and you will be able to lead 
from the dummy and take the marked finesse through RHO’s 10-x.

	The play of the low diamond from J-x toward dummy is called a 
“Morton’s Fork” coup.  The name is derived from Cardinal Morton, Chancellor
under King Henry VII of England, who raised money for the king’s coffers 
by taxing the merchants.  If those merchants lived an ostentatiously lavish
lifestyle, Morton felt that he could tax them with a heavy hand, since they
obviously could afford to pay.  And if others of the time lived an outwardly 
frugal lifestyle, he figured they must be saving and amassing wealth, and 
so concluded that they could equally afford to pay.  So however you lived,
you were doomed to be impaled on “Morton’s Fork.”

	The play of the same name in bridge is used to describe the lead
through a defender’s honor ----  in this case, the ace of diamonds ----
whereby the defender loses whether he wins or ducks the trick, essentially
a “damned if you do / damned if you don’t” choice.  Notice that it is 
essential to resist the impulse to play dummy’s ace of clubs at the first
trick.  If you play the ace early, you will be forced to take an immediate
discard of a diamond or a spade.  Leaving the ace in dummy affords you 
the flexibility of deciding how best to use that discard later in the hand,
depending on the ensuing play.

	There is one further point worth mentioning:  if there had been 
additional entries to dummy, you could execute the Morton’s Fork against 
either opponent.  In fact, since the placement of the ace of diamonds is 
a guess, you might be inclined to play RHO for that card, on the basis 
that many players in the opposite hand, when on opening lead against a slam,
will tend to lead an ace if they have one.  To illustrate the point, let’s
place the queen of trumps in the dummy in exchange for one of the spots,
and have the trumps divide 2-2, so that the deuce of hearts also allows an
additional entry to dummy. If you as declarer decided to play RHO for the 
diamond ace, you would ruff the club with the 7, play the ace and queen of 
trumps (saving that deuce), ending in the dummy, and play a low diamond
toward the closed hand. RHO, if holding the ace of diamonds, would face 
the same dilemma as the one described earlier.  If he were to duck and 
the jack held the trick, you could lead a spade to the king, discard your 
low diamond on the ace of clubs, ruff a minor-suit card to get to your 
hand, and lead up to the jack of spades.  If LHO showed out, the jack 
would force the queen, and you would still have a trump entry to dummy 
to take the remaining spade play through the 10.  On the actual hand, 
you would have gone wrong, as the jack of diamonds would lose to the ace,
and you would have to fall back on the spade finesse, resulting in down one. 
Sometimes it’s better not to have an option.

Hands From Daytona

	The following hands came my way at a recent Regional tournament
in Daytona Beach.  These hands are much more ordinary and routine than 
those usually shown on this site, and perhaps might not even be considered 
column-worthy by many.  Still, some readers may find them interesting 
enough, so I offer them for whatever value they may have.  Comments are

	In a pairs game, with neither side vul, I pick up as dealer:

	       ♠ ---     ♥ AKQJ4     ♦ KQ863     ♣ KQ7

          I open 1♥, LHO overcalls 1♠, my partner raises to 2♥, and RHO 
jumps to 4♠.  What call would you make?

        I reasoned that partner had to have an ace and perhaps even a working
jack or two, since there are very few other high-card points out there that
could be in her hand.  Of course, if she happened to hold the spade ace or 
other honor wastage in spades, that would be bad luck, but the bidding 
suggests otherwise.  So I chance 6♥.  The opening lead, somewhat to my 
relief, was the ace of spades, but partner’s dummy was:


                               ♠ ---

        Some may elect not to raise to 2♥ with her hand, having flat 
distribution and the queen of spades, which is likely to be a wasted value,
but I don’t object, in spite of my disappointment.  The odds are against 
my making this, but I have been in worse contracts.  I have a chance if 
the red suits break evenly and the ace of diamonds is on my right.  I ruff
the opening lead with the jack of hearts, then continue with the ace and 
king.  I am happy to see both opponents follow; so I lead my low heart to
dummy’s 10, drawing the last trump and giving me access to dummy so as to
play a diamond.  RHO follows low and I put up my king, which holds.  So 
I play my low club to dummy’s ace to lead a second diamond.  RHO plays 
the ace, and LHO follows suit, so I can claim 12 tricks now.  A lucky hand:
I estimate this favorable layout to be about a 20% chance.  The only point
here is to take care to ruff the opening lead high, so that you can use 
the 10 of hearts as an additional entry to make two diamond leads.  If you
were careless and ruffed the opening lead low, you would have only one 
entry to dummy, in which case,  you would use it to make one diamond 
lead, then lead a low card back, hoping for RHO to have started specifically
with a doubleton A-x, making an already poor prospect considerably worse.

