Analyses 7X88 Main Challenge

The Falcon Is Found!

Scores  by Richard Pavlicek

These six problems were published on the Internet in June 2004 as a contest open to all bridge players. On each problem, you are declarer in a spade contract (what else) from 1  to 6 , and all you have to do is choose your line of play from the choices offered.

Problem 1

2

3

4

5

6

Final Notes

It’s been a hectic month, as I had an unexpected visit from Joel Cairo, who broke into my office at gunpoint. “I am prepared to pay five million dollars for the figure’s return,” he exclaimed. “Do you have it?”

I pled ignorance, of course, but he persisted and began to search the premises. Fortunately, before he could walk into the den, I caught him by surprise. We scuffled for a minute, but his puny muscles were no match for mine, and I had to resist the urge to beat him to a pulp. “Look what you’ve done to my shirt!” he whined.

I could almost laugh at his pathetic presence, as a gardenia-scented perfume permeated the room. I lied through my teeth about having the figure, but he was hardly convinced. “But if it isn’t here,” he argued, “why do you risk serious injury to prevent my searching for it?”

“Why should I sit around here and let people come in and stick me up?” I countered. “You can tell whoever you work for that five million is peanuts. That’s right, peanuts. Put up some real dough, and I might be able to produce that falcon… er, figure. The going price is $27 million, but in your pitiful case I’ll make it an even 30.”

Julka Kowalska Wins!

This contest had 891 entrants from 117 locations, and the average score was 37.88. Congratulations to Julka Kowalska (Poland), who was first of three with perfect scores. Also scoring 60 were Bruce Neill (Australia) and Andrzej Krakowiak (Poland). In close pursuit at 59 were Lajos Linczmayer (Hungary); Rolf Mattsson (Sweden); Carsten Kofoed (Sweden); and Javier Carbonero (Spain). Almost a European sweep, saved by one token Aussie.

In the overall standings, the top two spots were unchanged, as Zahary Zahariev (Bulgaria) and Leif-Erik Stabell (Zimbabwe) retained their sizzling 59.50 average. (Zahary is first by tiebreaker.) Quite a ways back with 58.00 but closing fast is Lajos Linczmayer (Hungary); followed by Dean Pokorny (Croatia) with 57.57; and John Lusky (US) and Charles Blair (US), each with 57.50.

Some of the problems this month were tough, or at least tricky, as the slightly low average score of 37.89 suggests. Well, that’s good news for me, as I’m still trying to get even from February when you broke the bank with 19 perfect scores. The average score of all 23 play contests is now 39.22; highest was 42.75 in February 2002; lowest was 37.19 in February 2001. Hmm. Can’t trust those short months.

Grrr… I have two participants from Malta, and neither of them entered this contest — plus I was hoping to get more. Wouldn’t you know it? They started this whole story and wouldn’t even show up for its final chapter. Oh well; I guess they were too busy falcon around.

A new country was added this month: Welcome to Paul Fauvet of Mozambique (MZ). This makes 87 participating countries to date.

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 is scored on a 1-to-10 scale based on my judgment, which is also aided by some of the comments received.

Analyses 7X88 Main Challenge

Scores Top The Falcon Is Found!

Problem 1

IMPs E-W Vul	K J 10 9 5 2 9 7 4 3 A J 4		West 1 All Pass	North Dbl	East Pass	SOUTH 1 1
Lead: Q
1 South	A Q 8 7 A 6 4 3 K 5 9 6 2

After winning the A:

Next Play	Award	Votes	Percent
D. Win A; lead 5	10	192	22
A. Lead the 3	8	229	26
C. Lead the 5	7	115	13
B. Lead the K	6	90	10
F. Finesse the J	3	144	16
E. Win A; lead 3	1	122	14

One spade? Somehow, it’s hard to picture Sam Spade or Humphrey Bogart playing a one-bid. Surely, the deal would be thrown in to save time. Time is money! Even 1  doubled is far-fetched since Bogey would have redoubled. Nonetheless, at IMPs we’re stuck by the rules to play it out.

At first glance, seven tricks look easy: four spades, two aces and a heart ruff in dummy. Then you realize that repeated trump leads when you concede hearts will force you to win the second trump in hand, wasting an honor, which may result in the loss of a trump trick. Consider this layout:

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

After winning the A, suppose you win the A to guard against East pitching his clubs on hearts and concede a heart (Line D). The trump return is won in dummy; another heart is lost, then the next trump must be won in hand. This leaves the following with South on lead:

win 3	K		Trick	Lead	2nd	3rd	4th
	—		7 S	6	8	K	8
	9 7 4 3		8 N	4	Q	6	10
	J 4		9 E	6	5	J	3
9		6	10 W	A	4	8	K
J 8		—	11 W	K	J	6!	9
A J		Q 10 8 6	12 E	Q
K 10		Q 8	Declarer fails
	A 8
	6
	K 5
South leads	9 6

Note that East has pitched a club (a key discard). Next you must ruff your heart to have any chance, and East pitches another club. Now, no matter what you do, you cannot prevent West from scoring the 9 with an overruff. For example, if you exit with a club, East wins and returns a diamond to the jack; A; K which East ruffs to gain the lead to deliver the trump promotion.

Suppose you try a different tack. Instead of going for a heart ruff, play to ruff two diamonds in hand, which comes to seven tricks by a dummy reversal. West is marked for the A, so just win the first trick and lead a low diamond (Line C); win the trump return in dummy; concede a diamond, and win the trump return in dummy. This leaves:

win 4	K		Trick	Lead	2nd	3rd	4th
	9 5		6 N	7	8	Q	7
	9 7		7 S	2	7	A	3
	A J 4		8 N	9	10	A	8
9		6	Declarer succeeds
J 10 8 7		—
—		Q 10 8
K 10 7		Q 8 5 3
	A Q
	6 4 3
	—
North leads	9 6 2

Bingo! Now it’s simple to ruff a diamond, cross to the A, and ruff the last diamond. No defense could stop this, even if West had cashed a heart or two. This was the solution I had in mind when composing the problem, based on an actual deal with the above spade layout.

Alas, deeper study sometimes pokes holes in first beliefs, and so it did here. Suppose the deal is:

IMPs	K J 10		Trick	Lead	2nd	3rd	4th
E-W Vul	9 5 2		1 W	Q	2	K	A
	9 7 4 3		2 S	5	J	3	2
	A J 4		3 W	J	5	3	3
5 4		9 6 3 2	4 W	10	9	5	4
Q J 10 8 7		K	5 W	A	4	6	K
A J		Q 10 8 6 2	6 W	8	10	8	6
K Q 10 7		8 5 3	Declarer fails
	A Q 8 7
	A 6 4 3
	K 5
1 South	9 6 2

If you lead a diamond from hand at trick two, West wins and cashes two hearts, allowing East to pitch clubs. West next wins the A and leads a fourth heart, ruffed in dummy, as East gets rid of his last club. Now, no matter how you squirm, you cannot come to seven tricks. It would not have helped to cash the A early since the late club entry is crucial to the dummy reversal.

It could be argued that West would lead a trump with the second hand, but this is moot. In fact, it wouldn’t even beat you; while a trump lead with my first example would send you the way of Archer and Thursby. There are also many deals where East has five spades, in which only Line D will succeed. So which play is better?

Rather than attempt a complex calculation, I ran a 1000-deal simulation. I gave West Q-J-10-8-7 and 10+ HCP for his vulnerable overcall, less than five spades (else he would probably use Michaels) and less than five diamonds (else he would probably bid 2  over 1 ). I also ruled out a singleton diamond, as East would surely reopen with 2  holding at least Q-J-10-8-6-2 and the K. Below are the results with double-dummy play:

Play	Success
D. Win A; lead 5	945
A. Lead the 3	789
B. Lead the K	773
C. Lead the 5	773
F. Finesse the J	515
E. Win A; lead 3	141

While the double-dummy result of any given deal is often different from practical play, the overall differences tend to balance out. Therefore, this leaves no doubt that Line D is best and Line E is worst. It’s a close call for second, but it will go to Line A — not just because of the slight edge in the simulation but because it might yield an overtrick, whereas Lines B and C cannot. Curiously, the simulation found no difference between leading the K and 5, so Lines B and C are ranked by the voting.

