Analyses 7X32  Main Challenge

Delusions of Grandeur

Scores  by Richard Pavlicek

These six play problems were published on the Internet in April 2003 as a contest open to all bridge players. As South on each problem, you become declarer in a grand slam and have to choose your line of play from the choices offered.

Problem 1

2

3

4

5

6

Final Notes

John Reardon Wins!

The overall rankings shifted slightly. John Reardon took over the top spot with a 59.25 average. Even with this extraordinary average, he only did so by a double tiebreaker over Charles Blair. Both had a first place as their best finish, so it went to an average of six scores, and John narrowly won. Close behind are Rob Stevens with 59.00 and N. Scott Cardell (Pullman, Washington) with 58.75.

A new country was added this month: Welcome to Andrew Fernandes of Bahrain (country code BH). This makes 78 countries that have participated in these polls and contests since I began in the fall of 2000. While still way short of the 192 countries in the world (at last count), a realistic goal might be to reach half that number. Come on, bridge players; I know you’re out there.

Bidding is standard (except as noted) 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 may be influenced by comments received.

Problem 1

Matchpoints	K Q 7 3			West	North	East	South
None vul	2			LHO	Partner	RHO	You
	A 7 3 2				1	Pass	1
	A 8 6 4			Pass	1	Pass	2
				Pass	3	Pass	4 NT
Lead: 10		East plays 3		Pass	5	Pass	7
				All Pass
	A 5 4
	A K Q J 4
	4
7 South	K Q J 10

After winning the J, you cash the K ready to claim.
West follows but… Oh no! East pitches the 6.

Your Next Play	Award	Votes	Percent
D. Ruff heart, K, A, A	10	250	34
F. Win A, A	8	103	14
A. Win K-Q	6	94	13
B. Win K, A	5	39	5
C. Win K, A, A	4	105	14
E. Ruff heart, win A, A	2	141	19

East’s show-out on the first club aborts your claim, but chances are still good. The basic plan is to lead high hearts through West until he ruffs, but first you should cash as many side tricks as absolutely necessary, else West may defeat you by pitching those cards instead of ruffing. How many spades do you need to cash? In common situations, you need West to have at least two spades to succeed. Here’s a typical layout to consider:

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

After winning the J and cashing the K, suppose you follow Line C as shown. Assume you next cash a heart, pitching a diamond from dummy to leave this ending:

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

You continue with a high heart. If West ruffs, you can overruff and draw trumps, eventually squeezing East in the majors to win the rest. But wait! West should not ruff. Now you must commit yourself with your discard from dummy. If you pitch a diamond (retaining the squeeze threat), West refuses to ruff the next top heart as well and must get a spade ruff to set you. If instead you pitch the 7, West will ruff the top heart; then you cannot ruff your heart loser and enjoy the Q. Down one.

If only you had ruffed a heart earlier! The consensus was right on the money to spot this, correctly choosing Line D. After ruffing a heart, you win K, A, A as before to reach this ending:

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

Now when you lead good hearts, West is history. If he ruffs at any time, you will overruff with the ace, draw trumps and have all winners. If he discards, you pitch spades and eventually crossruff. This ending is hardly spectacular but shows the importance of foresight.

Line D succeeds against many distributions, essentially just needing West to have at least two spades and at least four cards in the majors; i.e., it fails against 2=1=5=5 shape, but so does every other line.

Is it possible to succeed if West has a singleton spade? Yes, but only if West has four or more hearts, which is odds-against. Further, if West had a stiff spade, he would probably lead it to restrict your transportation early on. Line F will cater to this, but then you will fail against the more common layout in my example. You can’t cater to both.

Lines A and B are essentially equal if followed up correctly, but clearly inferior, failing not only in my example but also when Line F will work. They are ranked by the voting.

Line C has the same chance of success as Line A or B but goes down two tricks in some failing cases. For example, if West has 1=2=5=5 shape, he will ruff the A and tap you with a diamond; then another trick must be lost.

Line E is the worst. Despite its similarity to the correct line, it fails against common distributions. For instance, you won’t even succeed with spades 3-3 if West is 3=2=3=5 (he’ll pitch spades before ruffing).

Comments for D. Ruff heart, K, A, A

John Reardon: I am now ready to run hearts through West; if he ever ruffs I can overruff with the ace and draw trumps while the Q is still in dummy. If he waits until the last moment, I can throw the Q and ruff my spade loser.

Zahary Zahariev: There are several patterns for West where success is possible. Against 1=4=3=5 (5.78 percent) Line F wins; against 1=5=2=5 or 1=6=1=5 (about 2 percent) Lines E and F win. Line D wins when West has 2=2=4=5 (10.83 percent). Against 3=1=4=5 (4.82 percent) Lines A, B and D win; against 4=1=3=5 (2.89 percent) Lines A, B, D and E win. In other cases, all lines always lose or always win.

