Analyses 7V16  Main Challenge

Notrump Wonderland

Scores  by Richard Pavlicek

These six play problems were published on the Internet in December 2000, and all bridge players were invited to submit their answers. On each problem you are declarer in a notrump contract, and your opponents are presumed to be strong players using standard leads and carding.

Problem 1

2

3

4

5

6

Final Notes

John Reardon Wins!

Bidding is standard, and your opponents use standard leads and signals.
For a reference see Standard American Bridge. Assume all players are experts.

Each problem offered six plausible lines of play (A-F). The merit of each choice is scored on a 1-to-10 scale, based on my judgment, so a perfect score would be 60. This proved to be a difficult set of problems (or tricky, as several respondents mentioned). The high-end scores ran a little below my last contest, though the average score was 0.26 points higher.

Problem 1

IMPs	8 5 4 2			West	North	East	South
None vul	K 6 5			LHO	Partner	RHO	You
	J 6 2						1 NT
	K J 9			Pass	2 NT	Pass	Pass
				Pass
Lead: 4		East plays Q
	7 6 3
	A 8 2
	A K 4
2 NT South	A 6 4 2

Your Play	Award	Votes	Percent
A. Win first heart, lead spade	10	53	26
C. Win first heart, lead club to jack	9	93	46
B. Win first heart, lead club to nine	7	55	27
D. Win second heart, lead spade	3	0	0
F. Win second heart, lead club to jack	2	0	0
E. Win second heart, lead club to nine	1	0	0

Oops! I just discovered that receiving no answers for D, E or F was not a statistical phenomenon but an error in my web submission form. Anyone who chose D, E or F was credited with A, B or C, respectively. So, a few people evidently got a lucky break in the scoring. Consider it a holiday gift.

This innocent-looking partscore problem has proved to be the most difficult to analyze. First, let’s consider the 4 opening lead combined with East’s play of the queen (assuming North played low). This is consistent with six possible heart holdings for West: J-10-7-4-3, J-9-7-4-3, J-10-7-4, J-9-7-4, J-9-4, and J-7-4. The last two are surely remote, so for practical purposes let’s assume West has four or five hearts. A first-round holdup is unlikely to offer any advantage and is dangerous — East might be looking at five spades (e.g., A-K-J-10-9) and set you immediately — so win the first heart. That’s the easy part.

Now let’s compare the finessing options in clubs. You probably need four club tricks (unless Q falls) and the best chance a priori is to finesse the nine — 24 percent versus 20.6 percent for finessing the jack. This ratio, however, is no longer valid because of the early plays. With West likely to have heart length, the chance of his holding both club honors decreases; plus, some favorable cases for the double finesse are impossible (e.g., if West has four hearts, we can rule out Q-10-x-x-x by bridge logic).

The following table shows the true percentages of different club holdings for West, according to the two likely heart divisions.

Percents of West Club Holdings

Case	West Clubs	Hearts 5-2	Hearts 4-3
1	—	1.70	0*
2	Q	2.27	1.47
3	10	2.27	1.47
4	x	9.09	5.91
5	Q-10	2.27	1.97
6	Q-x	9.09	7.88
7	10-x	9.09	7.88
8	x-x	13.63	11.83
9	Q-10-x	6.82	7.88
10	Q-x-x	10.23	11.83
11	10-x-x	10.23	11.83
12	x-x-x	6.82	7.88
13	Q-10-x-x	5.69	8.87
14	Q-x-x-x	3.79	5.91
15	10-x-x-x	3.79	5.91
16	x-x-x-x	0.95	1.47
17	Q-10-x-x-x	1.51	0*
18	Q-x-x-x-x	0.38	0*
19	10-x-x-x-x	0.38	0*
20	Q-10-x-x-x-x	0*	0*

*Holding is deemed to be impossible based on West’s choice of leads. The percentages of the realistic holdings have been increased proportionally to achieve a 100-percent basis.

To win four club tricks, finessing the jack succeeds in cases 5, 9, 10 and 18 (19.70 percent with hearts 5-2, 21.68 percent with hearts 4-3), while finessing the nine succeeds in cases 5, 9, 13, 17 and 20 (16.29 percent with hearts 5-2, 18.72 percent with hearts 4-3). The table also shows (left to reader to calculate) that finessing the jack is the better play to win at least three club tricks. Therefore, Line C is clearly better than Line B.