Comments for D. Win A; lead 5

Bruce Neill: There are basically two possible lines: Ruff a heart in dummy; or ruff two diamonds in hand. If I plan to ruff a heart, it is prudent to take the A at once to stop East from throwing all his clubs, e.g., 9-x-x-x K Q-J-x-x-x x-x-x. However, this generally fails if West has 9-x-x or better, e.g., 9-x-x Q-J-10-x-x A-x K-x-x. Then I need to ruff diamonds. I looked through about 100 deals where West had this heart suit and 10+ HCP; in 17 cases, ruffing a heart works but ruffing diamonds fails; in 15 cases, the other way around. Further, in some of the latter cases West doesn’t have a very robust overcall, so ruffing a heart seems clearly better.

Lajos Linczmayer: If East has two [or three] clubs, the A must be cashed before leading a heart.

Carsten Kofoed: Very complicated, but I get seven tricks whenever West doesn’t have 9-x-x-(x).

John Lusky: If West has four or more clubs, I may lose the A if I don’t take it now. Opponents will not be able to stop me from ruffing a heart, although I may have to overtake the second spade to do it. I hope to solve the problem of the 9 in the endgame…

Dean Pokorny: When East holds five spades, this is necessary to prevent him from discarding all his clubs on West’s hearts.

Charles Blair: “I distrust a close-mouthed man” -Kasper Gutman. Why is East leaving me in 1 ? If he has at least four clubs, Line B or C is best. However, perhaps he has five spades, in which case this is the only winner. If West takes playing strength into account for vulnerable overcalls, 1=5=3=4 seems more likely than 3=5=3=2 or 3=5=2=3 with the 9. “You have always, I must say, a smooth explanation ready.” -Joel Cairo

Thanks for reminding me of that gardenia-scented twerp. Just don’t expect a cut when I unload the Bird!

Tim DeLaney: I win the A as a precaution; West could have x Q-J-10-8-7 A-x K-x-x-x-x, in which case East could discard his clubs on hearts…

Radu Vasilescu: I need to cash the A when East has five spades and three clubs; then I will be able to ruff a heart in dummy. This line loses when West has only two diamonds and at least three spades [including the 9], but then East probably would have balanced.

Manuel Paulo: … On the bidding, East is likely to have four or more spades, so this is clearly best. For instance, if West has x Q-J-10-8-7 A-J-x K-10-x-x, leading hearts or diamonds, or finessing the J, allows East to discard clubs on hearts… Cashing the A then leading diamonds doesn’t work because the opponents can draw trumps in time to stop a heart ruff in dummy or two diamond ruffs in hand.

Bill Erwin: I need to cash the A so East doesn’t pitch all his hearts. I’ll have to overtake one of the spades to ruff the fourth heart and play for the 9 with East or doubleton on either side.

Julian Pottage: This may be essential if East is 5=1=4=3.

Antonio Ney: I need to make one heart ruff without risking the loss of the A — which is what could happen if I lead a small heart immediately…

Paul Huggins: Aiming to ruff the fourth heart in dummy for my seventh trick. I cash the A first, just in case East can pitch all his clubs on West’s hearts and ruff the ace later.

Sebastien Louveaux: I plan to ruff a heart in dummy and hope to score the 8 at the end. Cashing the A early is to prevent East from discarding too many clubs on hearts.

Brad Theurer: Going for a heart ruff, but I cash the A first in case East can rid himself of all his clubs. …

Adrian Petculescu: Trying to ruff a heart in dummy and avoid…club discards by East when West has [four or] five clubs.

Gerald Murphy: Ruffing in dummy should be fine. The only danger is 9-x-x in West, but I will play East for that card. I should come to four spades, one club, one heart and a ruff.

George Klemic: Take the A early before East can discard…clubs on hearts; then proceed with the heart ruff.

Anthony Golding: Set up the heart ruff first, then worry about other suits. I may be able to get an endplay even if the 9 is wrong.

Conor Moore: Play for a heart ruff, but take the A first in case East discards clubs.

Sandy Barnes: I need to ruff a heart before opponents can lead three spades, while not getting my A ruffed.

D.C. Lin: Use before expiration date.

Jeff Mayhew: Before East can pitch on hearts, say, with 4=1=6=2 shape. I plan on five spades and two aces.

Bill Jamerson: I have four spade tricks and two aces, and the best chance for a seventh trick is to ruff the fourth heart. Win the A first to prevent East from sluffing clubs…

Don Hinchey: A cautionary measure before going after my seventh trick via a heart ruff.

Bill Cubley: I plan to ruff a heart in dummy, and this prevents East from pitching all her clubs — she is Brigid O’Shaughnessy, of course.

Analyses 7X88 Main Challenge

Scores Top The Falcon Is Found!

Problem 2

IMPs None Vul	Q J 10 9 6 5 2 10 7 6 9 6 2		West Pass All Pass	North 2 1	EAST 1 Pass	South 1 NT 2
Lead: Q
2 South	K 8 2 A K 7 4 Q 3 A 7 5 4		1. Jacoby transfer

After winning the A:

Next Play	Award	Votes	Percent
B. Win the K	10	140	16
F. Lead the 4	9	127	14
E. Win the A	7	34	4
D. Lead the 3	5	289	32
C. Lead the Q	3	205	23
A. Lead the 2	1	97	11

A peaceful partscore, but where is the eighth trick? Obviously, you’d like to ruff a diamond in hand, but the defense will surely realize your intentions and probably be able to thwart it. Starting a low diamond (Line D) offers the slim chance that East has both A-K and A-x, so a third trump can’t be led, but there must be something better than that.

What about establishing your long club? An even club break is a reasonable chance, surely better than normal odds based on the bidding and defense.* Note that you can’t combine chances by leading diamonds first, then fall back on clubs if trumps are led, because you’ll be a tempo behind; opponents can cash a third diamond before you can develop the club.

*West’s decision to lead the Q should rule out a singleton club, and with a void (East having K-Q-J-10-8-3) there would usually be more bidding. This suggests clubs are either 3-3 or 2-4.

Consider this typical layout:

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

With clubs not breaking, and no time to develop a diamond ruff, you seem destined to fail. Maybe not! An effective play in many situations like this is to equalize your trump length. This creates more flexibility and sometimes brings pressure on an opponent. Suppose you win the K (Line B) and ruff a heart (with the 9, just in case) then return to hand with the A to leave:

win 4	Q J 10 6		Trick	Lead	2nd	3rd	4th
	—		5 S	7	J	10	?
	10 7 6		Declarer succeeds
	9 6
7 3		A 5 4
J		—
K 9 5 4 2		A J 8
Q		K J 10
	K 8 2
	7
	Q 3
South leads	7 5 4

Next lead your last heart and ruff with the 10, and East… hmm. Just what does East do? He can’t afford to overruff because the remaining trumps will split 2-2, and you’ll be able to ruff a diamond. If he pitches a club, you will lead a club to establish your long club (assuming trumps are cleared, else crossruff). If he pitches a diamond, you will lead a diamond, and either enjoy a diamond ruff or establish the 10. A good gumshoe might have figured the 10 was there for something — not just a pretty face.

Observe that when East shows up with only three hearts, and presumably at most three spades (to have a chance), he is marked with four clubs, else he would have opened 1 . Hence, the diamond lead from dummy is your only hope after he pitches a diamond. Had East followed to four hearts, you would lead a club and hope for a 3-3 club break if opponents clear trumps.

Among the other choices, pursuing a 3-3 club break is clearly better than chasing a diamond ruff. Between Lines E and F, ducking the first club lead (Line F) is better because it allows you to succeed when East is 2=4=3=4 with A-J-x or K-J-x, eventually leading to a neat triple squeeze — which, by the way, fails with Line B, so Line F gets a close second. Between Lines C and D, leading a low diamond (Line D) is considerably better.

Last and surely least is to lead trumps (Line A), a costly loss in tempo that ruins most of your original chances; e.g., you can’t even succeed now if clubs are 3-3. To paraphrase Sydney Greenstreet as the Fat Man: I always distrust a man who leads trumps; if he has to be so careful not to lead some other suit, it’s because he’s not to be trusted when he does. (Yeah, I know; it makes no sense to me either, but if you play it back on a 1941 phonograph, it’s cool.)

Comments for B. Win the K

Lajos Linczmayer: I hope East has A-x-x x-x-x A-K-J Q-10-x-x. I trump a heart, play a club to the ace and trump my last heart. East will be squeezed in three suits.

Carsten Kofoed: East-West can choose my way to eight tricks.

Neelotpal Sahai: If East has A-x-x 10-x-x A-K-J K-Q-J-x,…after two hearts are cashed and the remainder ruffed in dummy, East gets squeezed in three suits. Either a club or diamond can be set up depending upon his discard.

Rob Stevens: … After I ruff the last heart, East, holding, say, A-x-x x-x-x A-J-x K-Q-x-x, will come under pressure in a strange three-suit squeeze — one of them being trumps.