Charles Blair: If West has only one spade, he can set me by ruffing when dummy has only one spade left; [so I must try to cash two spades].

Rob Stevens: West must have at least four major-suit cards, with at least a doubleton spade — unless he has four or more hearts, which is unlikely.

Carsten Kofoed: If I only take one spade, West can ruff at the wrong time.

Franco Baseggio: Now run hearts pitching spades. If this gets ruffed early, draw trumps and claim. If two more hearts survive, I can crossruff.

Paulinho Brum: I think this is the best I can do, guaranteeing the contract if East does not have five spades.

Hailong Ao: I am OK if these cards win. Line F may win if West has exactly one spade and four or more hearts.

Sivakumar Salem: With trumps breaking badly, I am lucky it is West who has five. After I ruff a heart and cash the K, A and A, I run hearts. Whenever West ruffs, I overruff and claim; else I discard spades and crossruff.

David Johnson: I then run hearts; and if West ruffs, I overruff with the ace, draw trumps and claim. If West doesn’t ruff, my last pitch is the Q and I crossruff the last four tricks.

Pekka Viitasalo: If all these survive, I can claim. Line E requires less [to cash] but fails when West ruffs a heart after exactly one spade honor has been discarded [from dummy]. There is a slight snag in the problem setting: Suppose East discards when I ruff the heart. Now Line E is the only winner, as West must hold x 10-9-8-x-x-x x 9-7-x-x-x.*

*Good analysis, but it is safe to assume that I would tell you if something extraordinary were about to happen. Hence, any unknown issue should be resolved for normal situations. -RP

Neil Morgenstern: I need to set up a position whereby I can lead winning hearts through West; and as I only have one side winner in hand, I must take that last. Thus I must start by ruffing a heart (they could be 5-2), then cash one of dummy’s top spades and the A, then a spade to hand. Now I can play top hearts…

Jinzhou Loo: Placing West with x-x 10-x K-J-x-x 9-7-5-3-2, I plan to ruff my small heart and cash K, A and A; then lead hearts, planning to draw trumps when West ruffs. If I do not cash the K, West can ruff at [an inconvenient] time. Since West led a heart, chances are he does not have a singleton spade.

D.C. Lin: Timely cashing K and A is important, and so is a heart ruff. Even with 20 points, I still have to worry about entries!

Leif-Erik Stabell: If I have survived so far, I play hearts and claim. Chances are that East does not have five spades (no “automatic” spade discard at trick two); and if West is 2=2=4=5, this is the only winning line.

Poon Hua: West can break the contract [in many situations] if I only cash one round of spades.

Dale Freeman: Line F will work if West has at least one spade and four hearts… Line D will work if West has at least two spades and two hearts. I think D is more likely.

Gabriel Nita-Saguna: I can take seven club tricks and the A, so I need to win five tricks in the majors. Line F works when West has one spade and at least four hearts. Line D works whenever West has three or more spades and any number of hearts; or if he has two spades and at least two hearts. Not only do I believe there are more hands covered by Line D but also that West would have led a trump if he started with [long] hearts.

Deniz Unlu: It’s cold if West has at least two spades, one diamond, and four cards in the majors.

Toby Kenney: Now lead hearts. If West ruffs, overruff with the A, draw trumps and claim; otherwise pitch spades and crossruff. Not cashing the K fails because West will ruff the last heart, leaving me unable either to draw trumps (lack of tricks) or crossruff (inability to get rid of dummy’s spade).

Neelotpal Sahai: … If hearts are 5-2, it is important to ruff the small heart at trick three. Now I have to hope that West started with at least two spades. Once in hand, I will lead hearts and keep discarding from dummy till West ruffs. …

Rainer Herrmann: This succeeds whenever West holds at least two spades and at least four cards in the majors.

Grant Peacock: I’m going to lose to a stiff spade with West, or 2=1=5=5 shape. Both of these [holdings] are contraindicated somewhat by the diamond discard. If West is 1=4=3=5 or 1=5=2=5, then Line F prevails; but I think I have to play him for shortness in the suit led.

Manuel Paulo: Against West’s prosaic 2=2=4=5 distribution, this is the only winning line. It also wins when West’s lead is a singleton, provided that he has three or more spades.

Irina Levitina: Then lead hearts, pitching spades, and crossruff.

Perry Groot: Then continue hearts, throwing spades from dummy. Two things can happen: (1) West ruffs before I can throw all of North’s spades; then overruff with the A, pull trumps and claim, or (2) West does not ruff and North has no more spades; then finish with a crossruff.