	The remaining hands come from Bracket I team events.  In a Compact
KO match, I pick up this hand, in 4th seat:

	         ♠ AQJ4     ♥ AKJ6     ♦ AQJ8     ♣ 5

        This hand type, the strong 3-suiter, is very difficult to bid 
in standard methods.  Either you start with an opening bid of 1♦ or a 
strong and artificial 2♣.   I suspect that most players would bid 2♣, not
being able to stomach the thought of hearing 1♦ get passed out.  The 2♣ call,
however, has several disadvantages:  (1) you have used more than a level
of bidding without yet naming any of your suits—-and you have three of 
them which you would like to name,  (2) rebidding suits naturally after
2♣ - 2♦ implies 5-card length, which you do not have, and (3) partner 
won’t introduce new suits after a sequence like 2♣ - 2♦ - 2♥  unless he
holds 5-card length himself, making it very difficult to find a 4-4 fit.
On the other hand, if you open 1♦ and partner can dredge up a response,
or if the opponents overcall or pre-empt, you will probably be able to 
make sensible follow-ups.  If the bidding does go 1♦ - all pass, and it 
turns out that you do have a game, hopefully you will have sympathetic 
teammates.   Players who use Precision or other strong 1♣ systems will 
have an advantage here.  Anyone out there with further suggestions, at 
least for those who want to stick with standard methods?

        However, I was somewhat relieved not to have this problem, since
my RHO opened 1♣ in third position, giving me an easy takeout double.  My
LHO bid a pre-emptive 3♣, and my partner surprised me somewhat by calling 
4♣, showing a willingness to play game, probably looking for me to choose
a major.  As an aside, we had played a KO match against this same pair 
earlier in the week, and on one deal they had talked me out of a slam by
taking several bids on weak hands, and the memory of that experience was
still fresh.  So even if my partner may be pushing a little, I am going 
to bid a slam here, and since my suits are virtually equal, I throw the
ball back at her with 5♣.  The full auction was, with everyone bidding 
clubs at some point:

	         P  -   P   -   1♣   -   dbl
                3♣  -  4♣   -    P   -   5♣
                 P  -  5♠   -    P   -   6♠

        Partner’s hand was:

	        ♠ K10762     ♥ 109543     ♦ 6    ♣ A4

        The queen of hearts came down doubleton on her left, so 13 
tricks were easy, and the board was a push.  Do you think we should have
bid the grand slam?

	Then later in the same event, but against a different team, I 
pick up in 3rd seat, with nobody vul:

	        ♠ 74   ♥ A109763   ♦ AJ42   ♣ J

        My partner as dealer opens 4NT.  I alert this call, and explain 
to my opponents that partner has a two-suited hand with both minors and 
great distribution, typically 6-6 (I’m not a strong advocate of this 
treatment, but my partner likes it, and I go along).  My RHO passes.  
I decide to take the risk that my partner’s possible singleton is either
a heart, or that maybe I’ll get a heart lead and be able to discard her
losing spade, if she has one.  So I call 6♦.  This is passed out, my LHO 
leads the king of hearts, and the dummy comes down:

		                ♠ ---


        Prospects look fairly good.  I will need to set up the club suit,
and since the likely split is 4-2, I may need to ruff three times in my 
hand, possibly using high trumps to prevent an overruff.   I don’t think
I can afford to test trumps at this point, because if I play one high 
trump and then a club, that hand may win and play a second trump, limiting
me to just two club ruffs.  So after winning the ace of hearts, RHO playing
the 8, I play the jack of clubs at trick #2.  LHO wins the king and plays 
an insidious small heart, putting me at a crossroads:  should I ruff low, 
or can I afford to spare one of dummy’s high trumps?  What would you have 
done in my place?

