Hand 6A.

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

This deal occurred in the Vanderbilt Cup, in Seattle, March 1959. North-South were vulnerable, West was the dealer, and the scoring basis was imps. Crawford was North, Stone was South.

West	North	East	South
3	double	4	6
pass	pass	pass

Hand 6B

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

West	North	East	South
	1	pass	1
pass	2	pass	6
pass	pass	double	redouble
pass	pass	pass

Without preamble, let's go directly to the discussion and solution of hand 6A. This was the entire deal:

	North
	A 3 2
	A 10 7 6
	A K 5
West	10 9 5	East
Q J 10 9 8 6 4		K 7 5
Q 5		K 9 8 4
9 6		Q 10 7 2
8 6		7 3
	South
	–
	J 3 2
	J 8 4 3
	A K Q J 4 2

And these were the pertinent conditions, as stated:
  North-South were vulnerable, West was the dealer, and the scoring basis was imps. Crawford was North, Stone was South.

West	North	East	South
3	double	4	6
pass	pass	pass

West opened the spade queen. In Stone's position, how do you plan the play–and why?

Stone ducked the opening lead in dummy and ruffed in his own hand, then cashed the ace and king of trumps. As it happened the adverse trumps fell.
  Stone led a low heart and, with West playing low, put in dummy's ten. East won and returned a spade. Declarer ruffed again and led his other low heart. West's queen was smothered by the ace, the spade ace was cashed for a diamond discard, the diamond ace was cashed too, and declarer led the club ten to his hand and ran trumps until the situation all around was:

	North
	–
	7 6
	K 5
West	–	East
J 10 9		–
–		9 8
9		Q 10
–		–
	South
	–
	J
	J 8
	4

On the last trump, now cashed, dummy discarded the small diamond–and East was squeezed. He elected to give up the diamond ten. Stone thereupon led the diamond eight to the blank king, returned to his own heart jack, and cashed the diamond jack for the fulfilling trick.
  If East had chosen to keep his diamonds, letting go of a heart, Stone would have cashed the heart jack immediately, of course, and dummy's last heart would have been good. There was no way of East's avoiding this squeeze.
  All of this, of course, came off nicely because of the opposing set-up, but now let's discuss the theoretical, "percentage" side of the hand from declarer's point of view. Note the "things Stone had running for him" in the line he used.
  If West had a singleton heart honor–a possibility, particularly considering the three spade opening–the ace would win and a low heart would be led from dummy. East would have to duck; otherwise he would give declarer three easy tricks in the heart suit. So, declarer would win with the heart jack, go to dummy in diamonds, discard his last heart on the spade ace, and lead the other high diamond honor and the diamond five, losing only one trick in diamonds and none in the other suits.
  If West had the doubleton K-Q of hearts (instead of a blank honor) and smothered South's heart jack on the following lead from dummy, a squeeze would still develop against East unless his partner had 6-2-3-2 distribution and the queen of diamonds. With East holding the guarded diamond queen and four hearts, and in this case with dummy coming down to the 10-7 of hearts (after cashing the top diamonds and the spade ace), declarer would finally hold a low heart and the diamond jack–and East would have to surrender his heart stopper or his diamond queen.
  Observe that declarer, playing as indicated, does not give up the chance to drop the diamond queen doubleton.
  Observe further that a different line of play (which no doubt will be the choice of some contestants) has much less percentage in its favor. That is, South might play for East to hold three spades to the king, three hearts to the K-Q, four or five diamonds to the queen, and three or two clubs. The winning line against this holding would be to take the first trick in dummy, discarding a heart, then to ruff a spade, cash the trump ace, go to dummy's trump ten, cash one top diamond and ruff the last spade. Now, take out the trump still outstanding and pass the heart jack to East, end-playing him.
  Due reflection, however, will make it clear that this East-West set-up is not nearly as probable as those covered by our recommended line. The very fact that West is presumably queen-high in his own spade suit (there would be no sense in his falsecarding the opening lead if he had the king) makes it all the more likely that he has the king or queen of hearts–perhaps both. As for the possibility of West's having the well guarded queen–what can South do about that?