Gonzalo Goded: In case East is 3=3=3=4 with A-J-x, he will be squeezed on the fourth heart, ruffed in dummy. If he has A-K, I may still succeed finding A doubleton.

Marcus Chiloarnus: The supreme irony of life is that no one gets out of it alive.

True, but if Wilmer gets hold of your comments, you might not make it past middle age.

John Reardon: If East has something like A-x-x x-x A-J-x-x K-Q-10-x, it is necessary to cash the K and ruff a heart; then cross back to the A and ruff my last heart. What can East do? He is squeezed in a strange way.

Manuel Paulo: … If East has, e.g., A-x-x x-x-x A-J-x K-Q-10-x, I can win the K; ruff a heart; come back to hand with the A, and ruff my last heart. East has no idle card to spare.

Jim Munday: … I can combine chances by taking A-K; ruff a heart high; club to ace, and ruff a heart high…

Weidong Yang: At first glance, it is easy to hope East has A-K and [ A-x] so I can ruff a diamond to ensure five trump tricks; but this is a trap to avoid. East’s 1  bid suggests he is likely to have less than four diamonds, and he shouldn’t have five clubs else West would lead a stiff club… which means East is very likely to have 3+ trumps. One more point: West is likely to have the A or K since East didn’t open 1 NT. Don’t worry. I will get my eighth trick by a squeeze…

Nigel Guthrie: Continuing with a heart ruff; A; heart ruff. I may be washed out by these efforts, but East will be caught in the backwash with A-x-x x-x A-K-J K-J-x-x-x.*

*Nigel is evidently a devout weak-notrumper. At least his example shows you can be backwashed on either side of the pond.

N. Scott Cardell: If East has A-K and exactly A-x, I can play avoidance against West by leading the 3 and continuing with the Q next to force a diamond ruff… This also succeeds when East has a A-J or K-J doubleton, but it’s against the odds; and if it’s there now, it will be there later. A much better line is K; heart ruff high; A; heart ruff high. If East has, e.g., A-x-x x-x-x A-J-x K-J-x-x, he is caught in an unusual squeeze…

Len Vishnevsky: Paradox: Why can’t I lead diamonds if I want a diamond ruff? Opponents have the tempo to draw trumps — unless I ruff hearts for the backwash squeeze.

Conor Moore: … East might not be able to protect both minors and retain a third trump on the final heart ruff.

Analyses 7X88 Main Challenge

Scores Top The Falcon Is Found!

Problem 3

IMPs None Vul	A K 10 6 5 4 3 J 8 4 2 A 5		West Pass 3	North Pass 3	EAST 1 Dbl All Pass	South 2 Pass
Lead: 2
3 South	Q 10 9 8 6 5 — K 6 3 Q 7 4 2

After ruffing the first trick:

Next Play	Award	Votes	Percent
F. Duck a club	10	74	8
E. Win A; lead 5	9	562	63
D. Win A; lead 2	7	45	5
C. Win A; lead 4	6	39	4
B. Win K; lead 5	2	100	11
A. Win K; lead 2	1	72	8

No more cheap contracts! Opponents are pushing you higher and higher. As the goon Wilmer might say, “If they keep it up, they’re gonna be pickin’ iron out of their liver.” East apparently has more than a minimum, since West couldn’t scrape up a heart raise over 2  when he is known to have three hearts. East also rates to be short in spades, likely a singleton.

The first trick pinpoints the heart distribution but doesn’t disclose much about the enemy heart honors. East’s play of the ace is routine from any holding because it’s the card he is known to hold.* His hearts could be as weak as A-Q-9-8-7 or as strong as A-K-Q-J-9; the only thing you can rule out is West having an honor sequence (K-Q-2 or Q-J-2).

*It is also possible that East played the ace as suit preference for diamonds.

The A is a big favorite to be onside, so assume it. A club ruff in dummy brings the total to eight, and the ninth trick may come from establishing the Q or scoring all your trumps in hand. The latter will require an eventual endplay against West unless the J drops. Consider a likely layout:

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

After ruffing the first trick, suppose you win the A and lead a club (Line E) — the majority choice. It makes no difference, but assume you put up the queen losing to West. A trump is returned, then you ruff a heart and ruff a club to reach:

win 4	—		Trick	Lead	2nd	3rd	4th
	10 6 5		7 N	2	5	K	9
	J 8 4 2		8 S	3	7	8	10
	—		9 E	A	6	Q	4
J 7 4		—	10 E	K
Q		K J 8	Declarer fails
9 7		A Q 10 5
10		—
	Q 10 9
	—
	K 6 3
North leads	7

A dead end. If you lead a diamond (East ducks) to the king and exit with a diamond, East cashes two diamonds allowing West to pitch his last heart; then a heart seals your fate. If you instead ruff a heart, you will have to exit with a club; then West has several ways to beat you, e.g., a trump return gives you the 10 but endplays you in diamonds.

Suppose you try a different tack, using dummy’s A entry to ruff a heart, then exit with a club. After the obvious trump return, you ruff a heart and ruff a club to reach:

win 3	—		Trick	Lead	2nd	3rd	4th
	10 6		8 N	2	A	3	9
	J 8 4 2		9 E	K
	—		Declarer fails
J 7 4		—
—		K J
9 7		A Q 10 5
K		—
	Q 10
	—
	K 6 3
North leads	Q

Still no good. If you next lead a diamond, East hops with the ace to lead a good heart; then if you ruff, you get overruffed; or if you discard to prepare an endplay, you will never make the K. It also wouldn’t help to lead a diamond at trick three, as East will duck (or play the 10); then West can ditch a heart on the third diamond to ruin your trump reduction. Alas, there seems to be no way to get the timing right.

But wait! The difficulties arise because if you lead diamonds, East will duck allowing West to pitch a heart; or if you lead hearts, East will continue hearts allowing West to pitch a diamond. The solution is to make the defense commit first. The key play is to duck the first club (Line F). Suppose a trump is returned. Next lead a diamond, and it makes no difference what East does; suppose he ducks, and you win the king. Cross to the A; ruff a heart; ruff a club, and ruff a heart to reach:

win 2	—		Trick	Lead	2nd	3rd	4th
	10 6		9 S	3	7	8	10
	J 8 4		10 E	A	6	K	J
	—		11 E	K	Q	4	6
J 7 4		—	West is endplayed
—		K J
7		A Q 10
K		—
	Q 10
	—
	6 3
South leads	Q

With the trump reduction complete, and the K in the bank, just exit with a diamond and wait — don’t ruff when East leads a heart. West is obliged to ruff first, then you will score the 10.

Line F is by no means foolproof, but I’m convinced it is best because it has several fallbacks. For example, if East had a second trump and hopped with the A to return it, his shape would usually be 2=5=3=3; then you will get home by establishing the long diamond (note the A is still in dummy as an entry).

Line E is a strong contender and would be the winner if the contract were four spades, as it offers the only real hope for 10 tricks — needing the A and K onside, plus the J to drop. Unfortunately, we forced Bogey to play another partscore, for which Line E is slightly inferior as explained. Lines C and D are also decent, with various chances.

Worst by far are Lines A and B, as taking out dummy’s trumps is almost like playing for the wrong side. I was running short of options, and I knew that drawing trumps will always draw some bullets, er, I mean, ballots. To trump drawers everywhere: Your troubles ain’t over ‘til the Fat Man sings.

Comments for F. Duck a club

Bruce Neill: I’m amazed; great problem. I generated random hands where East had 5-4-3-1 or 5-4-4-0 shape, 12+ HCP and the A (allowing a falsecard at trick one). I’ve checked six hands, and in all of them ducking a club works; in four, it’s the only play that works. I wouldn’t have believed it.

Lajos Linczmayer: As East’s A can be a falsecard, West may have the K. If West has the K and his shape is 5=3=2=3 or 4=3=2=4, I must duck a club and ruff a club in dummy. If East has the K and his shape is 0=5=4=4, 1=5=3=4, 1=5=4=3 or 2=5=3=3, this play also works.

Neelotpal Sahai: East has either the A or K (not both) along with A-Q-J. If the A, this line will work; if the K, the contract will probably not make anyway. I have to create entries in dummy to ruff three hearts. Since East is likely to have 1=5=3=4 or 1=5=4=3 shape, West will get endplayed in the last three cards.

Rob Stevens: The Q is a red herring. Whether West holds four or five trumps, with careful timing in the former case, I can engineer a trump endplay to score seven trump tricks… The danger in using one of dummy’s entries to lead a club is that the K isn’t quite marked with East, then I will lack the entries to shorten my trumps sufficiently.