Nonetheless, I think Line A (leading spades) is better yet. This is difficult to analyze exactly because it depends on a variety of factors, some of which are subjective. In a nutshell, if hearts are 4-3, Line A basically is hoping for a 3-3 break in spades instead of clubs, which is obviously a toss-up. The advantage is that you will usually have a second chance when spades do not break, and you may even succeed when neither black suit breaks. Consider this routine layout:

IMPs	8 5 4 2		Trick	Lead	2nd	3rd	4th
None vul	K 6 5		1. W	4	5	Q	A
	J 6 2		2. S	7	Q	2	J
	K J 9		3. W	J	6	9	2
K Q		A J 10 9	4. W	7	K	3	8
J 10 7 4		Q 9 3	5. N	4!
Q 9 3		10 8 7 5		Declarer can succeed
Q 8 7 5		10 3
	7 6 3
	A 8 2
	A K 4
2 NT South	A 6 4 2

Assume West wins the first spade and leads the J, which you duck to discover the heart break, then another heart drives out the king. When you now lead a second spade, it is impossible for the defense to win the long heart and the long spades. If East wins to cash his spades, West will get squeezed in the minors. If West wins the second spade and cashes his fourth heart, you can still succeed by a throw-in against West (double-dummy, perhaps, but at the table you might deduce the 4-2 spade break from the enemy tempo).

If you discovered that hearts are 5-2, you would fall back on the club finesse, with only a slight loss from the original Line C — you lose only in two rare events: (1) when the Q is falling and the clubs could be developed for three tricks with the finesse losing, and (2) when East wins the second heart and is able to cash four more spade tricks.

In my example deal it is interesting to note that even Line A can be defeated, but it requires double-dummy defense. After winning the first spade, West must return a low heart or his remaining spade, then when East gains the lead he must refuse to cash his good spades and return a diamond. With Line C, however, any reasonable defense would prevail — the main difference being that you have weakened your entries with the premature club finesse.

Comments for A. Win first heart, lead spade

N. Scott Cardell: 1. Hope to get a better count. (If hearts are 5-2 then a club to the jack is much better than a club to the nine.) 2. East rates to have the 9 or 10, so West may not continue hearts. (Hence, I may get to test the spades.) 3. Ducking the first heart is unwise; I don’t want to see a diamond switch, and East just might run five spade tricks.

Venkatesh Ramaratnam: West holding either Q-x-x or Q-10-x-x in clubs is only about 16 percent, hence I don’t want to commit myself early in the game. I’d rather lead a club to the jack at a later stage because there are endplay options even if the clubs don’t break.

Carl Hudecek: If hearts are 4-3 and spades are 3-3, I should start by winning the first heart and leading spades immediately and at every opportunity. I can later hook clubs and have many chances. Ducking a heart will not gain except in the rare case where RHO has A-K-Q…

George Klemic: Ducking a heart then leading spades loses if East can cash five spades. Playing on spades early will tell you if you need to risk the J finesse later. There is nothing they can do (except 6-0 spades) that you can’t decide to play on clubs later.

Marsha Rayton: Spades weren’t bid and weren’t led, leading me to think they might break favorably.

Andrei Varlan: Give them what they’re allowed to make.

Problem 2

IMPs	K 4 3			West	North	East	South
Both vul	A 7 5			LHO	Partner	RHO	You
	J 10 6 5						1 NT
	Q 8 4			Pass	3 NT	Pass	Pass
				Pass
Lead: J		East plays 8
	A 9 2
	K 8 4
	Q 4 3 2
3 NT South	A K 10

Your Play	Award	Votes	Percent
A. Win K, lead diamond to queen	10	46	23
C. Win A, Q, lead diamond to queen	8	9	4
B. Win K, K, lead diamond to jack	6	4	2
D. Win A, lead diamond to jack	5	36	18
E. Win second spade, lead diamond to queen	4	55	27
F. Win second spade, lead diamond to jack	3	51	25

First let’s consider West’s J lead. It must be from a doubleton or J-10-x, because the 9 and 8 (East’s signal) are visible. Note that with J-10-7-x-(x) the proper lead is fourth best. Therefore, East has the longer spades.

The main issue to consider is which spade honor to win (or to duck). Ducking can only help if West has a doubleton and the diamond honors are split, but this is too dangerous — a switch to hearts would be fatal. Further, if West has a diamond honor, the heart switch stands out, since he can read the holdup (else partner has A-Q and a continuation can wait).

Proper play is to win the K, because it lets you block the development of spades when West has J-10 doubleton. If West wins the first diamond and leads the 10, East cannot overtake, so you can duck. This narrows the choice to Lines A and B, and Line A wins because it starts diamonds the right way. East is more likely to have a blank diamond honor, because he is longer in spades.