	The odds of a 5-1 heart split are very low, but seem enhanced 
with the opening lead and continuation, and I would hate to go down at 
this point by ruffing low and getting overruffed.  Against that possibility,
I could afford to ruff high if either the diamonds divided 2-1 or the 
clubs 3-3, which offers a very high combined chance.  So I play dummy’s 
10 of diamonds, and I’m a bit regretful to see RHO follow with the jack
of hearts.  I lead a club and ruff low, both opponents following, ruff 
a spade low in dummy, play a third club and ruff high, LHO showing out. 
Another spade ruff and a 4th club, ruffed with the ace.  Now I lead the 
last (low) diamond from my hand, and…  LHO shows out.  Rats!  RHO has to
get a trump trick now with his 98x.  Figuring that I just lost the match,
I forget the pre-emptive effect that the 4NT call had on the opponents, 
the full deal being:

		               ♠ ---

                 ♠J1096532                   ♠AKQ8
                 ♥KQ42                       ♥J8
                 ♦ ---                       ♦985
                 ♣K9                         ♣A1053


        At the other table, my partner’s hand did not open, and the 
bidding started:

	             pass -  1♣  -  2♥  -  2♠ 

        Our hands competed to 5♦, our teammates bid to 5♠ and the 
opponents decided to let them play it there, making 12 tricks for +480
and a substantial gain on the board.  Maybe that 4NT call isn’t such 
a bad method after all.

	In a 3-way match of a Compact KO, I hold, with both vul:

	         ♠ AQ65   ♥ AK87   ♦ K2   ♣ 1052

        My partner opens 1♣,  I respond 1♥, and my partner raises to 
2♥.  How would you continue?

        This hand feels too good not to make a slam try, with all its
controls and concentrated high-card strength.   My partner and I have 
recently decided to adopt 2NT as an asking bid here, after opener has
raised a major, a treatment which seems to be gaining favor with many 
players.  It is especially useful where partnerships have an agreed style
for opener to frequently raise responder’s major with 3-card support. 
Opener responds:

	     3♣ with minimum values and 3-card support,
             3♦ =  3-card support, maximum values,
	     3♥ =  4-card support, minimum
	     3♠ =  4-card support, maximum.

        The method is most useful when making game tries, but also can
work when you feel you are in the slam zone. in cases such as this one.

	My partner responds 3♠ to my inquiry, the best hand possible,
so after checking for key-cards to find that we are only missing the
queen of trump, I bid 6♥.  LHO leads the 9♣, and dummy shows:



	This looks reasonably good.  If the king of spades is onside,
I can ruff my small spades with dummy’s high trumps and can even stand 
being overruffed with the queen of trumps.  And if the king of spades 
loses, I still have chances if the queen of hearts is onside, provided 
RHO has four spades.

	Well, you can guess that both cards were offside and I went down.
I wouldn’t mind this bit of bad luck normally—-but the effect is severe. 
The slam was not bid at the other table, so we lose 13 IMPs on the board 
instead of gaining 12 (had the slam made), and we lose the 6-board match
by -24 instead of winning by +1: a 25-IMP swing. I know that I am supposed
to disdain matchpoints and embrace IMPs, but the effect of one card offside 
on this type of hand at this form of scoring seems highly punitive. In a 
matchpoint event, I might be able to make this up on the next hand by 
scoring an overtrick on a partscore, but this results in a huge deficit at
IMPs, especially in a short match.

	But then fortune comes our way after all:  this match was part 
of a three-way round, we win our second match—-by all of +1---and it turns
out that the third team lost both of its matches.  So we advance to the 
next round, in spite of our net negative -23 IMPs.  This somehow doesn’t 
feel right either, but having endured my share of bad luck, I am happy 
to accept the good, when it comes.