Dean Pokorny: Ducking a club immediately preserves control and an entry to dummy… It’s the only way to succeed if West holds J-x-x-x K-x-x x-x K-x-x-x.

Marcus Chiloarnus: When it comes to a crossruff, imagination is more powerful than knowledge.

Charles Blair: “Can he cover up by marrying her?” -Miles Archer. “When you can elope, there is hope.” -Geza Ottlik.

And when you can’t elope… You’re a melon. -RP

Tim DeLaney: Assuming East has the A, this covers all the bases. In most continuations, I will ruff hearts to reduce my trump length to fewer than West’s, assuring I can endplay him. But if East has x-x A-K-Q-x-x A-Q-x K-x-x, I may have to guess right later on.

John Reardon: The main danger is when West is 4=3=3=3 or 5=3=2=3 and the K is wrong.

Manuel Paulo: I consider East’s likely distributions to be 0=5=4=4, 1=5=4=3 and 1=5=3=4. My aim is to win the K, K and A, ruff three hearts in hand and a club in dummy; then endplay West to lead into my trump tenace. If East has, e.g., — A-Q-J-x-x A-Q-x-x J-10-x-x, I need to lose a club trick [early]. I remember Kasper Gutman’s line, “I’ll make him an offer he can’t refuse,” and so I found the bird — Line F for Falcon.

Nigel Guthrie: Playing East for the A rather than the K.

Julian Pottage: This may be essential if West is 4=3=2=4 with the K.

Gabriel Nita-Saguna: Playing East for spade shortness and the A. The main idea is to be able to get the K, a club ruff and three heart ruffs without West being able to reduce his trumps, and this is the only line that gives the proper timing. In the end I will be able to score two more tricks with Q-10.

Jing Liu: Spades should be 4-1, and the A must be onside. Assuming a trump return, I lead a diamond next. Then I can get two more heart ruffs and a club ruff, leaving West’s trumps longer so he can be thrown in.

Madhukar Bapu: East [likely] has 1=5=3=4, 1=5=3=4 or 0=5=4=4 shape and the A. Assume a trump is returned; I next play a diamond to the king (if East ducks); A; heart ruff; club ruff; heart ruff. Then I exit with a diamond and make the Q-10 on an endplay. The  Q is an hallucinogen — take it away, and there is no problem.

Bob Boudreau: Retaining control of when the third round of clubs is played.

Dick Yuen: Whoever wins the club has to lead a trump (else I can arrange two club ruffs). …

Analyses 7X88 Main Challenge

Scores Top The Falcon Is Found!

Problem 4

IMPs N-S Vul	Q J 8 6 Q J 5 Q 5 J 6 4 2		WEST Pass Pass All Pass	North Pass 3	East 2 Pass	South 2 4
Lead: J
4 South	A 10 9 7 2 A 7 4 K 7 2 A 3

Note: East will play the A only if you play the queen.

Play	Award	Votes	Percent
C. Play Q; win second diamond; lead 3	10	99	11
D. Play 5; win first diamond; lead 2	8	183	21
A. Play Q; win second diamond; lead 7	7	291	33
B. Play Q; win second diamond; lead A	6	133	15
E. Play 5; win first diamond; lead A	4	122	14
F. Play 5; win first diamond; lead 3	3	64	7

A slightly optimistic bid on your part; but as the quiz format suggested, partscores are now history — kind of like Miles Archer, except he didn’t even make it out of the first chapter. Clearly, you need East to have a major-suit king. If it happens to be the K, even Joel Cairo could make this contract, so assume it’s the K in a layout like this:

IMPs	Q J 8 6		Trick	Lead	2nd	3rd	4th
N-S Vul	Q J 5		1 W	J	Q	A	2
	Q 5		2 E	9	K	3	5
	J 6 4 2		3 S	7?	2	6	4
K 5		4 3	4 N	Q	3	2	K
10 9 8 3 2		K 6	5 W	10	Q	K	A
J 3		A 10 9 8 6 4	Declarer fails
K 10 8 7		Q 9 5
	A 10 9 7 2
	A 7 4
	K 7 2
4 South	A 3

With routine play, you are destined to lose a trick in each suit. The only slim hope is to catch West in club-heart squeeze. Suppose you win the second diamond and ruff the 7 (Line A) as West pitches a heart; then the Q loses to the king, and West shifts to a heart; queen, king, ace. You must give up a club, then a second heart kills dummy’s entry — along with Floyd Thursby and your squeeze chances.

A more delicate approach is required. After winning the second diamond, suppose you win the A and lead a club, ducked to East. Assume a spade return, ducked to West, and another spade. Win in dummy; ruff a club; ruff a diamond, and lead the Q; king, ace. Then finish the trumps to squeeze West. Voila! Oops, not quite. East could defeat you by returning a third club, then West could kill the club threat when he won the K.

Even more delicacy is required. After winning the second diamond, you must lead a low club (Line C). West must duck (else the queen ruffs out), and you carefully cover with the jack to ensure East wins the trick to prevent a heart shift. Nothing matters, but assume a spade is led, ducked to West, and a spade is returned. Cash the A; ruff a diamond; ruff a club; then cross to dummy with a trump to reach this ending:

win all	—		Trick	Lead	2nd	3rd	4th
	Q J 5		10 N	Q	K	A	8
	—		11 S	A	?
	6		West is squeezed
—		—
10 9 8		K 6
—		10 8
K		—
	A
	A 7 4
	—
North leads	—

Next lead the Q, which East must cover (else his king falls on air) to the ace. Then the last trump squeezes West in the rounded suits. Many variations in the play are possible, but the defenders are helpless to escape their demise.

What about playing low from dummy and winning the K at trick one? This may seem better — perhaps averting a fatal diamond ruff in the rare event East has a seven-bagger — but it destroys the timing for the squeeze. If you next lead a low club (Line F), East can win and return a club. If you then give up a diamond, a third club is led; then West can lead a fourth club when he wins the K. If instead you return a diamond at trick two (Line D), East can lead a third diamond; then if you run the Q or duck a club, West can attack hearts; or if you play ace and a club, East can lead a third club.

Line C involves almost no risk.* East could hardly have a singleton heart (where a heart switch, ducked, would lead to a ruff) since West would then have a weak two-bid (note the vulnerability). If East had a singleton club, he would surely lead it at trick two; then you would change tack, reasoning that West must have both honors (East would never lead clubs from K-x-x or Q-x-x). Further, if East has K-Q-x (where you could establish the J if you didn’t waste it), he could hardly have another king as well; so you were destined to fail anyway.

*Closer scrutiny shows that Line C gives up a chance to make when West has both club honors, which is workable with Line A but arguably double-dummy. Playing for split club honors, however, is almost twice as likely; so there’s no doubt that Line C is superior. Further, holding K-x 10-9-x-x-x J-x K-Q-x-x, many players (count me in) would compete to 3  over 2 .

Of the remaining options, there is little difference among common distributions. Lines A, B and D are essentially the same; aside from predetermined fate, they all include the extra chance that West has the hand in the preceding note. I gave the edge to Line D because it gains against some fluke distributions, such as East having seven diamonds or 0=2=6=5 shape, albeit far-fetched at the vulnerability. Between Lines A and B (Astor and Bogart?) I went by the voting, or “ladies first” if you prefer. Lines E and F, also ranked by the voting, tie for worst because they lose the “extra chance” cited above.

Comments for C. Play Q; win second diamond; lead 3

Bruce Neill: If East has the K, it’s easy. If not, I need East to have the K; then maybe I can squeeze West in hearts and clubs. This works if East has something like x-x K-x A-10-9-x-x-x Q-x-x, [provided] I play the Q at trick one, win the diamond return, and lead a low club. If I play low from dummy on the J, East can break up the squeeze by playing clubs or diamonds at the wrong moment.

Lajos Linczmayer: If the K is in West, East must have the K and 2=2=6=3 shape. If West has one club honor, he will be squeezed in clubs and hearts. If West has both club honors (less likely), a different play works.

Carsten Kofoed: [This prevents] East-West from eliminating the club threat.

John Lusky: This will gain if East has something like x-x K-x A-10-9-x-x-x Q-x-x. The opponents will not be able to stop a round-suit squeeze against West. Playing the A first would allow them to destroy the club menace.

Neelotpal Sahai: To save a heart loser [when East has K-x], West has to be kept off lead. This play will lose if West has both club honors, but I expect him to have only one.

Rob Stevens: The main chance is the K with East, but there is a small extra chance if East holds K-x and Q-x-x (or K-x-x). Then West cannot afford to rise with his club honor to wipe out dummy’s heart entry by leading hearts twice. Playing the A first is incorrect, for it allows the defense to excise the club threat before the squeeze matures.