Below is a typical layout that shows the importance of winning the first spade with the king:

IMPs	K 4 3		Trick	Lead	2nd	3rd	4th
Both vul	A 7 5		1. W	J	K!	8	2
	J 10 6 5		2. N	5	7	Q	A
	Q 8 4		3. W	10	3	5	9!
J 10		Q 8 7 6 5		Declarer succeeds
J 9 6 2		Q 10 3
A 9 8		K 7
J 9 6 3		7 5 2
	A 9 2
	K 8 4
	Q 4 3 2
3 NT South	A K 10

If West wins the first diamond and continues with the 10, you are able to hold up since East cannot afford to overtake. Note that if you won the A first, you would fail. The recommended play also works if East has both diamond honors, because you can duck East’s spade return to the blank 10.

Comments for A. Win K, lead diamond to queen

John Reardon: If spades are 4-3, your main chance is to establish two diamond tricks. East is more likely to be short (since the lead may well be from three spades) so you should allow for East having a singleton K or A.

N. Scott Cardell: The lead looks like it is from J-10-x (missing the eight and nine West would probably lead low from J-10-x-x-(x).) West would probably have led from a five-card suit if he had one, so no singleton in the West hand. This leaves the danger of four diamonds with West. Line A works against any four diamonds with West. (You duck the second round of spades, just in case East does have five.) Ducking the first spade is bad because a heart switch could be fatal. …

Charles Blair: Looks like West may have J-10 doubleton, but the play of the eight is questionable. If I’m right about this, East is more likely to have singleton diamond honor.

Grant Peacock: I guess I’ll cater to a stiff diamond in the East hand. Ducking trick one is wrong because they can switch to hearts.

Radu Mihai: West, with long spades headed by J-10 and without the nine or eight, would have led low. So, the long spades are with East. No reason to duck; they can attack hearts and eventually take three major tricks and two diamonds. It’s a greater chance for East to have a singleton diamond honor because he has longer spades, so the diamonds must be led low from dummy. It’s better to take the first spade in dummy (when West takes the first diamond and leads a second spade (having J-10 doubleton), East cannot overtake and I can duck).

Tonci Tomic: Have to win the first spade; West may switch to hearts. Win with the king because it is possible to guard against J-10 doubleton in the West hand.

Shyam Sashital: If you do not win the first spade, opponents can switch to hearts. In diamonds, play for 3-2 or 4-1 with a bare honor. After the opening lead, East is the one short in diamonds (West led from J-x or J-10-x, i.e., did not have an attractive four-card suit to lead from). Hence, lead low toward the queen.

Carl Hudecek: The opening lead plus my spade spots suggest West has J-10-x or J-10. With the spade length on my right, I wish to lead diamonds from dummy first. Also, by winning the first spade [with the king] I render the defense helpless when West started with J-10 doubleton.

Ufuk Cotuk: Quickly develop two tricks before they attack hearts, what they should and would do if I duck first trick: down one, losing one spade, two hearts and two diamonds! :( …

Steve White: Can’t duck; they may shift to hearts. West appears to be shorter in spades, so East is more likely to have a stiff diamond honor than West. …

Problem 3

IMPs	A K Q			West	North	East	South
E-W vul	6 5 2			LHO	Partner	RHO	You
	K Q 6 5				1	Pass	1 NT
	K Q 5			Pass	3 NT	Pass	Pass
				Pass
Lead: 4		East plays J
	6 4 3
	A K 9
	J 7 2
3 NT South	J 7 4 2

Your Play	Award	Votes	Percent
F. Win second heart, club to king, lead K	10	35	17
D. Win second heart, diamond to king, diamond to jack	9	35	17
E. Win second heart, club to king, diamond to jack	7	82	41
C. Win first heart, club to king, lead K	5	13	6
A. Win first heart, diamond to king, diamond to jack	4	9	4
B. Win first heart, club to king, diamond to jack	2	27	13

West’s heart lead (combined with East’s play of the jack) is consistent with: Q-10-8-4-(3), Q-10-7-4-(3), 10-8-7-4-(3), Q-10-4, 10-8-4 and 10-7-4; of which the dangerous cases are when West has five. A first-round holdup is crucial when East has J-x and the minor-suit aces are split (else you would have to guess which minor to lead first). The only time the holdup could lose would be if East has Q-J doubleton and West has both minor-suit aces — quite an unlikely parlay — so duck the first heart and win the return.