	On another hand, still IMPs and both vul, I hold in 4th seat:

	         ♠ 6     ♥ AQ9763     ♦ AJ952     ♣ 3

	LHO and my partner pass, and RHO opens a 15-17 1NT.  This is 
certainly a hand where you want to be playing a method of showing a 
two-suiter.  My partner and I play Cappelletti, so I bid 2♥, showing 
that suit, plus a minor.  LHO bids a non-forcing 2♠, which is passed 
back to me.  I decide to continue bidding with 3♦, LHO passes, and my
partner shows interest and surprises me a bit by bidding 4♥, which is
passed out.  The opening lead is a low diamond, and dummy comes down:
                              ♠ K752
                              ♥ K8
                              ♦ Q107
                              ♣ K972

                              ♠ 6
                              ♥ AQ9763
                              ♦ AJ952
                              ♣ 3

	This hand is remarkably similar to one that was presented in 
one of our earlier columns, and illustrates how to evaluate hands with 
6-5 distribution.  One should tend to bid these hands fairly aggressively,
if the honor cards are located in the long suits, and especially if the 
honors provide good working combinations, along with good intermediates. 
My partner figured that I was likely to have either extra shape or extra
values when I continued bidding by myself to the 3-level, vulnerable, 
and guessed that I was likely to be 6-5.  As a supporting hand, she
figured that her red honors—-notice even the importance of the lowly 10
of diamonds on this hand—-had to be worth their weight in gold, even 
though her black kings could probably be put in the trash.  A good 
decision on her part.

	As an aside:  for those of you who like to read up on bridge 
theory of hand evaluation, I highly recommend Mike Lawrence’s “I Fought 
the Law…”, which presents a rebuttal of the Law of Total Tricks and offers 
instead a method of predicting the trick-taking power of a hand by measuring
two different factors, which he calls the “Short-Suit Total” and 
“Working Points”.  The numerous examples may feel tedious at times, but
I found the arguments to be strong and compelling.  

	As to the play:  the diamond lead was probably a singleton, so I 
put up the queen to entice RHO to cover, but he didn’t bite and correctly
played low.  I have only two black losers, so I can afford to give up the
king of diamonds, as long as the hearts don’t split 4-1, in which case I 
would lose a heart.  But LHO wouldn’t lead a stiff diamond unless he had 
some trumps, so I decide that can’t be the case.   I therefore play the 
top hearts, and they do turn out to split 3-2, so I just give up the king
of diamonds and settle for ten tricks, the full hand being:


                 ♠QJ843                       ♠A109
                 ♥1052                        ♥J4
                 ♦6                           ♦K843
                 ♣10865                       ♣AQJ4

	It is not a good idea to lead a singleton on opening lead into
a suit bid by declarer, especially if the bidding suggests that partner
might have finessable strength in that suit.  Would declarer have possibly
gone down if LHO had led a spade?  Probably not.  Declarer would ruff the 
second spade, and could start by playing the ace of trumps, then low to 
the king.  If LHO showed out here, declarer would know he would be losing
a trump trick, and would therefore take the diamond finesse.  Once both
opponents follow to two heart leads, declarer can play it safe by ruffing
a spade, drawing the last trump, and just give up the king of diamonds.  
I believe this would even be right at matchpoints, because you would have
to figure that you would be scoring well by just getting to game and would
therefore want to protect that score, rather than risk going for a top.  

	If on the diamond lead, you decided to get greedy, play only two
trumps, ending in the dummy, so as to repeat the diamond finesse, you 
would go down.  RHO would refuse to cover as before, LHO would ruff, 
and the defense would play on black suits, forcing you to eventually 
play diamonds out of your hand, to lose the setting trick there.

	The tournament, scheduled in early November, lasts a full week.
The weather is very pleasant at that time of year, the ocean temperature
is quite tolerable for swimming, and you can walk for miles on one of 
the most beautiful beaches I have experienced.  You might want to consider
going.  See you there next year?

Bridge Column

                       TEST YOUR PLAY (V)

                       by Stephen Rzewski

            vul:  N-S
           dealer:  N




              bidding:   N      E      S      W
                        1♣     2NT    3♠      5♦
                        5♠      P     6♠ (all pass

	             opening lead:   ♦2

	Today's deal came from a recent STAC tournament.  The opponents'
hands have been modified to make a more suitable problem.  Plan the play.

    *         *          *          *         *         *         *


                         ♠ A1053
                         ♥ A3
                         ♦ A109
                         ♣ Q865

              West                        East

              ♠ 96                       ♠ 8
              ♥ Q65                      ♥ K98742
              ♦ Q632                     ♦ KJ754
              ♣ J1073                    ♣ 4


                          ♠ KQJ742
                          ♥ J10
                          ♦ 8
                          ♣ AK92

	There is a heart loser you can do nothing about, and there is no 
further problem if the clubs divide 3-2, so you should assume they will
split 4-1 or worse, which is quite likely, given East’s “Unusual 2NT” 
call, showing great length in the red suits.