Gonzalo Goded: To matter, East must have the K and West the K; then East has to be 2=2=6=3 to make. … West is unlikely to have K-Q, so leading the 3 (and playing J from dummy) will force East on lead so he can’t harm my heart communication; then West will later be squeezed. This will also succeed if West has K-Q-x.

Marcus Chiloarnus: If I don’t want to annoy anyone, there’s little point in playing bridge.

Charles Blair: “My way of learning is to heave a wild and unpredictable monkey-wrench into the machinery.” -Sam Spade

Tim DeLaney: If East has the K, I am home with an eventual trump finesse. An added chance: If East has K-x and fewer than four clubs, West gets squeezed in the rounded suits.

Radu Vasilescu: The only way to make when East has x-x K-x A-x-x-x-x-x Q-x-x (or K-x-x). The ending is a heart-club squeeze against West.

John Reardon: I must play the Q or lose to many likely hands. I need one king with East; and if it’s the K, it must be singleton or doubleton. By ducking a club now, I am preparing to squeeze West later.

Jim Munday: If the spade hook works, I have 10 tricks. If it loses, an extra chance is the K onside and either K-Q ruffing out or a squeeze. West must have something like (1) K-x-x 10-9-x-x-x J-x K-Q-x or (2) K-x 10-9-x-x-x J-x K-x-x-x. … Against Hand 2, I need to prevent opponents from killing the club threat, so I’ll force East to win the first diamond (if I duck and play a low club, East can continue clubs). … If I hook the spade too early, West can lead a heart; then a second heart from either opponent will break the squeeze. Winning the A first will also lose, as East can play a third club, and West a fourth. Line C leaves all options open. …

Bill Erwin: I need either the K onside; K-Q-x somewhere; or East with K-x and Q-x-x (or K-x-x). I must cover West’s club play so the heart threat can’t be compromised by two heart leads, begun by West. Winning the A first would permit the defense to eliminate the club threat.

Jouko Paganus: East must have the K or K; and if the latter, I must arrange a squeeze against West when he has five hearts and four clubs.

Julian Pottage: I need a heart-club squeeze if the spade finesse fails, e.g., if East has x-x K-x A-10-9-8-x-x Q-10-x.

John S. Robson: Might there be a club-heart squeeze if West has five hearts and four clubs, and East holds K-x? Leading the 3 first prevents a third round of clubs from being led before the spade finesse is lost.

Toby Kenney: The main chance is the spade finesse; but if that fails, I might still squeeze West with K-x 10-x-x-x-x J-x K-x-x-x. Of course, I’ll look stupid when my A gets ruffed next trick. :)

Ulrich Nell: … I play clubs so that West can be squeezed if East started with no more than two hearts and no more than three clubs. The small club first retains control to prevent [a third club lead prematurely] to break up the squeeze.

Gabriel Nita-Saguna: If the trump king is off, I need East to have precisely K-x and Q-x-x (or K-x-x), in which case I hope to succeed by squeezing West in clubs and hearts. If I won the A first (Line B), opponents could remove the club threat by continuing clubs.

Julian Wightwick: The main chance is the spade finesse, but if East has 2=2=6=3 or 3=2=6=2 shape with K-x, I might be able to squeeze West in hearts and clubs. (East will have to cover the first heart, so I will have a heart entry to dummy.) The club duck prepares to isolate the menace. I can’t start with the A because the defense could [eliminate] clubs. One fly in the ointment is that West could switch to hearts after winning the first club; so I must hope the club honors are split… There is also an outside chance of West holding K-Q-x.

Jing Liu: If the K is onside, I can ruff a diamond and get 10 tricks. If not, the K must be onside with East having 2=2=6=3 shape; then I can squeeze West in hearts and clubs.

N. Scott Cardell: I must lose a diamond and a club; so if West has both major kings, I am down. If East has the K, I will make. The point of leading toward the J is to force a 10th trick when East has something like x-x K-x A-10-9-x-x-x Q-x-x, or x K-x A-10-9-x-x-x x-x-x-x. If East wins the club, he cannot profitably lead a heart; if he returns a club, I will ruff a diamond and take the trump finesse; West can do no better than lead the 10 (jack, king, ace); then I can ruff one club to isolate the club threat and squeeze West in the rounded suits. If West plays an honor on the first club lead in order to lead a heart, I will later get a chance to ruff out the remaining club honor and score the J for a 10th trick.

Douglas Dunn: It looks like the K has to be with East, but there’s an extra chance to squeeze West in hearts and clubs. East will have to have K-x and K-x-x (or Q-x-x).

Linlin Hu: The simple chance is the K with East; but if East has 2=2=6=3 shape with K-x, I may have a squeeze on West. Leading A then 3 will ruin the squeeze (East can play a third club, then West a fourth when he wins the K). If I play a low diamond from dummy at trick one, opponents can [disrupt my entries or timing] to ruin the squeeze.

Jordi Sabate: Playing for East to have K-x and Q-x-x (or K-x-x). I have to prevent West from leading a heart early, as I prepare for a heart-club squeeze.

Richard Stein: If West has four clubs to an honor, he cannot afford to win this trick. I’ll win the club return, ruff the 7 and finesse trumps. If it loses, I need East to have K-x so West can be squeezed in hearts and clubs. If I start clubs with ace and another, the defense can…wipe out the threat. Argh, I have a use for every piece of slush and mush on the board; fancy that.

Gerald Murphy: … The best East can do is to lead a third diamond. Now I give West the K and hope that, when I ruff a club and lead the Q, West will be squeezed in hearts and clubs (East having 2=2=6=3 distribution with K-x).

Kees van Schenk Brill: Preparing the heart-club squeeze against West.

Daniel de Lind van Wijngaarden: I will assume West has the K (otherwise always made) and East the K (otherwise down). I have a chance if West has K-x 10-x-x-x-x J-x K-x-x-x (or Q-x-x-x). … If East returns a diamond, I take the spade finesse; win the A; spade to dummy; lead the Q (covered by king and ace); another spade to dummy, ruff a club, and lead the last trump to squeeze West. This also succeeds if East returns anything else at trick four. East might have disturbed the timing by leading a spade at trick two (West can switch to hearts if I finesse); I could still prevail by taking the ace and leading a club to the jack, but this would be a losing play if East had the K.

Bob Boudreau: This lets me control when the [third club] is ruffed…

Frances Hinden: Trying to make with either major-suit king onside.

Pieter Geerkens: If the K is onside, I am home; if not, I need the K onside and either K-Q-(x) in one hand or a [squeeze].

Roderick Ewan: Tricky one. Assuming the K is wrong, this is all about the club suit and how I time the play.

Analyses 7X88 Main Challenge

Scores Top The Falcon Is Found!

Problem 5

IMPs None Vul	A J 3 2 A J 8 7 6 5 A 5 3		WEST 1 Pass Pass All Pass	North Pass 4 5	East Pass Pass Pass	South 3 4 5
Lead: K
5 South	Q J 10 9 7 5 3 A K 2 Q 8 4

Play	Award	Votes	Percent
D. Win A; lead J	10	92	10
C. Win A; lead 2	8	150	17
A. Win A; A; lead J	7	29	3
E. Win A; lead 5	5	280	31
F. Duck the first trick	4	176	20
B. Win A; A; lead 5	3	165	18

Four spades would have been a lot cozier, but you were blinded by visions of slam — or in the words of the villainess Brigid O’Shaughnessy, “I’ve been bad; worse than you could know.” Now you need an 11th trick, and with West marked for almost all the missing high cards, you should dismiss any idea of leading toward the Q. Conditions are ideal for a minor-suit squeeze against West.* The problem is to rectify the count without letting East gain the lead for a killing club switch.

*West might also have Q-x-x-(x), in which case he would be squeezed in three suits, making the play much easier. The location of the Q, however, is immaterial; all you need is for West to have the K along with his indicated diamond holding.

Consider this plausible layout:

IMPs	A		Trick	Lead	2nd	3rd	4th
None Vul	J 3 2		1 W	K	A!	4	2
	A J 8 7 6 5		2 N	5	6	7	3
	A 5 3		3 S	A	4	2	5
K 2		8 6 4	4 S	K	9	3	6
10 9 4		Q 8 7 6 5	5 S	3	2	A	4
K Q 10 9 3		4	6 N	J!	Q	9	10
K J 9		10 7 6 2	7 S	Q	K	6	8
	Q J 10 9 7 5 3		West is endplayed
	A K
	2
5 South	Q 8 4

Line F (duck the K) comes to mind, as it immediately rectifies the count. If West shifts safely to a trump or heart, you can force out the K and ruff a diamond in the process (to learn the distribution) then West will be squeezed when you run trumps. Oops! Think again. All West has to do is switch to the K at trick two (or lead clubs twice) to wipe out dummy’s entry; then you can never enjoy the A and must lose a club — down one.

