December 2017 - 57

Intermediate Players

Better Bridge with Bergen
BY MARTY BERGEN

martybergen.com

Bergen's best bridge tips - part 17
How much can you figure out?
You are sitting West and pick up a
modest hand:
♠K ♥8 7 6 2 ♦K 6 5 4 ♣8 6 4 3.
With both sides vulnerable, your
partner opens 1♦ and your RHO
jumps to 4♠. You pass, and when no
one else has anything to say, you are on
lead. Based on partner's 1♦ opening
bid, you lead the ♦4.
North tables his dummy:
♠- ♥A J 9 5 4 ♦10 8 3 ♣10 9 7 5 2.
You are pleased to see that dummy
doesn't have any trumps. Declarer
calls for a low diamond from dummy.
Partner plays the 9 and declarer wins
the queen. That is certainly a surprising and disappointing trick.
However, I hope you will not merely
bemoan your luck that your normal
opening lead worked out badly. Instead, even though the other three
players have turned their cards over
and are ready to move on, I hope that
you are not. As is sometimes true, there
are clues galore available to you. In
fact, if you analyze the first trick and
keep partner's opening bid in mind, on
this deal not only can you know the exact diamond holdings for your partner
and declarer, but believe it or not, you
can also figure out the complete distribution of both concealed hands!
Although declarer is ready to lead
to the second trick, you should not be
ready to proceed. Instead, I hope you
kept your card face up. By doing so, in
case you don't remember the exact diamonds played, you can force the other

three players to turn their cards up and
leave them there until you are ready to
proceed. For the record, the diamonds
played at trick one were 4, 3, 9, queen.
If your partner had the ♦A, he would
have played it, so declarer has the ♦A.
And based on the wonderful (and critical) defensive principle of "cheapest of
equals," because dummy has the ♦8,
once partner played the ♦9, he denied
the ♦7. If he had that card, and lacked
the ♦A or ♦Q, his correct play for
the purposes of forcing out declarer's
diamond winner would be the 7.
You now know that declarer has
the ♦A Q 7 and your partner played
the ♦9. The only diamonds that are
unaccounted for are the jack and 2.
But partner opened 1♦. He obviously
would not have done that with one
or two diamonds. You now know that
partner has the ♦J 9 2, so you know
everything about the original diamond
holdings of the two concealed hands.
You may remember that I earlier
made the hard-to-believe statement
that "you could also figure out the complete distribution of both concealed
hands!" Were you able to do this? For
those who succeeded - congratulations!
For those who weren't able to make
the connection, let me try to help
you. In standard bidding, when does
a player open 1♦ with a three-card
diamond suit? The only time is when
he has no five-card major, but only two
clubs. Therefore, once you know that
partner's 1♦ opening was made in a
three-card suit, his original distribu-

tion must be 4=4=3=2, namely four
spades, four hearts, three diamonds
and two clubs.
As for declarer's distribution, as
always, "Once you know three, you can
know four."
You Dummy Partner Total
♠: 1 + 0 + 4
= 5
So declarer has eight spades.
♥: 4 + 5 + 4
= 13
So declarer must be void in hearts!
♦: 4 + 3 + 3
= 10
Declarer started with three diamonds.
♣: 4 + 5 + 2
Declarer has two clubs.

= 11

So, after the completion of a mere
one trick, the opportunity existed for
you to know that declarer started with
8=0=3=2 distribution! And the only
"mathematics" involved was adding
and subtracting with small numbers.
You are now ready to proceed. For
convenience, here are the remaining 12
cards for you and dummy:
♠- ♥A J 9 5 4 ♦10 8 ♣10 9 7 5 2
♠K

♥8 7 6 2

♦K 6 5

♣8 6 4 3

At trick two, declarer leads the ♠10.
You are delighted to win your singleton
king. A club is discarded from dummy,
and partner follows with the ♠8. What
card will you lead at trick 3?
Uh oh. My editor just informed me
that I am at the end of my page. So
although you will have more decisions
to make on this deal, they will have to
wait until next month.
◾
December 2017 Bridge Bulletin

57
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Table of Contents for the Digital Edition of December 2017
