MORE COUNTING AT
BRIDGE
By Larry Matheny
Let’s return to
that seemingly mysterious element of bridge: Counting. This intimidates many players because they
are certain it is too difficult.
However, in many cases it involves little more than counting to
thirteen. Let’s begin with some easy
examples. The first one involves
counting high card points.
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West
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North
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You
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South
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1NT*
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Pass
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2NT
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Pass
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3NT
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Pass
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Pass
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Pass
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*15-17 hcp
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Your partner leads
the ten of hearts and declarer wins the king.
Next, declarer takes the diamond finesse. You win the king and what next?
Adding all of the
known high card points you realize if South has the 16-17 points his 3NT
promises, West is broke. There still may
be a way to beat the hand...lead a low spade. Declarer will win the king in dummy and lead a
low club. You jump up with the ace and
cash four spades to beat the contract by two tricks. This is from a team game and at the other table
after winning the king of diamonds, East led a low club hoping to find his
partner with an honor. That South easily
made his contract with three hearts, four diamonds, and two clubs.
If declarer held four spades including the jack this defense would not have
worked, but you took the best chance you had. Note you must win the first club or declarer has
nine tricks. Defense is sometimes
difficult but in this hand, all you had to do was some simple math.
Here is the entire
hand:
Let’s try counting
points again:
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You
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North
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East
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South
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Pass
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1NT*
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Pass
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Pass
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Pass
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*12-14 hcp
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The vulnerability
kept you out of the auction but you start the defense by leading a low diamond. Declarer guesses wrong by playing the ten
from dummy and he wins partner’s jack with the ace. He continues with a low heart to your queen and
the ace. Next, he plays a heart to his
jack and your king. You cash your
diamond king and then the nine. On the
third diamond, your partner discards the deuce of clubs. This message is "I don't have anything in
clubs". Now what?
Let’s add up declarer's
known high card points: 1 in hearts, 4 in diamonds, and (most likely) 8 in
clubs. That meant East must hold both
the king and queen of spades. It is
now easy to shift to the ace, jack, and
ten of spades to beat the contract by two tricks. As you saw, proper defense
involved nothing more than good communication and simple math. Here is the entire hand:
Now instead of
points, let’s count distribution.
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West
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North
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East
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YOU
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Pass
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2NT
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Pass
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7NT
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Pass
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Pass
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Pass
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West leads the ten of diamonds and
you stop to count your tricks. The inventory shows 3 spades, 3 hearts, and 3
diamonds so you have to bring home the club suit. What is your plan?
Rather than assume the suit will divide 3-2, try to find out more about
the distribution. After winning the diamond in dummy, cash the top three spades
and discover that West only follows once. Then finish the diamonds and see that West had
five. You continue with the hearts and
they both follow to all three rounds. You now know (by simple math) that East had
started with 6 spades, 2 diamonds, and (at least) 3 hearts. That means East can hold (at most) 2 clubs. Now you confidently play the king and queen of
clubs and discover that West held four cards in the suit. Grand slam bid and made. Here is the entire hand:
Now let’s count the
opponents cards in order to find a queen.
Scoring: Matchpoints
(Pairs)
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West
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North
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East
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You
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1
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Pass
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2
Pass
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DBL
Pass
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Pass
Pass
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3
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West leads a low spade and you quickly see you
must lose two spades and two diamonds. This
means you must find the queen of clubs to make your contract. East wins the spade ace, cashes the king-ace
of diamonds, and returns a low spade to West's king. Now the defense switches to a trump and you
have to decide who has the queen of clubs.
Let’s examine what we have learned. East held the ace of spades along with the
diamond ace-king and West has owned up to the king of spades. It would seem that East needs one of the
black queens for his opening bid and West needs the other for his raise. Well?
If you just think
about the play in the spade suit you will know that East holds that queen. West could have won the second spade trick
with the king to conceal the queen, but he would never have under led the
king-queen of spades at trick one.
Therefore, you can confidently (okay nervously) finesse West for the
queen of clubs.
Here is the entire
hand:
Sometimes you can’t
discover the complete distribution of the opponents’ cards so you must use the
best information you have.
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West
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North
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East
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You
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2NT
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Pass
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4NT
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Pass
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6NT
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Pass
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Pass
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Pass
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West leads a diamond against your slam. You can count 11 tricks: 2 spades, 4 hearts, 1
diamond, and 4 clubs. With any other
lead you could merely concede a spade for an easy 12 tricks but now you must
discover who has the spade queen. To
gain as much information as possible and perhaps establish a squeeze position, you
duck the first diamond and win the second. It appeared that West had led from a five-card
suit headed by the queen. Next you play four
rounds of hearts and learn West started with four. You continue with a club to dummy’s king with
both following. What now?