Assuming the heart suit is under wraps, the rest looks easy — just establish two tricks in each minor. Well, not so fast. Suppose you lead each minor suit once, and neither ace appears. Your next minor-suit lead could find a defender (probably East) with five cards, and if he captures an honor he can clear the suit while he still has the other minor-suit ace. Here’s a layout that would be dangerous:

IMPs	A K Q		Trick	Lead	2nd	3rd	4th
E-W vul	6 5 2		1. W	4	2	J	9!
	K Q 6 5		2. E	7	A	3	5
	K Q 5		3. S	2	3	K	6
J 9 7 5		10 8 2	4. N	K!
Q 10 8 4 3		J 7		Declarer succeeds
4		A 10 9 8 3
9 8 3		A 10 6
	6 4 3
	A K 9
	J 7 2
3 NT South	J 7 4 2

If you followed Line E (club to king, diamond to jack) and next led a diamond, you would fail. The same fate could befall you if you next led a club and East were 5-3 the other way. The solution is to plan your attack so the second lead in diamonds is low to the jack — hence, East cannot capture an honor, and you can switch back to clubs. Lines D and F both accomplish this, but the nod has to go to Line F because it includes one round of clubs as well. (Line D would fail and Line F would succeed if West held x-x-x Q-10-8-4 A-10-9-8-x A.)

It would also be fine to lead a diamond to the king, followed by the K, then a diamond to the jack; but this was not among the choices.

Comments for F. Win second heart, club to king, lead K

Charles Blair: Loses if West has ace-fifth diamonds, club ace, and ducks the diamond king (my next play is a diamond to the jack).

Franco Baseggio: Need to duck in case hearts are 5-2, then need to worry about someone having five of a minor with both minor-suit aces. Next play is diamond to the jack…

Grant Peacock: And then a diamond toward the jack.

Walter Lee: Slightly better than Line D because you get to play three kings in a row.

Venkatesh Ramaratnam: Heart duck is essential to cut the communication (there is no chance if person with five hearts has both the minor aces). If any defender has five cards in a minor suit and both the minor aces, hand needs to be played carefully. If both the minor kings are ducked (no problem if either of them is taken), cash a spade winner and decide on the future course of action. …

Jojo Sarkar: Hard problem. Seems right to duck the heart because no switch hurts. … Seems right to play the K because there will always be spade entries to the dummy and that makes the J an entry to the closed hand. Most people (including me, probably) would just win the second heart and start leading minor suit cards.

Problem 4

IMPs	A Q 9 8 2			West	North	East	South
Both vul	6 5 2			LHO	Partner	RHO	You
	10 3						2 NT
	6 5 2			Pass	3 1	Pass	3
				Pass	3 NT	Pass	Pass
Lead: 8		East plays 2		Pass
				1. Jacoby transfer
	K 10
	A K 3
	A Q 7 5 4
3 NT South	A 7 3

After winning the 10:

Your Next Play	Award	Votes	Percent
C. Duck a club	10	16	8
A. Duck a heart	8	7	3
B. Duck a diamond	6	32	16
F. Cash the top spades	5	25	12
D. Lead 2 and finesse 10	4	76	38
E. Win K, lead 10 and let it ride	3	45	22

Even after the friendly lead (dummy’s 10 wins) you have only eight sure tricks, but there are lots of options. Finessing plays in spades (Lines D and E) may seem cute — and indeed got most of the votes — but in fact they do nothing to improve your chances. Surely, any strong defender looking at J-x-x-x-(x) would refuse the trick, which leaves you with the same number of spade tricks you always had. The only thing the spade finesse might do is give away your overtrick when the J is falling.

Another possibility is to lead diamonds to establish your fifth card. This is likely to work if West started with only four diamonds, but I’d bet heavily on five for two reasons: (1) Few players would lead from K-J-9-8 into a 2 NT opener, especially on this sequence with the spade fit denied, and (2) East’s play of the two suggests a singleton since it would be normal to give standard count when you can’t beat dummy’s 10.