	If West has four clubs which include the J-10, an endplay can be
executed in the following manner:  win the ace of diamonds, ruff a diamond
high in the South hand, draw trumps with the king and ace of spades.  Then
ruff dummy’s last diamond (a third round of trumps can be played should 
they prove to divide 3-0).  

	Now comes the key play:  play one high club honor from the South 
hand, followed by the ace of hearts.  The position at that point will be:

                         ♠ 105
                         ♥ 3
                         ♦ ----
                         ♣ Q86

              West                       East

             ♠ ----                     ♠ ----
             ♥ Q6                       ♥ K987
             ♦ Q                        ♦ J7
             ♣ J107                     ♣ ----


                         ♠ Q7
                         ♥ J
                         ♦ ----
                         ♣ K92

	Now simply exit with a heart.  If East wins the trick, he will be
forced to give you a ruff-and-sluff of your club loser.  If West wins, 
unless he does the same, he will be forced to return a club.  If he plays
the jack or 10, let this come around to your king, and you will have a 
finessing position against his remaining honor-7.  

	It is essential to play one high club before exiting with the 
heart, or else East can win the trick and exit with his singleton club.

	If your club holding were weaker still, such that you were 
missing the J-10-9, the contract could still be made along the same 
lines, provided that East’s singleton happened to be one of those cards.

Bridge Column

                          A SURE THING

                       by Stephen Rzewski

             vul:  none

                           ♠ K973
                           ♥ A6
                           ♦ J764
                           ♣ K107

                           ♠ AJ865
                           ♥ 3
                           ♦ K52
                           ♣ AQJ6

	        bidding:  S      W      N      E
                          1♠     3♥    4♠   (all pass)
                       opening lead:   ♥ Q

	Today’s hand came up in a Swiss teams event at a local 
club.  Declarer won the heart lead in dummy, then played the king 
of spades, on which both opponents followed with low spot cards. 
When a low spade was played next, East followed with the 10.
Should declarer now finesse the jack or instead play for the drop
of the queen by going up with the ace?  Why? (take no credit unless
you give the correct reasoning)

    *          *          *          *          *          *

	The full deal:	


                            ♠ K973
                            ♥ A6
                            ♦ J764
                            ♣ K107

              West                         East

              ♠ 4                         ♠ Q102
              ♥ QJ109874                  ♥ K52
              ♦ A83                       ♦ Q109
              ♣ 98                        ♣ 5432


                            ♠ AJ865
                            ♥ 3
                            ♦ K52
                            ♣ AQJ6

	At the table, declarer successfully finessed the jack of 
trumps, rejecting the old adage of “eight ever, nine never”, which
suggests that when missing five cards including the queen, one 
should finesse, but instead play for the drop when missing only 
four cards. Later in the play, declarer led a diamond to his king 
and lost three tricks with the unlucky layout in that suit, but at
least fulfilled his contract.  So why did declarer take the finesse?

        It is true that in a vacuum the odds favor playing for the 
drop, but the mathematical advantage for that choice is slight, and
if there are other factors to take into account, one should consider 
the alternative play.  Here there is the matter of West’s pre-empt,
which shows great length in hearts, normally a 7-card suit, increasing
the chances of his holding a singleton spade.  The queen of spades 
is not a relevant card in the bidding, as West would probably be just
as inclined to make the same pre-empt if he held Q-x of spades as well
as a small singleton.  But with 8 of West’s cards inferentially known 
(7 hearts + 1 spade played), that leaves only five cards in his hand
that could be the queen of spades.  Whereas only five of East’s cards
are known (2 spades played + 3 presumed hearts), there are 8 cards 
in his hand which could be the queen.  That leaves much more room in
East’s hand to hold the queen, indicating that the finesse is a 
distinct favorite.

