andy (12/01/82)
A Double Dummy problem from Truscott's column in the NY Times last summer:
(Reprinted there from Bridge World)
S AKxxx
H KTx
D void
C Txxxx
S void S QJT9xx
H J9xx432 H void
D xx432 D KQx
C void C xxx
S 7
H AQx
D AJTx
C AKQJx
That's about as well as I can reconstruct the hand, but
modulo the x'd spots, this is right....
After a rather busy auction, South was declarer at 7C,
East made a Lightner double, and West found the killing
Heart lead. North, a results player, complained that
South should have bid 6NT. An interesting conversation
ensued in which it could not be determined if the
contract was makable, even in double dummy play...
The problem is, given all play perfectly, can South
make 6NT. If so, what is the winning line? If not,
what is the killing defence?
-------------------------------------------------
Solution?
If West leads any card, bar the Heart J, the contract
is in South's pocket with an entry-shifting squeeze:
Win in dummy with the Heart T, play 5 rounds of
clubs ending in dummy, leading to this position:
S AKxxx
H Kx
D void
S QJT9
irrelevant H void
D KQx
S 7
H AQ
D AJTx
West must hold the seven cards shown, for if
she comes down to 3 spades, play spade AK, and
another. Now the heart K is an entry to the twelfth
trick. If she comes down to 2 diamonds at any point,
(worst case is when in dummy), play Heart K to the A,
Diamond A and small. Now the spade return and the
Heart Queen lets you get to the established
diamonds.
So, now lead the small heart from dummy! If East
parts with a Spade, win in hand with the Ace, play
AK and another spade, and the K of hearts is the
ticket home. If East parts with a Diamond, play the
heart Queen in hand, then Diamonds A and another, and
the heart A gets you to the last diamond.
However, if West leads the heart J, then the
entry-shift seems to be off, for if we win on the
board, there is no entry to the board in hearts if
West holds the 9. if we win in the hand, we can
get at most one entry to the hand for the same reason.
I suspect that the following is the correct answer, but
haven't given it much thought:
Six NoTrump cannot be made with perfect play.
The Killing defence is for West to lead the J of Hearts
and hold on to the 9 at all costs. Now East must hold on
to the same seven cards shown above.
Now in order to get another trick in spades(when in
either hand), South must have at least one entry to the board
after playing AK and low. For a diamond trick, (if in dummy)
South must have two entries in hearts and clubs to capitalize.
So on trick seven, if south is in dummy (worst case) and
plays either heart or club (anything else is suicidal), then
with only one more card in a free suit between each of
North and South hands, East can know which hand contains an
entry. If the free suit entry is to dummy, then abandon
diamonds, for you can lock declarer in dummy with a spade
return and must get another spade eventually. If the free
suit entry is to hand, abandon spades, for after two spades
and another the diamond King will guarantee another diamond
eventually.
The argument is rambling and informal, but I think it
is essentially correct. Can anybody put it better, or
refute it?
Andrew Greenberg
Cornell University
(cornell!andy)