Your best chance (assuming the J doesn’t drop) is to develop a throw-in against West in diamonds, and for this to work you must remove his exit cards. The correct way to prepare for this is to duck a club immediately (Line C). It might seem just as good to duck a heart, but that would fail against sharp defense. Consider this typical layout:

IMPs	A Q 9 8 2		Trick	Lead	2nd	3rd	4th
Both vul	6 5 2		1. W	8	10	2	4
	10 3		2. N	2!	4	7	8
	6 5 2		3. W	Q	5	9	3
7 5		J 6 4 3	4. W	10	6	J	A
9 7 4		Q J 10 8	5. S	K	5	2	3
K J 9 8 6		2	6. S	10	7	A	4
Q 10 8		K J 9 4	7. N	Q	6	3	?
	K 10			Declarer succeeds
	A K 3
	A Q 7 5 4
3 NT South	A 7 3

If a heart is ducked, the defense may continue hearts (an immediate spade switch also beats you). Then, if you duck a club, a third heart knocks out your last heart stopper. Another club duck is necessary, then East could cash his long heart — the fourth defensive trick, which kills any hope of a throw-in.

If a club is ducked, the defense has no recourse. If clubs are continued, win your ace on the third round. Next cash the top spades (discarding a heart) and West is history — if he pitches a diamond, you can establish your long diamond; if he pitches his exit card in hearts, you can endplay him. The defense does no better by switching to hearts after you duck a club — just duck the heart, and duck a second club; eventually you will endplay West by ducking a diamond to him. If the defenders instead switched to spades, just duck a second club to achieve the same denouement.

The early club duck does not require West to have specifically 3-3 in hearts and clubs. You can also succeed when West is 4-2 either way, though you may have to guess which distribution to play for if the defense is accurate. The club duck also works in most cases when West has the spade length instead.

Comments for C. Duck a club

John Reardon: This leaves endplay possibilities to establish another diamond trick if spades do not come in.

N. Scott Cardell: You hope to postpone testing spades, so Lines D, E and F are foolish. … The only relevant cases are when spades don’t run. The most likely situation is that West has two spades and five diamonds (with 4-4 in hearts and diamonds, West would probably have led a heart; with 4-4 in diamonds and clubs, West might have led a club). If West is 2=3=5=3, 2=4=5=2 or 4=2=5=2, the best the defense can do is lead spades twice, as you duck two clubs. You sluff a heart on the third round of spades and cash the A. At the end you either set up a diamond or endplay West. …

Charles Blair: … Squeeze West out of his exit cards, then throw him in with diamond.

Franco Baseggio: Finessing 10 then ducking a club might be right against weaker opponents, but here I fear a second spade before I’m ready.

Grant Peacock: Fascinating hand. Do you mind if I write a book on it?

Yes. [Ready to torch manuscript]. OK, OK, we’ll read a few chapters:

Grant Peacock: … I prefer to try for an endplay against West. So, I am going to begin stripping him of clubs and hearts by ducking one or the other. Say, for example, I duck a heart, and the defense cooperates by attacking clubs. I duck two rounds and win the third. Now the count is rectified to two losers and the hand is cold provided that (1) West is out of clubs… and (2) I can make an approximate guess as to West’s shape. I cash my winners in the suit where he is short, and he has no answer. … If I duck a club, they [are likely to] switch to hearts. I win the second heart with the ace and duck another club. Say another heart comes back. Now I’m making as long as West is out of hearts. … By the way, whichever suit I duck, the best defense is spade returns at the first two opportunities. I don’t expect that, but the next best defense is to attack the suit that I ducked. …

Walter Lee: Buying time. Maybe East has missorted his hand and plays the J on the club.

Ufuk Cotuk: I have eight tricks with the 10. If spades behave I make 10, but surely they wont! :) But I can test it later anyway. Finessing the 10 or letting it ride is tempting, but no expert player would fall into the trap. :) So my ninth trick should come from diamonds, and I must endplay West for that. Surely, he led from a five-card holding. If I manage to strip West from his cards I am home. …

Jojo Sarkar: Things will go much better if they don’t lead clubs, so we can try and talk them out of it. The spades are not likely to run; RHO is going to hold up with J-x-x-x (his side gets the same trick whether or not his partner has the king, and dummy has no more entries). … LHO probably has K-J-9-6 behind my A-Q-7-5… With eight tricks on top, I have excellent chances for an endplay…

Problem 5

IMPs	4			West	North	East	South
None vul	K Q 5 4			LHO	Partner	RHO	You
	8 5 4 3 2						1 NT
	A 3 2			2 1	Dbl	3 2	3 NT
				4	Pass	Pass	4 NT
Lead: J		East plays 7		Pass	Pass	Pass
				1. artificial for majors
	K 10			2. weak
	J 3 2
	A K J 10 9
4 NT South	K 5 4

Your Play	Award	Votes	Percent
C. Win K, A, lead heart to king	10	73	36
E. Win second club with king, A, lead heart to king	7	54	27
D. Win K, A, lead J	6	33	16
F. Win second club with king, A, lead J	4	23	11
A. Win A, lead heart to jack	2	11	5
B. Win A, lead K	1	7	3

Note: West will pitch a spade on the first diamond lead.