	Nevertheless, in the context of the complete deal, declarer 
should have played for the drop.  The finesse might be a good calculated
risk at matchpoints, where overtricks can bring heavy premiums, 
especially in normal contracts like this one, but at IMPs scoring, 
making the contract has the highest priority.  If declarer had played
the ace of spades at the critical juncture, and the queen had dropped,
the contract would have been assured.  But what if West had then shown 
out, as in the actual layout?  Declarer would then have a sure line
of play as follows:  a club to dummy to then lead and ruff out dummy’s
remaining heart**, followed by the play of the remaining club winners.
Then a trump is led, putting East on lead, who will have to break the 
diamond suit (or play his last heart, which would give declarer a fatal
ruff and sluff).  As long as declarer plays a low diamond from his hand
when East leads low, he can not be deprived of a diamond winner, no 
matter how the honors in the suit are distributed.

	So going up with the ace of spades is a heads-you-win, tails-
you-win play.  No need to resort to guesswork when a sure thing is 

	**An afterthought:  my good friend, Michael Klein pointed out
that declarer could improve his technique by ruffing dummy’s small heart
at trick #2, before touching trumps.  This would provide for the case 
where a defender with the third trump and a club void, probably West,
with something like: 

                  ♠ Q10x   ♥QJ10xxxx  ♦ Axx   ♣ ---

might be able to ruff in and exit safely with a heart before dummy’s 
heart could be removed, forcing declarer to break and guess the 
diamond suit himself.

	It is also worthy to note that there is a standard safety 
play with this card combination of starting the play of the spades 
with the ace rather than the king, which one might consider at this
form of scoring.  This play guards against the possibility of a 4-0 
trump split in either hand, and ensures the loss of no more than one
trump trick.  However, since LHO is highly unlikely to hold four 
spades along with the presumed 7-card heart suit, the initial play 
of the king in this case will likely work out just as well.

Bridge Column

                              REVERSE PSYCHOLOGY

                              by Stephen Rzewski

	Often during the play of the hand, the defense will be in a 
quandary as to which suit it should be attacking.  Sometimes when declarer
plays on a particular suit, a defender may assume that it is contrary to 
his side’s interest to continue on that suit and may therefore shift to 
another.  This is a natural and logical human reaction, which is frequently
correct, but occasionally declarer can exploit this tendency to his own 

	Playing in a Regional Open Swiss against one of the top pairs in 
New England, I pick up:

	              ♠ 973   ♥ AK10852   ♦ J106   ♣ A

	Neither side is vulnerable, and I am in 4th seat.  The dealer passes,
as does my partner, and RHO opens 3♣.  I have an easy overcall of 3♥, and my
partner raises me to game.  The bidding has been:

                       P       P       3♣      3♥
                       P       4♥   (all pass)

	LHO leads a small club, and the dummy proves to be a huge 

                                 ♠ J64
                                 ♥ QJ93
                                 ♦ 832
                                 ♣ KQ4


                                 ♠ 972
                                 ♥ AK10852
                                 ♦ J106
                                 ♣ A

	Who would have guessed all that duplication in clubs?  Well, at least
they didn’t annihilate me right off by cashing their six winners in diamonds 
and spades.  I can throw two of my losers on the king and queen of clubs, but 
that still leaves me one down.  It is tempting to simply concede that result 
and save some time and anguish, but even when facing what looks like a hopeless 
situation, one should always look deeply for any chance, no matter how slight,
especially since there are teammates involved.   Is there any way I can actually
bring home this dreadful contract?

	Interestingly, I probably can infer more about the lie of the honor 
cards in the two weak suits than the opponents can about each other’s holding.
For instance, if LHO had a holding such as AK in either, he would likely have 
led one in preference to a club.  That would mark my RHO as a favorite to hold 
at least one high honor in each of those suits. Since he has club length, he
will have shortness in one or more suits outside of clubs. Obviously, if I am
to make this contract, I will need some mistakes from the defense, but a small
ray of hope is beginning to show itself.

	After winning the club lead, I play the ace of hearts, everyone 
following, then lead a low heart to the queen.  On this trick LHO follows,
and RHO discards the jack of clubs, which is probably intended to show strength
in spades.  I now cash the two high clubs, discarding low spades, on which 
both opponents follow.

	So RHO had only six clubs to the J10 for his pre-empt.  This is not
all that surprising, since many players make tactical pre-empts in third 
seat which will depart significantly from the normal sound textbook pre-empts.  

