Hand of the Week, 04/13/95

by Rowen Bell

Here's a hand which arrived in my mailbox recently, as part of an advertisement for a novices-oriented bridge magazine called The Bridge Companion. The hand was presented there as a "double-dummy" problem (in which all four hands are given, and you are to find the correct line of play given the actual distribution of the cards), but I've decided to present it here as a best-line-of-play problem.

You are South, declaring a contract of 7H. The North-South hands are as follows:

				S   AQ4
			North	H   AKQJ
				D   QJT987
				C   void


				S   void
			South	H   65432
				D   AK
				C   A65432

Q: How will you make 13 tricks?
A: What's the problem? I've got 5 hearts, the black aces, and 6 diamonds--that's thirteen.
Q: Okay, play it out.
A: If you insist....what's the opening lead?
Q: Let's say it's the king of clubs.
A: Win the club ace, pull three rounds of hearts (leaving the fourth heart as my last board entry), cash two top diamonds in the hand, return to the board with the remaining heart, cash the ace of spades and run dummy's diamonds.
Q: Okay, that line of play will work unless the hearts split 4-0 (or unless the opening lead is ruffed).
A: But the hearts never split 4-0!
Q: They split 4-0 9.6% of the time, and you should prepare for it. If hearts are 4-0, then your line of play will fail if the defender with four hearts has fewer than 2 diamonds, for then she'll have one heart left with which to ruff one of your high diamonds from the hand.
A: Grrrr....
Q: And given that the hearts split 4-0, it is not unlikely that the diamonds will split poorly with the shortness being located with the heart length. In fact, if you do the mathematics, you find that this happens 2.8% of the time, so that the line fails 3.0% of the time.
A: So what do you want me to do about it? Going down 3% of the time in a 30-HCP grand slam isn't so bad.
Q: I suppose not--but you can do something about this one. What about an alternate line of play? Think about why your line of play might fail.
A: It might fail because the diamond suit is blocked by the ace-king in my hand. If dummy's diamonds were high, I could just pull all the trump and run the diamonds, no problem.
Q: But dummy has the QJT987, so if you could get rid of the AK in your hand...
A: What, you want me to drop them on the floor?
Q: No--I want you to get rid of them legally. How might you do that?
A: Well, I guess that when I'm on the board with a heart, I can cash the spade ace, pitching one of my high diamonds.
Q: But this still leaves you with one diamond to rid yourself of. Have you considered a dummy reversal?
A: That means, I take enough ruffs in the long hand so that the short hand becomes the long hand, so to speak...
Q: Right. See what happens if, instead of cashing the spade ace, you ruff dummy's low spades in the hand. Play it out.
A: Okay....I win the club ace in the hand. Since you seem to want me to ruff dummy's low spades, I guess I'll have to throw a diamond on the club ace--which gives up a trick, I remind you... I play a heart to the board, and now you want me to ruff a spade.
Q: Right. Continue.
A: I play another heart back to the board, and I guess you want me to ruff another spade.
Q: Yes. What do the North-South hands look like after you ruff the second spade?
A: They look like this:


				S   A
			North	H   AK
				D   QJT98
				C   void


				S   void
			South	H   6
				D   AK
				C   65432

Q: So, what now?
A: I see....I play two hearts, which will get rid of the enemy trumps even if they were 4-0. On the second heart, I can throw the diamond king from hand...
Q: The reward of your dummy reversal.
A: ...and now I can cash the spade ace, discarding the diamond ace from hand, and I win the last 5 tricks with dummy's diamonds!
Q: Making 7. It's true that you only take 5 diamonds this way--but you take 6 hearts instead of 5, plus the black aces as before.
A: Cool!
Q: Calm thyself....when will this line of play fail?
A: Well, I no longer have to worry about hearts being 4-0....but the opening lead could still be ruffed, and more importantly I could get overruffed when I ruff the low spades from dummy.
Q: And that can't happen as long as spades are 8-2 or better--which seems much more likely than relying on hearts and diamonds, right?
A: How much better?
Q: Spades will be 8-2 or better 98.4% of the time, so this line only fails 1.8% of the time, as opposed to 3.0%.
A: Doesn't seem like much of a gain to me...
Q: Ah, but think of this. Suppose that your hearts were T9432 instead of 65432. Then as long as you ruff the spades high, you never have to worry about being overruffed! This dummy reversal line would then fail only when the opening lead is ruffed by East, or 0.2% of the time--whereas your original line would still fail 3.0% of the time.

(In the original double dummy problem, West had 3 spades, 4 hearts, a diamond void, and 6 clubs--thus making it necessary for South to pitch both top diamond honours to make the grand slam.)

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