Therefore, you must win the A. You next lead a low diamond, which East ruffs, else you could pitch a club to rectify the count. Overruff; cash both top hearts; cross to the A; ruff a heart (important); then exit with the Q. Look at this! West is endplayed, forced to establish a diamond trick for dummy or lead a club from his king. Note that if West had a third spade or a fourth heart as an exit card, his shape would be 3=3=5=2 or 2=4=5=2; then his K will fall on air to give you the contract.

The above play looks pretty, but it contains a serious flaw. Suppose diamonds are 4-2 as in this layout:

IMPs	A		Trick	Lead	2nd	3rd	4th
None Vul	J 3 2		1 W	K	A!	4	2
	A J 8 7 6 5		2 N	5	9	3	3
	A 5 3		3 S	A	4	2	5
K 2		8 6 4	4 S	K	9	3	6
10 9 4		Q 8 7 6 5	5 S	5	2	A	4
K Q 10 3		9 4	6 N	J	Q	9	10
K J 9 7		10 6 2	7 S	Q	K	6	6
	Q J 10 9 7 5 3		8 W	10!	J	8	10
	A K		Declarer fails
	2
5 South	Q 8 4

If you try the same line, East will follow to the second diamond, and you can’t afford to pitch because the 9 will win the trick. Therefore, you must ruff. Suppose you cash A-K as before, cross to the A and ruff the heart when East produces the queen; then lead the Q. Now West can exit safely with a low diamond*, which East ruffs to stop you from pitching, then you’ve exhausted your resources and must fail. Obviously, you could have succeeded this time by ducking the first trick — the club shift is no threat since the A cashes — but how do you know?

*Note that if West had K-x-x (so that East is unable to ruff the diamond), West would simply exit with a trump — and you can’t rectify the count by ducking that!

The proper solution, which caters to almost any layout consistent with the bidding, is to lead the diamond jack at trick two (Line D). If East follows, just pitch a club; then a subsequent diamond ruff will either set up the suit (in the unlikely event diamonds are 3-3) or mark West with the only stopper for the minor-suit squeeze.

What if East ruffs the J, as in the first diagram? No problem. Just proceed as before (ruffing the third heart); then put West on lead with the K in this position:

win 5	—		Trick	Lead	2nd	3rd	4th
	—		8 W	Q	6	7	4!
	8 7 6		9 W	10	7	8	7
	A 5 3		10 S	J	9	3	2
—		—	11 S	10	?
—		8 7	West is squeezed
Q 10 9		—
K J 9		10 7 6 2
	J 10 7
	—
	—
West leads	Q 8 4

West will now exit safely with a diamond, or so he thinks; but you will just pitch a club to rectify the count, then ruff the next diamond and finish trumps for the squeeze. Again, note that if West had any exit card (a third trump, or a fourth heart), he could have only two clubs, so you would still succeed.*

*The failing case is when West is 3=2=5=3 without the Q, in which case he is able to exit with a spade, and his K won’t drop. You can cater to this hand by leading a third diamond from dummy instead of ruffing the J, but then you lose to common layouts. The failing case is extremely unlikely because few experts would pass 1  with 4-2 Q-8-7-6-5-4  4  9-7-6-2 (worst case for all spot cards).

Of the other choices, Lines A and C are pretty good but come up short when West holds K-x x-x-x K-Q-10-9-3  K-J-x. With Line A you cannot remove West’s exit card in hearts; and with Line C (assuming you use the A to eliminate hearts), West can exit with a low diamond since East will have a trump left.

Considerably worse are Line E (losing to 10-4 or 9-4) and Line F (losing to a stiff 4). Between the two, Line F may seem better with only one losing holding, but that’s not true because it loses outright; whereas Line E can recover if West is 2=2=4=5 or has the Q (any shape). The basement goes to Line B, which loses some of the recoveries in Line E. Or to paraphrase Bogey: Sorry, Line B, but when you’re slapped, you’ll take it and like it.

Comments for D. Win A; lead J

Bruce Neill: I want to lose a trick to West, throwing a club from hand, to rectify the count for a minor-suit squeeze. …

Lajos Linczmayer: If West has K-x x-x-x K-Q-10-9-3 K-J-x, or K-x x-x-x-x K-Q-x-3 K-J-x (East cleverly sparing his higher diamond), I can rectify the count and squeeze West in the minors.

Carsten Kofoed: Tempo adjusting.

John Lusky: If West has the black kings, as seems likely, he can be squeezed in the minors if I can rectify the count without losing the lead to East. I will pitch a club on the J (unless East ruffs, then I will overruff)… Ducking the first trick fails [if East has a singleton diamond] and West switches to the K (or any club if East has three spades) as I will never score the A.

Neelotpal Sahai: West is likely to have most of the points (surely both missing kings). I will discard a club [if East follows or discards] and later squeeze West in clubs and diamonds.

Rob Stevens: Intending to let the J run in an attempt to rectify the count for a squeeze against West in diamonds and clubs. I cannot let East gain the lead, so if diamonds are 5-1 and East ruffs, I will overruff and try the same maneuver in hearts.

Dean Pokorny: [Intending] to throw a club to develop a squeeze position… The J is better than a small diamond because East could have 9-4 [or 10-4] and ruin my plans. If East ruffs the J, I [will overruff] then eliminate hearts.

Dale Rudrum: And ditch a club, as West surely has the K and K, and will [eventually] be squeezed. If East ruffs the second diamond, I will overruff and play A-K; A (that’s why I didn’t cash it early); then the J…

Gonzalo Goded: Discarding a club for the likely minor-suit squeeze… I can ruff a third diamond when in dummy with the A in case diamonds are 3-3.

Charles Blair: A drama about preventing something (the lead) from falling into the wrong hand (East).

Tim DeLaney: I cannot duck, for West, with five diamonds, would find the killing K lead to break the squeeze and maroon the A. … I lead the J in case East has 9-4 [or 10-4]. Ducking (Line F) in case East is void is also useless; East can still ruff and play a club to sink the contract [or West could shift to the K].

Radu Vasilescu: I’ll discard a club to rectify the count, then squeeze West in diamonds and clubs. Cashing the A first might be wrong when East has only one diamond — he’d ruff the J, and I can’t let him win the trick as a club return will break my squeeze.

Manuel Paulo: I assume West holds both black kings and the Q. I want to rectify the count to squeeze West in the minor suits; but I must avoid losing a trick to East, fearing a club lead. First, I will not duck because if West has K-x-x Q-x-x K-Q-10-9-3 K-x, he can lead the K. Second, I don’t cash the A because if West has K-x-x x-x K-Q-10-9-3 K-J-x, East can ruff my next diamond lead. Third, I don’t lead a low diamond because if West has K-x-x x-x K-Q-10-3 K-J-x-x, East will win the trick.

Jim Munday: If the K is not singleton, I need to duck a trick to rectify the count for a minor-suit squeeze against West. I can’t lose the trick to East, as a club through the queen would be fatal. If I duck the first trick and diamonds are 5-1, a club shift (king, or two club plays) will remove my entry to the A… This is better; if the J is not ruffed, I will pitch a club…

Weidong Yang: I have a sure squeeze on West, but I must adjust the count by losing a diamond to West so he cannot attack clubs. …

Nigel Guthrie: In case East has two diamonds or ruffs.

Bill Erwin: [Intending to] pitch a club to rectify the count without letting East on lead to play a club. A low diamond might permit East to win the 9 or 10. …

Julian Pottage: I may need to lose a trick to set up a squeeze in the minors, and I want to keep East out.

John S. Robson: I intend to discard a club if East follows suit or discards. …

Toby Kenney: If East doesn’t ruff this, I will discard a club to rectify the count (West can’t attack clubs to break up the squeeze). …

Sebastien Louveaux: Planning to squeeze West, as the bidding marks him with all three kings. I will duck a trick early to West (to avoid a club switch from East) to rectify the count.

Gabriel Nita-Saguna: I am trying to correct the count for a squeeze in the minors against West by discarding a club on the J if East doesn’t ruff it. …

Steve White: This will prevent East from winning with 10-4 or 9-4 and shifting to clubs. …

Douglas Dunn: [Intending to] throw a club to rectify the count for a squeeze if West has both black kings. If East [ruffs], I will overruff and eliminate hearts; then throw West in with the K. …

Gerald Cohen: I must rectify the count and prevent East from gaining the lead.