With the
information available you know ten of West’s cards so the odds favor East to
hold the queen of spades. Lead the jack
and let it ride. It wins so now you unblock
the king of spades and return to dummy with a club. Note the importance of keeping two clubs in
dummy. If East covered the jack of
spades with the queen, you would have had to use a club to get back to dummy
and then another to return to your hand.
This play could have lost to the queen of spades but mathematically you made
the best play. Also note since West held
the long diamonds, there was no squeeze.
Here is the entire
hand.
Let’s try another
defensive problem.
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You
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North
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East
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South
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Pass
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1
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Pass
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3
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Pass
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4
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Pass Pass
Pass
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You lead the queen
of diamonds and declarer wins the ace.
Declarer then cashes the king of diamonds followed by two rounds of
trumps. Next, declarer ruffs a diamond
in his hand and exits with the 10 of hearts.
Your partner wins and returns the three of hearts to your ace. It appears partner started with five hearts
so you realize declarer has no more red cards.
What do you do?
Just stop and count
and you will find declarer’s original distribution was 5-2-2-4. That means a sluff/ruff will not help
him. Return a heart (in case declarer
has one more) and wait on your side’s club trick. At the table, West panicked and rather than
concede the ruff/sluff put the jack of clubs on the table and declarer made his
contract. Here is the entire hand.
Now let’s try using
our advanced knowledge of counting and declare a slam.
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West
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North
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East
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YOU
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1
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Pass
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3
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DBL
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Pass
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3
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Pass
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4
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Pass
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4
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Pass
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5
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DBL
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6
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Pass
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Pass
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Pass
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When the auction
began you certainly didn’t think you would be declaring a slam but here you
are, so clear your head and give this your best shot. West leads the jack of hearts and you stop to
analyze the hand. It is clear East needs
the club king for his opening bid so that is one loser. However, you can discard two diamonds on the
hearts and ruff the other in dummy so you might be okay. How do you proceed?
As is always a good habit, you should review
the auction for any additional information.
It seems a certainty that West holds seven hearts and that along with
the lead directing double, means East has none. It would seem there was a heart loser along
with a club trick, but there is a solution – duck the first heart lead! Next, ruff the heart continuation, draw
trumps, and discard your three small clubs on the heart honors. The heart is your only loser. While counting was involved, reviewing the
auction gave the solution.
Here is the entire hand.
Your improvement is
obvious, but let’s try another defensive problem.
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West
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North
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You
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South
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1
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1
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Pass
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2
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Pass
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4
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Pass
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Pass
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Pass
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Your partner leads
the jack of diamonds and you win the queen followed by the ace and king. Your partner discards a low spade on the
third round. What is your plan to defeat
the contract?
Stop and count the
points! Your thought process should be
"South's jump to game marks him with most if not all of the missing
honors. Therefore, my only hope of
defeating the contract is a fourth round of diamonds in an attempt to promote
the jack (or less likely the queen) of hearts". Here is the entire hand.
Now that you are good
at counting, let’s try another problem hand that requires a bit of reasoning.
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West
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North
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East
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You
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Pass
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1
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1
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Pass
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2
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Pass
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3
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Pass
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4
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Pass
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Pass
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Pass
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West leads a low
spade and East quickly wins the first two tricks. At trick three, East leads a
low diamond and you play???
It seems right to
play East for the ace; after all he did open 1. Is it just a guess or is there enough
information on which to base your decision?
Just as the great Sherlock Holmes asked "Why didn't the dog
bark?" you should wonder why didn’t West lead his partner's suit? The answer is leading an ace often works out
poorly, so West simply tried to find a safer one. As you can see, if West had led the ace of
diamonds, you would have no problems. Another
thought is that you need the king of hearts to be on your right and East may
have opened 1NT holding the top two spades along with the heart king, diamond
ace, and a jack. Here is the entire
hand.
Now that you are
very good at counting, let’s close with this one from a very important team
game.
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West
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North
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East
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You
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1
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Pass
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3*
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DBL
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Pass
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3
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Pass
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4
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Pass
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Pass
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Pass
*Weak
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You ruff West's diamond lead in dummy. Your game looks safe as long as the trumps
behave. You lead the queen of spades
which holds the trick. You see the seven
from West and continue with ???
Since you only need
ten tricks, just cash your clubs and hearts and allow the opponents to win their
three spades. This limits the defense to just those three tricks and you chalk
up your game. At the other table,
declarer led a second spade and lost control with the 4-1 trump break.
In a team game it is correct to ensure the contract. Playing a second round of trumps hoping to
make an overtrick may be okay in a pair’s event, but in a team game it most
certainly is not. Count your tricks!
I hope these
examples will help you when defending and declaring. Happy counting!