A word about the auction: Several respondents mentioned, and others probably thought, that South’s 4 NT bid was terrible, since the contract obviously has no play (down two) with a spade lead. I disagree. Would you rather defend 4 doubled? I hope not, because it’s cold. It is arguable that 5 would be a better choice (down one barring misdefense), but the decision to bid 4 NT is certainly reasonable at matchpoints. I would just describe it as unfortunate, or in this case fortunate since you can make it with the non-spade lead.

As far as the play choices, Lines A and B (killing dummy’s entry) can be quickly rejected — I admit these were fillers to reach the six-choice quota. The main problem is whether to win or duck the club lead. Well, you survived the opening lead, so it doesn’t make sense to give West a second chance. In view of the two heart tricks you can establish in dummy, West should surely find the spade shift at trick two. So, win the K.

After cashing the A and discovering the void, it is obvious to lead hearts. But which one? Leading the J would force West to take his ace (else you score three heart tricks) which builds an entry-threat in the heart suit. In many cases this would be a good plan for squeeze purposes — alas, not here. You certainly have a chance for a squeeze, but this is not the garden variety. You must save the J as a potential late entry to your hand. Here is a typical layout:

IMPs	4		Trick	Lead	2nd	3rd	4th
None vul	K Q 5 4		1. W	J	2	7	K
	8 5 4 3 2		2. S	A	2	2	6
	A 3 2		3. S	2	8	K	7
A Q 5 3 2		J 9 8 7 6	4. N	3	7	J	3
A 10 9 8		7 6	5. S	K	5	4	Q
—		Q 7 6	6. S	10	8	5	6
J 10 9 8		Q 7 6		continued below…
	K 10
	J 3 2
	A K J 10 9
4 NT South	K 5 4

At trick three you must lead a low heart (Line C) which West ducks to the king. Next finesse and run the diamonds. This is the ending you would reach:

NT win 4	4		Trick	Lead	2nd	3rd	4th
	Q 5 4		7. S	9	Q	8	7
	8		8. S	10!	A	4	8
	A 3		9. W	10	A	6	4
A Q		J 9 8 7	10. N	Q!	6	3	9
A 10 9		6	11. N	3!
—		—		Declarer succeeds
10 9		Q 6
	K 10
	J 3
	9
South leads	5 4

Your last diamond squeezes West. If he pitches a heart, establish the hearts. If he pitches a club, he can be endplayed with the fourth heart after cashing the A to remove his exit card. The strongest defense is for West to pitch a spade, then duck a spade to his blank ace. On the club return, win the ace (ducking would be fatal) and lead the Q (a low heart is fatal). West must duck to deprive you of an entry to your hand, then lead a club to East who must give you the K. Note that if East unblocked the Q under the ace, you must then exit with a club immediately to endplay West in hearts.

Comments for C. Win K, A, lead heart to king

John Reardon: This is the only way to succeed if West has led from a hand such as: A-J-x-x-x A-x-x-x -- J-10-9-x.

N. Scott Cardell: Clear. Next you finish the diamonds. West is squeezed and the contract is cold so long as West has the major-suit aces and a reasonable distribution for the bidding. (You can protect against both 5=5=0=3 and 5=4=0=4.) Ducking the first club is suicidal as West should switch to a spade. You need to save the A as a potential late entry to the last heart.

Jane Eason: We’ve stolen the hand. A diamond game is down…, and even the weakest players can make four or more spades. … Something doesn’t add up here, because if LHO didn’t have the A, he’d lead that suit; and if he did have it, RHO would overtake the club so I couldn’t duck that trick to LHO.

Radu Mihai: Need to extract all the minor cards in the West hand, but it’s too dangerous to duck (if West changes to spades, I’ll remain with eight tricks). If I win the A first and lead a heart, on a heart return, if I need the diamond finesse, I’ll have to use too early the only entry to dummy… so I have to choose between lines C and D. … Line C allows me … to lead a spade if West kept no other spade than the ace …, or to lead a heart … and eventually throw West in with a heart to receive a spade return. If I choose Line D, West can keep only one spade (the ace) and I’ll be unable to reach my hand for the K.

