Problem, 28:2006

Problem no. 28, 2006

The problem

I can't be the only one to consider Victor Mollo's classic Bridge in the Menagerie as the most entertaining bridge book ever written. When I reread the book a couple of years ago, I was surprised when I reached this deal, from the chapter "Leprechauns v. Gremlins (II)".

North dealer, East-West vulnerable

	–
	Q J 10 9 8 7 6
	–
	Q 10 9 8 7 6
A 6 5 4 3 2		Q J 10 9 8 7
–		K 5 4
K Q J 5 4 3 2		–
–		K J 5 4
	K
	A 3 2
	A 10 9 8 7 6
	A 3 2

South	West	North	East
RR	HH	Leprechaun	Gremlin
		3	3
4	6	7	D
7	7	pass	pass
Dbl	Rdbl	pass	pass
pass

The annual match between the Leprechauns and the Gremlins is about to start at the Griffins' Club, when the captain of the Leprechauns finds out that two players are missing, one from each team. He asks if two of the rubber bridge players care to fill in, which The Hideous Hog (HH) and The Rueful Rabbit (RR) does. HH is the star of the Griffins' Club, but he often loses against the club's worst player, RR, who compensates any lack of technique with an abilty always to land on his feet – call it luck if you want to.
  When a deal has been passed out, the Leprechaun suggest a Goulash. Instead of shuffling, the cards are sorted and placed on top of each other. Then they cut and deal the cards three at a time, to get more exciting distributions. The other players agree, and the resulting deal is shown above.
  After RR:s 7 hearts bid, HH wonders if he should go on to a grand slam or not. RR fumbles with his cards, and ... the spade king is suddenly exposed at the table. So, HH's problems are over. He was convinced that his partner hadn't any diamonds, but in a Goulash there was a risk of a trump loser. But now, with the king of spades lying at the table, he didn't have to worry about trump losers, so HH bid 7 spades and redoubled on principle when RR doubled with his three aces.
  The Gemlin accepted the king of spades as the opening lead. A few minutes later he had won one trump trick, ten ruffs and the king of clubs, established in the process. One down.
  Then Victor Mollo writes this: "Curious hand", observed the Senior Kibitzer. "On any other lead the contract is unbreakable. Declarer makes the king of whichever suit is opened and twelve more on a complete cross ruff. South follows suit all the way. Only when declarer leads his fourth club, and that is to the thirteenth trick, can South ruff. The king of spades is his last card and it falls under dummy's ace."

The king of spades happenes to be the only lead to defeat 7 spades, but not for the reason Mollo supplies. Why not?

Solution

If South leads the ace of hearts, East's king will be established, and the king of clubs falls on the third club ruff. Then, eleven trump tricks are enough, so East can draw trumps early. And the same is true if South leads a low heart (East discards a diamond from dummy).
  If South leads the ace of diamonds, East has more tricks than he needs; and if South leads a low diamond, East can indeed play on a complete cross ruff, but it's just as good to simply draw trumps and establish the king of clubs with three ruffs.
  If South leads the ace of clubs, East's king will be established, but it is impossible to win "twelve more on a complete cross ruff". Why? Because the first ruff was in dummy. That means the twelfth ruff will be in East's own hand, and even if South has to follow with the king of spades to that trick it won't "fall under dummy's ace", it will beat declarer's queen.
  From this you may think that the slam is defeated on the ace of clubs lead (I thought so myself first), but it isn't so. 7 spades will succeed even on the ace of clubs lead, since South can be squeeezed in three suits (one of them being trumps). This is how:
  East ruffs the opening lead, ruffs a diamond, cashes the king of clubs and cross ruffs six more tricks (two hearts and one club in dummy; three more diamonds in hand), to reach this end position:

	–
	Q J
	–
	Q 10
A 6		Q J
–		K
K Q		–
–		J
	K
	A
	A 10
	–

On the club jack, South is squeezed(!) If he throws a diamond, East can ruff away the diamond ace and draw trumps; if he discards the heart ace, East can draw trumps and cash the heart king; and if he ruffs, it will be a complete cross ruff after all.
But if South's opening lead is the king of spades, East can only win twelve tricks. The reason that this lead is killing is not that it stops a complete cross ruff (that was only possible on a low diamond lead, and even then it wasn't necessary) but that it breaks up the squeeze against South by forcing East to draw the trump round too early.

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