	At this point, I lead a diamond from dummy, deliberately playing the 
suit I fear most.  RHO plays low—I now have to hope, among other things, that
he started with a doubleton honor—and since I want to give the impression of 
strength, I play the jack from my hand.  LHO wins the queen, and thinks for 
a bit.  Eventually, he makes the play I am hoping for:  he puts the ace of 
spades on the table, and continues with a spade to his partner’s queen.  I 
ruff this in hand, lead a heart to dummy’s jack, then lead dummy’s last spade
and ruff in my hand, leaving:

                                  ♠ ----
                                  ♥ 9
                                  ♦ 83
                                  ♣ ----

                  ♠ ----                             ♠ 5
                  ♥ ----                             ♥ ----
                  ♦ A97                              ♦ K
                  ♣ ----                             ♣ 10

                                  ♠ ----
                                  ♥ K
                                  ♦ 106
                                  ♣ ----

	Now I simply lead the low diamond out of my hand, and the defense is
snookered.  If LHO plays low and allows his partner to win the king, that 
hand will be end-played into giving me a ruff and sluff.  And if LHO attempts
a “crocodile coup” by playing the ace to swallow his partner’s king, my 10 
will be established.

	Obviously, RHO made a serious error when he failed to play the king
of diamonds on the first lead of the suit, not anticipating the end position.
LHO might also have saved the day by heeding his partner’s earlier signal and
underleading the ace of spades, so that his partner could win the trick and 
unblock his king of diamonds.   Luckily for declarer, LHO had to follow to 
both hearts, since if he held the singleton, he would have undoubtedly signaled
with a high diamond on his first discard, making it easy for his partner to 
unblock the king. The full deal:

                                   ♠ J64
                                   ♥ QJ93
                                   ♦ 832
                                   ♣ KQ4

                  ♠ A108                             ♠ KQ53
                  ♥ 64                               ♥ 7
                  ♦ AQ975                            ♦ K4
                  ♣ 875                              ♣ J109632

                                   ♠ 972
                                   ♥ AK10852
                                   ♦ J106
                                   ♣ A

	At the other table, third hand opened only 1♣, my hand overcalled 
1♥ and was given a single raise to 2♥ by his partner.  This became the 
final contract, with the same club lead.  When the dummy came down, declarer
decided to simply claim nine tricks, a bit smugly, as our teammates reported,
since he felt he had stolen the contract, as the defense could have set him 
off the top.

Bridge Column

                           THE SQUIRM FACTOR

                           by Stephen Rzewski

	Today’s deal came up at a Regional tournament many years ago.  
My partner and I, along with two good friends,  had just lost an early
round of a Knock-Out team event, and we decided to all go out together 
to seek nourishment, lick our wounds, and try to re-energize for the 
upcoming events.   A topic of conversation over dinner addressed the 
problem of trying to read our opponents’ cards during the play of the 
hand.  One of our teammates, to whom I shall refer as Peter, offered a 
tip when faced with a two-way guess for a missing queen:  run a long suit,
if possible, and watch for an early discard. Often the person making the
first discard in that suit will be less likely to hold the critical missing
card, as he would have only small cards there with nothing to protect, and
can more easily throw one away.  This principle is not conclusive where a
player has extra length in the suit (such as Qxxxx), but often an inferential
count on the hand will be available and provide further clues.  

	After the meal was concluded, the four of us decided to enter the 
pairs event of that evening, as no team event was available.  As fate would
have it, the four of us bought entries in opposite directions, such that late
in the session, we sat down against each other as opponents.  On the 2nd board 
of the round, I picked up:

	               ♠A74   ♥Q842   ♦5   ♣K10752

Peter, seated on my right, opened 1NT (15-17), and the auction continued

	              1NT       P        2♣        P
                       2♦       P        3NT    (all pass)

I led my 4th-best club, and the following dummy came down:

                                  ♠ K863
                                  ♥ AJ93
                                  ♦ QJ2
                                  ♣ 98

                      ♠ A74                                       
                      ♥ Q842   
                      ♦ 5                                               
                      ♣ K10752             

	My club lead hit paydirt.  Partner produced the jack, declarer 
ducking, then came the queen from partner, declarer winning the ace. 
Feeling somewhat smug, I settled in to wait for the eventual spade lead,
on which I would pounce with the ace to cash my good clubs.  