Venkatesh Ramaratnam: Ducking a club is not required and could lead to an immediate set against alert defense. On the run of diamonds West is strip-squeezed (in the six-card ending, he has to either bare the A or come down to only one club provided he holds on to the hearts). Line D is inferior because West can win the heart and clear clubs thereby enabling him to bare the A in the endgame.

Carl Hudecek: I escaped by not getting a spade lead, so I don’t give them a second chance. I lead a low heart, because if I lead the J, West can win the A and lead a club. After I run diamonds I can decide how to finish. …

Michael Arnowitt: … When in dummy with the K, I will take the marked diamond finesse and run the suit. West will have to come down to six cards. If West doesn’t guard dummy’s long heart, I will lead hearts and have the A to enjoy the fourth heart… If West keeps three hearts to guard against this (probably coming down to A-Q, three hearts and a club), I will play the A and hearts to endplay West into leading a spade to my king.

Barry Rigal: After one club, one heart and five diamonds, West will be under some pressure…

Problem 6

IMPs	K 5 4			West	North	East	South
N-S vul	A 6 5 2			LHO	Partner	RHO	You
	A Q J 10 2					Pass	1
	2			2 1	3	Pass	4 NT
				Pass	5	Pass	5 NT
Lead: Q		East plays 7		Pass	6	Pass	6 NT
				All Pass
	A J			1. weak
	K 4
	K 4 3
6 NT South	A Q J 9 8 4

Your Play	Award	Votes	Percent
C. Win A, Q, lead 9	10	27	13
B. Win A, Q, lead J	7	46	23
E. Win K, Q, Q, lead J	6	63	31
F. Win K, Q, Q, lead 9	5	16	8
D. Win K, Q, Q, cash A	3	33	16
A. Win K, Q, Q, lead J	2	16	8

Note: When you finesse the Q, it wins.

On the bridge certainty that West has five or more hearts, there is a cinch double squeeze if the clubs don’t establish and East has the stopper (as is highly probable). The problem is that your entry conditions are delicate. Instinctively, it may seem better to win the K to maintain the entry-threat in the heart suit, but this would fail. When you lose a club to East, a shift to spades would destroy your communication for the squeeze. Try it on this typical layout:

IMPs	K 5 4		Trick	Lead	2nd	3rd	4th
N-S vul	A 6 5 2		1. W	Q	A!	7	4
	A Q J 10 2		2. N	2	5	Q	3
	2		3. S	9!	7	2	10
Q 6 3		10 9 8 7 2	4. E	10	A!	3	4
Q J 10 9 8 3		7	5. S	3	5	Q	7
6 5		9 8 7	6. N	2	8	K	6
7 3		K 10 6 5	7. S	4	3	A	9
	A J		8. N	J	2	4	8
	K 4		9. N	10	7	8	9
	K 4 3			continued below…
6 NT South	A Q J 9 8 4

What you need for the double squeeze is a late entry to South, either the K or the A, so you should win the A at trick one. After the club finesse wins, the correct continuation is the nine (Line C). It makes no difference if West held a doubleton 10, but it would be fatal to lead the jack if East held a doubleton king. Further, if you led the J to East’s king, a sharp defender might return a club — then you have to guess who has the 10 (note that if you win the A and West shows out, dummy is squeezed). When East wins the 10, he cannot upset your communication, and a club return would be foolish since he is marked with the king (unless West has made an incredulous duck at trick two).

After the 9 loses to the 10, assume a spade is returned. Win the ace and run the diamonds to reach this ending:

NT win 4	K 5		Trick	Lead	2nd	3rd	4th
	6 5		10. N	5	8	K	10
	—		11. S	A
	—			West is squeezed
Q 6		9 8
J 10		—
—		—
—		K 6
	J
	K
	—
North leads	A J

Finally, a heart to the king will squeeze East out of his spade stopper, then the A will squeeze West in the majors.

If the defense were able to return a heart when you ducked a club, the ending would be:

NT win 4	K 5 4		Trick	Lead	2nd	3rd	4th
	6		10. N	4	9	A	3
	—		11. S	A
	—			West is squeezed
Q 6 3		10 9
J		—
—		—
—		K 6
	A J
	—
	—
North leads	A J

Note that East has already been squeezed out of his spade stopper. Now a spade to the ace and the A squeezes West as before. The key to both endings is to have the late entry to the South hand.

I should mention that the recommended play could cost an overtrick. If East held K-x, Line D would win all the tricks on a club-heart simple squeeze. Nonetheless, it would be foolish to give up your other chances for such a long shot. And, even if this were the case, I’d bet that bidding and making 6 NT would still score well above average.