Tim Francis-Wright: I need to keep East off lead so I will have a possible…minor-suit squeeze against West. …

Pascal Wassong: To prepare a squeeze against West, I must lose a trick [besides the K] without allowing East to gain the lead to play clubs. … If East ruffs the J, I overruff; cash A-K; A; and lead the J, discarding a club unless East plays the Q (then ruff and lead the Q).

Analyses 7X88 Main Challenge

Scores Top The Falcon Is Found!

Problem 6

IMPs Both Vul	A 8 5 3 A 5 A K 3 A K 7 3		WEST 2 Pass Pass	North Dbl 3 6	East Pass Pass All Pass	South 2 4
Lead: K
6 South	K J 10 6 4 9 3 2 8 6 5 4 6

Note: The Q does not appear and nobody shows out of spades.

Play	Award	Votes	Percent
D. Duck; win second heart; A; K	10	170	19
A. Win A; A; K	9	225	25
C. Win A; finesse 10	8	63	7
B. Win A; A; finesse 10	4	221	25
E. Duck; win second heart; A; finesse 10	3	159	18
F. Duck; win second heart; finesse 10	2	54	6

Partner was rather ambitious, as you surely had your jump to 4 when you might have held nothing. If the contract fails, at least we will have a fall guy (Wilmer will be relieved) to hand over to the cops. Take North! Hmm… Could it be Fritz? Nah… last I heard he’s on a bird-watching trip to Iraq.

At first glance, it seems your only problem is to locate the Q, and percentages would dictate to finesse East because of West’s known heart length.* Alas, then you realize that even picking up the trump suit leaves you needing a small miracle.

*With nine cards missing the queen, normal strategy is to play for the drop. When there is a difference of two cards or more between known cards of each defender, percentages then favor a finesse through the defender with fewer known cards. (A difference of one card makes it a virtual toss-up.) In this case, West is known (or assumed) to have six hearts, and East two; so the difference of four indicates the finesse.

One possible miracle is to play for an endplay against West. Suppose this is the layout:

IMPs	A 8 5 3		Trick	Lead	2nd	3rd	4th
Both Vul	A 5		1 W	K	A	8	2
	A K 3		2 N	A	2	6	7
	A K 7 3		3 N	5	9	K	Q
Q 7		9 2	4 S	6	2	A	4
K Q J 10 6 4		8 7	5 N	K	5	3	8
10 7		Q J 9 2	6 N	3	9	10	Q
Q 8 2		J 10 9 5 4	7 S	4	7	K	2
	K J 10 6 4		8 N	A	9	5	10
	9 3 2		9 N	7	10	J	10
	8 6 5 4		10 S	9	J	5	7
6 South	6		West is endplayed

Win the A and cash both top trumps (Line A); win A-K (pitching a heart); ruff a club; win A-K and ruff the last club. Finally, exit with the 9, and West must lead another heart, allowing you to pitch the diamond loser from dummy and ruff in hand. This line also succeeds when West is 1-4 in the minors — or even 0-5, although far-fetched.

Another possible miracle is to play for a ruffout squeeze against East, which also works on the above layout, but you must duck the first heart. Assuming a heart continuation, win A-K (Line D); ruff your last heart, and return to hand with a trump to reach this position:

win all	—		Trick	Lead	2nd	3rd	4th
	—		7 S	10!	J	3	?
	A K 3		East is squeezed
	A K 7 3
—		—
Q J		—
10 7		Q J 9
Q 8 2		J 10 9 5
	10 6
	—
	8 6 5 4
South leads	6

Next lead a trump, pitching the 3 from dummy, and East is toast. If he pitches a diamond, your 8 will be good, and you still have a trump to reach it. If he pitches a club, you will ruff a club to establish the 7.

What if West shifts to a club or diamond at trick two instead of continuing hearts? No matter; the squeeze still functions. To verify, remove one trick (including dummy’s ace) from either minor suit in the above diagram. It was essential, however, to duck the first heart because the K must be used as the entry to ruff a heart.

So which is better? Either play (endplay or squeeze) requires trumps to break 2-2*, so Lines A and D are the obvious candidates. Shapewise, Line D is inferior, as it only works when West is 2=6=2=3 — about 42 percent (assuming a fixed major-suit shape). Line A also works when West is 2=6=1=4 or 2=6=0=5, which adds another 24 percent.

*Exceptionally, the endplay could be executed if West is 1=6=2=4 (low singleton spade) by taking a first-round spade finesse through East (Line C). Alas, playing for this chance is inferior since it can’t be combined; i.e., you then fail if West is 2=6=2=3 or 2=6=1=4 with Q-x.

Despite the shape advantage, Line A has a serious flaw in that it requires West to have 100 honors. Even considering the vulnerable weak two-bid, this is odds-against. I would expect the same bid virtually every time on K-Q-J-x-x-x or K-Q-10-x-x-x, which means West will have K-Q-J-10-x-x only 43 percent of the time.*

*There are 15 ways (6c2) to choose East’s doubleton from the missing hearts (J-10-8-7-6-4), but I excluded J-10 because it would give West a dubious bid. Only six of these include neither honor, so West will have K-Q-J-10 only 6/14 of the time. Also note that a decision to go for the endplay requires winning the first heart, so you would have no knowledge of East’s play.

In falconine figures (numbers that even Joel Cairo could understand): Line D succeeds all of time West is 2=6=2=3, or 42 percent. Line A succeeds against more minor-suit patterns (66 percent) but only 43 percent of time, or about 28 percent.*

*Line A can be improved slightly (1 or 2 percent) by winning the K first. If West is 1=6=2=4 with a blank Q and K-Q-J-10-x-x, you can still execute the endplay. When creating the problem, I was mainly interested in keeping the options parallel and didn’t notice this tiny improvement.

Line C is the only other strong contender. This gains versus Line A when West is 1=6=2=4 (low singleton spade) but loses to 2=6=1=4 or 2=6=2=3 and Q-x — all considered, only a small loss, which warrants a close third.

The remaining options (Lines B, E and F) have no chance, unless the Q pops doubleton in East. The main point is that a successful finesse against East’s Q-x-x leaves no winning layout. If the finesse wins, the Fat Man sings — albeit hard to picture a crooning Sydney Greenstreet. Rather than study these lines to determine the fewest undertricks, they’re ranked by the voting.

Comments for D. Duck; win second heart; A; K

Bruce Neill: I can either hope West has K-Q-J-10 and throw him in for a ruff and discard, or hope East has four diamonds and five clubs, and try to trump-squeeze him. In either case, I need West to have at most two diamonds, so it’s against the odds to play him for a singleton spade; and neither play works if West has Q-x-x. So I’m going to play for spades 2-2. Squeeze or endplay? I counted 100 hands: squeeze 31, throw-in 24; so I go for the squeeze. I need to give up a heart but don’t want West to play a third heart before I draw trumps;…so I duck the first heart, win the second and draw two trumps…

Rolf Mattsson: Trump squeeze. East needs to have at least four diamonds and five clubs; therefore, I play trumps from the top.

Carsten Kofoed: East must have 2=2=4=5 distribution if the squeeze shall work.

John Lusky: I need a ruffing squeeze against East to operate, thus West must have at most two diamonds and at most three clubs. So I will play for spades 2-2 (stiff queen with East would also work). I must duck the first heart because I will have entry problems if I play two top spades and then lead a heart — a minor suit return would then set me.

Neelotpal Sahai: I need West to have exactly two diamonds for this contract to make. [I might endplay West] by throwing a heart on the second club, eliminating clubs and cashing A-K, but it is safer to duck the first heart and play to ruffout-squeeze East in the minor suits.

Rob Stevens: I need a trump squeeze or an endplay. Neither can succeed unless West has only two diamonds and three clubs, so I must play for spades 2-2. The endplay needs West to hold K-Q-J-10, so the squeeze is clearly better, and I must duck immediately to rectify the count.

Gonzalo Goded: I need West to be 2=6=2=3 to win. After rectifying the count,…I end with a trump squeeze.

Marcus Chiloarnus: In my partnership I’m the boss; my partner is just the decision maker.