Problem 6B

In our opinion, this is one of the finest problem hands ever submitted to high-level contestants. And, to borrow from a very good source, the late Damon Runyan, "a story goes with it." This, however, will have to wait until we have taken care of the technicalities. The entire deal was:

	North
	Q J 10 8
	K 8 6 2
	A J 9 2
West	5	East
5 3		6 4
Q 10 4		5
4 3		K Q 8 7 6 5
J 10 9 7 6 3		A Q 8 4
	South
	A K 9 7 2
	A J 9 7 3
	10
	K 2

West	North	East	South
	1	pass	1
pass	2	pass	6
pass	pass	double	redouble
pass	pass	pass

West's proper return is the heart four.
  The fact is, of course, super-obvious when East, in the full diagram above, is shown to have had a singleton heart, but it should also be clear from the painstaking at-the-table analysis.
  The salient, crucial point is that declarer cannot have any hand consistent with the stated conditions that would make the heart by West wrong. Let's analyze:
  A diamond continuation by West is unthinkable in view of East's play of the diamond five, the lowest diamond outstanding, at Trick 1. There is no getting around this fact; no possible explanation of East's first-trick play except that he does not want another diamond led from West.
  This would apparently throw the weight squarely toward a club shift, and admittedly, a great many experts to whom we submitted this hand in person, gave that shift as their answer. Also admittedly, the club shift beats the redoubled contract a trick and gives East-West 400 points. Nevertheless and notwithstanding, the club shift is wrong, costing East-West 600 points of the 1000 points there were for the taking. It is only better than the diamond return which lets declarer make the hand!
  We regret to report that of the 32 outstanding experts we consulted, eight continued with diamonds, 24 shifted to clubs, and none returned a heart! Not one!
  But it was a different story when we put a simple question to these experts: "What hand can declarer possibly have to make the heart return a losing play?" Brows furrowed, lips moved in silent figuring, and pencils raced frantically across papers–but to no avail. Nobody, but nobody (not even Gimbels), could come up with an answer that satisfied even himself. Surrender was complete and without exception.
  Work on the question! Try to find a hand meeting the conditions, with special reference to East's first-trick of the diamond five, that makes West's heart return wrong... You will not find such a hand.
  The fact is that Bos, declarer, made an extremely cute and far-seeing play when he took the heart finesse at Trick 2. Granted, the pure mathematical percentage was against this finesse, in fact about 8% against it as compared to a play for the drop of the heart queen, but there are other percentages in bridge. These others can't be reduced to cold figuers–but take another look at the experts' poll, cited above. Eight of the 32–25%!–returned a diamond and let declarer make six spades redoubled! That, we submit, is very substantially better than the 8% edge for not taking the heart finesse. And let's not forget that the 32 players we put in West's position were recognized experts. Presumably, if we asked 32 run-of-the-mill players what they would lead after winning with the heart queen, there would be quite a few more than eight votes for the killing (that is, killing for the defense) diamond return.
  To clean up loose ends: It is true that after losing to the heart queen and getting the highly favorable diamond return, declarer needs some luck, namely, either a 2-2 trump break or another heart in the defensive hand that holds three trumps. One of these conditions is necessary to a dummy-reversal plan. (Declarer ruffs the diamond return, leads a trump to dummy, and repeats this process on the next two tricks. Then he must still be able to enter dummy twice: once to ruff the last diamond, and the other time to draw the still outstanding trump.)
  If, on the lead of a low heart from dummy at Trick 2, East happens to play the ten, declarer should not finesse. In that event he should put up the ace, draw trumps, and then make his decision in the heart suit, whether to let the jack ride against West or to play for the drop. This contingency, however, is not part of the problem, because East's play on the first heart was the five.
  Finally, to wind up this interesting hand: Although none of the 32 experts in reference came up with the proper heart return, every one of them gave the ungrudging, often enthusiastic praise to the "theme" of this hand after really analyzing the situation.