Comments for C. Win A, Q, lead 9

John Reardon: With 11 sure tricks, this play offers the best chances of a double squeeze for the 12th if clubs do not come in now.

N. Scott Cardell: Nice hand. The contract is guaranteed on a double squeeze so long as West has at least five hearts and East has the K. (This is almost a certainty at matchpoints; if West ducks twice with K-x-x and East wins the 10 and returns a club, these opponents are either crazy or much better than strong!) Winning the K at trick one is wrong because a spade return from East will then kill your entries for the squeeze. … Leading the J is inferior because with either K-x-x or K-10-x-x, East can win the K and return a low club. This squeezes the board and breaks up your double squeeze, so you end up needing to guess the clubs or finesse in spades.

Charles Blair: How bad a matchpoint score can I have for making 6 NT on a double squeeze?

Franco Baseggio: Need [to save] the K if I’m going to lose a trick before running diamonds. Can’t exit with the J because a third club might be embarrassing. If West ducked with K-x-x or K-x-x-x, he got me. …

Grant Peacock: [This] rectifies the count while all entries and threats are intact. Now East will be squeezed in the black suits and West will be squeezed in the majors. (The A is needed for the squeeze card against West at trick 11.) If East wins the 10 and returns a small club, I am repeating the finesse, since dummy is squeezed on this trick. I tried to improve my chances of making seven by playing for the same double squeeze, only without the count, but like many crazy ideas this didn’t work.

Walter Lee: This line should be safe so long as I’m not playing against Mr. Pavlicek himself. Against him the Q will win, the 9 to East’s ten, then a club; jack, king! Down one. … This brilliance can be overcome… Win the first heart with the ace, run five diamonds, then take the club hook. Now on the 9 exit, if East wins the 10 and returns a club, you can safely play the ace. Clubs will either run or West will get squeezed before dummy.

Sorry to disillusion you, but I’d win the K like anyone else. The problem with your alternate line is that you will have to guess West’s pattern (five hearts or six?) — and if West is tricky (or crazy) enough to be capable of the club duck, you can hardly expect any tell-tale discarding. -RP

Radu Mihai: Assuming five or more hearts in the West hand, after the club finesse succeeds, Line C is 100 percent. If the clubs are not good, East is the one with the stopper. Assume West wins the 10 and returns a heart. I cash all the diamonds, the last squeezing East in spades and clubs; … next come to hand with the A and cash the A to squeeze West in spades and hearts. If East wins the 10 and returns a spade, I win the ace and cash all the diamonds; then I come to my hand with the K and cash the A for the same double squeeze.

Tonci Tomic: … If East wins with the 10 and returns a spade, win with the ace, cash diamonds, go to hand with K and lead the A (double squeeze). Leading the J is bad because East can have a doubleton king, then you don’t have a squeeze anymore. If West has K-x-x-x, then congratulate him.

Shyam Sashital: The K is necessary as an entry to execute the double squeeze, and the 9 eliminates a guess in clubs should East win and return the suit.

Michal Nowak: Diamonds must precede the club ace.

Steve White: Preserve K entry for trick 10 in case East wins the 10 and leads a spade.

Final Notes

Thanks to all who responded, and especially those who offered holiday greetings and/or kind remarks about my contests and polls.

Comments are selected only from those supporting the correct solution of each problem. While this might be considered biased, I feel it’s the best way to ensure solid content and avoid potential embarrassment by publishing comments that are off base. On this basis, I included about 75 percent of the eligible comments. If you supplied comments that were not used, I thank you for the input.

Use of a comment does not necessarily mean I agree with it, but generally they are all worthy. Comments are quoted exactly except for corrections in spelling and grammar. Where I have included only part of a comment, an ellipsis (…) indicates where text was cut. Text in [brackets] was supplied by me to summarize a cut portion or fix an omission. Comments are listed in order of respondents’ rank, which is my only basis for sequencing. I am confident that my lengthy study of these problems, assisted by comments received, has determined the best solutions in theory, but oversights are possible. Feedback is always welcome.

And finally, one person even provided a digital analysis:

Jim Dooley: Wonderful problems. However, as I told Mabel when she urged me to enter the contest, answering the problems requires more fingers and toes than most bridge players have.

Analyses 7V16 Main Challenge

Scores Top Notrump Wonderland

Credits to Felix Bernard and Richard Smith, composers of “Winter Wonderland”
© 2001 Richard Pavlicek