Charles Blair: “What a swell lot of merry-go-round riding.” -Sam Spade. Before East plays to trick one, I think my best plan is to hope West has 2=6=2=3, ducking. After that, it’s too late to change my mind based on the 8, even if I wanted to. The answer [may] depend on the suit quality of West’s weak twos, or whether an expert East would play the 8 from 8-6 or 8-4 (presumably he would always do so from J-8 or 10-8, regardless of signaling agreements). My argument is that the throw-in gains over the ruffing squeeze only if West is 2=6=1=4 or 2=6=0=5 [with K-Q-J-10], and this is considerably less likely than 2=6=2=3 [without K-Q-J-10]. Finally, if I wanted to try for the squeeze after winning the A at trick one, I must play East for Q-x [with a first-round finesse], cutting my chances in half.

John Reardon: It is more likely that I will succeed if spades are 2-2. If West is 2=6=2=3 with, say, Q-x K-Q-J-x-x-x J-x x-x-x, the count is right to execute a ruffing squeeze on East; so there is no need for West to have the 10.

Nigel Guthrie: Cashing A-K is a little-known safety play against losing to a singleton or doubleton queen, then I claim on an obscure Pavlicek squeeze that no self-respecting tournament director or appeals committee would admit they don’t understand.

OK, wise guy. Keep it up and I’ll send Joel Cairo and Wilmer across the pond to rough you up.

Mike Sweet: Best chance seems to be a minor-suit squeeze against East if he has 2=2=4=5 shape. I duck the first heart so West can’t force me to win a minor-suit ace after I pull trump. If West shifts to a minor at trick two, I am OK since I can cash the A before pulling trump, ending in hand to take the ruff, then return to hand with dummy’s last spade. The penultimate spade will then squeeze East.

Toby Kenney: [After winning A-K], I will ruff the third heart and run spades for a trump squeeze against East.

Norm Gordon: Looks like a trump squeeze against East; threats are the 7 and 8, and the squeeze card will be the next-to-last spade in hand. West must have two diamonds and three clubs, so the guards are isolated to East; hence spades need to be 2-2, so just drop the Q. The five-card ending will be K A-K-7-3 facing 6d 8-6-4  6. …

Julian Wightwick: I need to finish with a trump squeeze on East in the minors, so East must have 2=2=4=5 shape… Thus, it’s wrong to finesse East for Q.

Steve White: From the heart distribution, I would favor the spade finesse; but I need East to have at least four diamonds and five clubs [to squeeze him], so he does not have three spades. …

Brad Theurer: In isolation, the spade hook is right; but here, a trump squeeze against East seems the only way. East must have 2=2=4=5 shape for that to work, so play for the drop in spades. Duck the first trick to rectify the count.

Douglas Dunn: Playing for a ruffing squeeze against East if he is 2=2=4=5. The ending will be A-K A-7-3 opposite 6d 8-6-5-4.

Thibault Wolf: Winning position is a trump squeeze against East, who must be 2=2=4=5. …

Jordi Sabate: My best option for a 12th trick is a club-diamond ruffing squeeze against East, which is possible only if West has a maximum of two diamonds and three clubs. So I need West to be 2=6=2=3. I duck the heart to avoid communication problems, and [after winning the A] I will play the top honors in spades.

Richard Stein: Picking up Q-x-x is useless since I need East to be 4-5 in the minors for a squeeze to work. Accordingly, I duck the lead because I need to ruff the third heart when in hand with the K. Even if West leads a diamond or club at trick two, I can’t be stopped.

Maybe so, but your last four words make me nervous.

Jerry Gaer: It looks like East must hold four diamonds and five clubs to be squeezed; therefore, he is 2-2 in the majors.

Gerald Cohen: Best shot is East having 2=2=4=5 shape, then once I have lost a trick it will be easy to pick up spades, [ruff a heart] and execute a trump squeeze.

Madhukar Bapu: Play East for 2=2=4=5 shape… Duck; win the A; A; K; and ruff a heart, forcing an early discard from East. Win two more trumps (pitching a diamond from dummy) and East is squeezed in the minors.

Adrian Petculescu: I need a minor-suit squeeze against East, who must have 2=2=4=5 shape.

Kees van Schenk Brill: A trump squeeze against East requires him to have at least four diamonds and at least five clubs; otherwise West can guard one of the suits. Together with two hearts, this leaves room for only two spades; hence, play for the drop.

Anthony Golding: I need East to have four diamonds and five clubs for the trump squeeze to work — if so, trumps will be 2-2.

Rainer Herrmann: Play for my only realistic chance, East being 2=2=4=5.

Nils Bierrum: If West has a singleton trump, there can be no ruffing squeeze on East.

David Wiltshire: If East is 2=2=4=5, I’ll make it on a trump squeeze…

Tibor Roberts: My only hope is a trump squeeze, for which I need East to hold nine cards in the minors; since he surely has two hearts as well, there’s no point in finessing him for the Q.

Sandy Barnes: I need to squeeze East in the minors, so he must be 2=2=4=5. After ruffing a heart, my next-to-last trump will force East to give up a minor.

Theo Chin: For the trump squeeze against East to work, West can have at most two diamonds and three clubs; thus, 2=6=2=3.

Daniel de Lind van Wijngaarden: I can succeed with a trump squeeze if East has four diamonds and five clubs. As West usually has six hearts, I will play East for 2-2 in the majors. After drawing trumps and ruffing the third heart, I lead two more trumps, discarding a diamond from dummy…

Mark Aquino: If West is 4-5 in diamonds and clubs, there will be a [ruffout] squeeze so long as…spades are 2-2.

Frances Hinden: As I need a trump squeeze for 12 tricks, East must be 2=2=4=5; so there is no point in the spade finesse.

D.C. Lin: I peep at the mirror behind East and see that he has x-x J-8 Q-x-x-x Q-x-x-x-x.

Yi Zhong: I need East to have 2=2=4=5 shape for a squeeze. A possible end position is A-K-3 7-3 opposite J-6 8-6-5. When I lead the J and pitch a diamond, East will be squeezed.

Marian Galesanu: One heart will have to be ruffed, then a minor-suit trump squeeze against East will have to work. This marks West with a mandatory 2=6=2=3 shape.

Leonard Helfgott: If West has only one spade, he has six cards in the minors, so the needed squeeze against East will fail. Also, if I win the first trick [and draw the enemy trumps], West will win the heart and lead [a minor] to break the trump (er, ruffout) squeeze. …

Jelmer Hasper: This looks like a…trump squeeze, which will work if East is 4-5 in the minors. In that case his shape will be 2=2=4=5, and I must cash A-K. …

Pieter Geerkens: My 12th trick must come from a minor-suit squeeze on East, which only works if West has two or three spades. An attempt to endplay West would fail if East held the J (or 10).

Xndq Liu: I need East to have 2=2=4=5 distribution for a squeeze to work.

Final Notes

I hope you enjoyed the contest, and reminisced with me on the Maltese Falcon story. I must admit that I dug out my videos and rewatched the film — can’t get enough Bogey, and the character actors (Lorre and Greenstreet especially) were great. Thanks to all who participated, and especially those who offered kind remarks about my web site.

Comments are selected from those above average (top 453), and on each problem only those supporting the winning play. While this might be considered biased, I feel it’s the best way to ensure solid content and to avoid potential embarrassment by publishing comments that are off base. On this basis, I included over 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 (combined with the input of comments) has determined the best solutions in theory, but oversights are possible. Feedback is always welcome.

“Yes, angel, I’m going to send you over. But chances are, you’ll get off with life.
That means, if you’re a good girl, you’ll be out in 20 years. I’ll be waiting.”

[Phone rings] Another buyer trying to bargain that Bird under $27 million. No way! You’d have to shoot me first.

[Addendum: Shortly after this page was published we attended the 2004 Summer NABC in New York City. On return we found our house had been robbed! I doubt it had anything to do with this story, but it certainly gave pause for thought. I suppose the good news was being away so I didn’t get shot!]

What’s that gardenia smell? Ah, it’s a cast reunion of the bit players:

Charles Blair: “That is an attitude, sir, that calls for the most delicate judgment on both sides.”

Gerald Cohen: Winning a Falcon would be the stuff that dreams are made of. Sadly, I am afraid that I played these hands like Wilmer.

David Olson: Getting up from the table after playing some tough hands, I went back to investigating Fritz’s mysterious disappearance. “When a man’s partner is killed, he’s supposed to do something about it. It doesn’t make any difference what you thought of him. He was your partner, and you’re supposed to do something about it.”

Anthony Golding: I expect to get the bird, as usual.

Bill Erwin: “The best good-byes are short. Adieu!”

Analyses 7X88 Main Challenge

Scores Top The Falcon Is Found!

Credits to Dashiell Hammett (1894-1961) and The Maltese Falcon
Photo is Humphrey Bogart as Sam Spade in the 1941 movie classic
© 2004 Richard Pavlicek