	At trick #3, declarer led a low diamond to dummy’s jack, which 
held the trick, followed by the queen.  Partner’s first two diamond spots 
indicated that he held an even number, which meant that declarer had a 
five-card suit to run.  Suddenly I realized that I was going to have to
produce a number of discards—four, in fact.  Before continuing, decide 
how you, reader, would have selected the next four cards in your hand to 
throw away, holding at this point:

                       ♠A74   ♥Q842   ♦---   ♣ K107

        Declarer was almost sure to have the king of hearts, and my queen
was finessable in front of dummy’s A-J.  I could throw two spades away 
easily, but on the 4th and 5th diamonds, I would have to choose between 
hearts or clubs.  

	Peter was a good declarer, and I knew he would be watching all of 
our cards carefully, looking for clues.  If I started discarding my good 
clubs, that would be revealing to him. Why would I throw away potential 
winners, unless I were protecting some other holding, and what else could
that be other than the queen of hearts?  Furthermore, if I discarded even 
one club, Peter could well figure that I would now not have enough club 
winners to set him, and he could simply lead a spade, establishing his 9th 
trick there without having to take the heart finesse.  No, I realized that 
my only chance was to unguard the queen of hearts.  If Peter did not hold 
the 10 of hearts, he was probably going to finesse me for the queen anyway.
Whatever I was going to do, I had to make my decision quickly.  If I started 
acting tentatively about my choice of discards, hesitating and squirming
uncomfortably, that would be a giveaway.  I also could hear Peter’s remark
made at dinner in the back of my mind, which he probably didn’t even remember. 
I felt a bit guilty about turning his own advice against him, but all’s fair
in love and war.    So at my first opportunity, I threw the 8 of hearts, 
in tempo.

	Peter turned to my partner and asked about our carding agreements. 
“Our carding is upside-down, count and attitude.” was the reply.  This meant
that in theory the discard of the 8, a high spot-card, signaled discouragement
for that suit.

	On the next two diamonds, I discarded first the 4, then the 7 of 
spades, an encouraging signal, to show that I had the ace.  On the 5th diamond
—in for a penny, in for a pound—I threw the 2 of hearts without pause, coming 
down to Q-4.  Partner, bless his soul, discarded a spade on the 5th diamond, 
keeping both of his small hearts. Then came a heart to the ace, and a low 
heart back from dummy.  My remaining cards were: 

                           ♠ A   ♥Q  ♣K107.

        Peter went into a long study, which must have lasted a full minute.
Had I thrown the heart too early, making the bluff obvious?  I was dying inside,
but knew my partner and I had to appear completely dispassionate and stone-faced.
Finally, Peter produced the 10, and I faced my hand and claimed the remainder,
for down two.  The full deal:

                                    ♠ K863
                                    ♥ AJ93
                                    ♦ QJ2
                                    ♣ 98

                      ♠ A74                           ♠ J95
                      ♥ Q842                          ♥ 65
                      ♦ 5                             ♦ 9874
                      ♣ K10752                        ♣ QJ43

                                    ♠ Q102
                                    ♥ K107
                                    ♦ AK1063
                                    ♣ A6

	In retrospect, pitching the 8 of hearts first might have looked 
suspicious, and maybe I should have started my discards with a low spade. 
But had I discarded a club and kept three hearts, declarer would almost 
surely have gotten it right, especially since it is more natural to finesse
the hearts through me, picking up the entire suit whenever I would have 
started with four and ending up with ten tricks.  Or, at the very least,
he would have led a spade instead and ensured nine tricks. 

        The point of this article is that when defending, one must try to
anticipate how the play of the hand will unfold and have one’s counterplays 
worked out in advance.  Although I had not done so here, a good time to 
project the play and defense is at the first trick, while declarer is making
his plan, so that one’s mind is already made up when the critical moments 
occur.  If one waits until the play has to be made, the squirm factor will
often give away the show.  

	(As a footnote:  I’m sure every reader of this column understands 
that it is highly unethical to feign hesitancy and pretend that one has a 
problem during the play when in fact no problem exists).