Sunday, August 23, 2009

Double-dummy defense

Here's a hand that came up on BBO the other day.

863
J94
AT76
AQ6
QT4
KT8
J985
T84
N
WE
S
J92
A63
K32
K752
AK75
Q752
Q4
J93

East-West vulnerable at Cross-IMPs
WestNorthEastSouth
PassPass1♣
Pass1♦Pass1NT
Pass2NTPassPass
Pass

It looks awfully hard for the defense. In addition to four top tricks, declarer has a second club and the queen of diamonds, and can drive out the ace and king of hearts for two more tricks. The key to the successful defense is that one of those heart leads must come from declarer's hand.

Let's say West leads the 4, and declarer plays small from dummy. East wins the king and continues the suit, putting declarer on the board. A heart to the queen and king follows, and West puts dummy in with a third club. Declarer cannot lead a heart here without giving the defense a third heart trick, so instead he plays spade to ace to get into hand and leads a heart, hooking the 9. East wins the ace. Now he can play spades to drive out the king, declarer's last entry into hand. Since the heart suit is blocked, East will eventually get back in with the king of diamonds and cash his last club.

Now suppose declarer plays spade to ace at trick three and leads a heart from hand. Either defender can win this trick, but say West goes up with the king. West puts dummy in with a club. If declarer continues with the jack of hearts, East wins the ace and puts down his club. This time, the heart suit is unblocked, and if East plays a spade, declarer can duck to establish the fourth spade as his eight trick. Instead, East lays down the club, which effectively squeezes declarer. He can't afford to give up a heart winner. Baring the queen of diamonds allows East to immediately play the king; winning the ace now establishes the jack, while ducking gives the defense the diamond trick immediately, allowing a spade switch. So declarer discards the spade, allowing East to safely make the spade switch, establishing a spade with another diamond on the way.

What if declarer instead leads a diamond his second time in dummy? Again assume declarer plays a heart from dummy at trick three, won by West. Upon winning West's club lead in dummy, declarer plays a diamond. East must win the king immediately; otherwise, declarer gets the queen of diamonds now and has only to drive out East's ace of hearts. Now, if declarer retains the queen, his diamond suit is blocked. If East leads a spade, declarer can unblock the diamond, but a heart lead now will draw another spade lead from East, resulting in a blocked heart suit. Alternatively, the defense can duck a heart, killing declarer's only entry into dummy.

If declarer instead plays the queen of diamonds under the king, his diamond suit is no longer blocked, but the heart suit still is. East cashes the club, declarer and West discarding spades, and continues with a spade to declarer's ace. Declarer still can't lead hearts from dummy, so must play a heart from hand. East wins the ace, and, with the heart suit still blocked, drives out the king of spades.

If declarer began by playing spade to ace and leading a heart from hand, then East, upon winning the diamond king and after cashing the club, can immediately drive out the king of spades.

That really only leaves declarer with one option: lead a diamond from hand at trick three. If East ducks this, declarer wins the queen and drives out the top hearts, and the defense will never be able to establish their spade trick in time. So East wins the king of diamonds and continues a club. Now declarer unblocks the diamond queen, with the added benefit of being able to break the heart suit from hand. West goes up with the heart king, and now declarer is stuck. He can't unblock the 9, since that kills the heart entry needed to pick up the diamond ace. With J9 left in dummy, West plays a spade, and when East gets in the ace of hearts, he will cash the club and lead another spade. Now declarer chooses between cashing Qx or playing heart to dummy and picking up the A; either way, the defense picks up a spade.

There is one more possibility: that declarer plays an honor from dummy's club suit at trick one. Even if declarer plays the queen of clubs, East must retain the king; otherwise, a club continuation will let declarer into hand with the jack. If declarer plays a heart from dummy (or spade to ace and then heart from hand), West wins the first round of hearts and can lead a club, so the prior analysis remains essentially the same. But what if declarer chooses to lead a diamond at trick two? East is forced to win the king, but now cannot continue the club suit!

Say declarer keeps his queen of diamonds. Now East leads a small spade; declarer must win this spade (and importantly, West must play small). Declarer unblocks the diamond queen and plays a heart. If East is forced to use his ace of hearts, he still can't establish his club, and declarer can set up his hearts before the East will be able to set up the club. So West must win the king.

If he continues a club, declarer will get dummy's ace of diamonds and drive the ace of hearts out. East gets the fourth club, but declarer has his eight tricks at the ready. But suppose he continues with the ten of spades, East playing the 9. Declarer can't allow this to hold, since a club will follow, and East will get his two club tricks upon winning the ace of hearts. So he wins the king of spades and leads another heart, and East ducks. Without an entry to hand, declarer can never pick up a second heart trick or the long spade. If declarer puts East in with the heart, East exits with a spade to West, who puts a club through. If he wins the ace and exits a club, East gets his long club. If he lets West win the second round of clubs, dummy is thrown in with the third round and must concede a diamond to West. Alternatively, if declarer exits dummy with the spade, the club from West comes now; if declarer allows East to win the king of clubs immediately, East cashes the ace of hearts and throws him in with a club.

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