Ed Davis: Then run hearts, pitching the two spades from dummy. If West ruffs, overruff with the ace and pull trumps; otherwise crossruff. This requires West to follow to one diamond and two spades.

Bill Powell: Making unless West is very short in the majors — any four cards, including two spades, is enough.

Gareth Birdsall: [Play explained]. The problem with Line E is that I must discard the potential 13th trick ( Q) on the penultimate heart, allowing West to ruff the last heart to leave me with only 12 tricks. Of course, after the heart ruff, K and A, I could think for ages then lead hearts from my hand. :)

N. Scott Cardell: In order to prevent any defense, I must cash two spades…and the A before playing high hearts. Lines A, B, C and F [may] work if properly followed up and hearts are 4-3, but Line D is better because it protects me against a 5-2 heart split (and some 6-1 splits). Line E is very bad; it destroys the timing and [requires] a whole lot of luck.

Marcus Chiloarnus: I now have enough ammunition to grind West into submission.

Anthony Golding: I think I need West to be [at least] 2-2 or 3-1 in the majors. Line E fails because he can pitch spades and ruff the fifth heart, then I have a spade loser if I overruff and draw trumps.

Nikolay Demirev: At matchpoints 7 NT is a reasonable spot (roughly 80 percent), going down only when both hearts and spades don’t split — and in addition half of the time a diamond must be led initially. Line D wins when West holds 4=2=2=5, 2=5=1=5, etc., when 7 NT fails… Line F caters to West holding a spade singleton but assumes hearts split 4-3, [but then 7 NT makes]. Line C looks like an improvement over Line D (if West is 2=1=5=5), but that’s an illusion…

Alex Dov: Then if West ruffs any heart, no problem; else I’m able to discard [spades and crossruff].

Kyoko Ohno: If West is 2=1=5=5, he’ll [pitch a spade and ruff the A] and I’ll be down. So West must have at least three spades [or 2-2 in the majors].

Bill Daly: The basic idea is to pitch spades from dummy on high hearts, then crossruff. If hearts break badly and West ruffs one of the high hearts, I’ll come up a trick short; so I need to ruff the small heart [early] to avoid this. [Technique explained].

Thijs Veugen: I need two spade tricks and a heart ruff before the heart train goes.

Douglas Dunn: If West didn’t ruff the A, I’m ready to claim again! Just keep playing hearts. If West won’t ruff, then discard [spades and crossruff].

Patrick Bocken: … This wins as long as West has at least two spades and [four major-suit cards]. The only case where another play (Line F) gets the edge is when West has a singleton spade with four to six hearts.

Jeff Goldsmith: [Most] of the other lines cause dummy to be squeezed in spades.

Doug Jobbins: Then run hearts and [overruff] if necessary.

Anil Upadhyay: Side winners have to be cashed, and hearts have to be used as a trump substitute. The only question is whether to cash one or two spades. If I just cash one spade, after I have thrown a small spade and an honor from dummy on two hearts, West ruffs the next heart winner, leaving me a trick short. Therefore, cashing two spades seems necessary…

Craig Biddle: Then pitch [spades] on top hearts if West does not ruff.

Bernard Danloy: I must force West to ruff and be overruffed; this corrects the timing.

Ashley Sawyer: Then run hearts. If West ruffs, overruff with the ace, cross back to hand with a trump and claim; if West discards, pitch spades and [crossruff].

Bill Jacobs: I think I need West to have two spades. I went through the play of Line E six times, and it just doesn’t work if West defends correctly.

Andrew de Sosa: I can’t make if West has only one spade unless he also has four or more hearts. I’ll play for the superior odds that he has at least two spades (three if a stiff heart) and one diamond (two if a stiff heart).

Mary Alice Bartish: Then lead hearts, pitching spades, until West trumps and I overtrump.

Venkatesh Ramaratnam: The crux of the problem is to find out the least number of major cards required by West to make the hand. West needs to hold at least a doubleton spade and at least four major cards.

Danny Kleinman: I must ruff a heart early to ensure no heart loser later. I must take the A early lest West discard all his diamonds when I run hearts. I need two spade tricks early because I will discard spades from dummy when West refuses to ruff, and I can’t afford to be left with both small spades when dummy has only one spade honor left. I need to be in my hand after ruffing the heart and taking three side-suit tricks, in order to continue hearts.

Sandy Barnes: I need to cash my side winners before leading out the remaining good hearts. Dummy will be able to overruff and I can return to hand in trumps.

Phil Grand: Personally, I would have ruffed a heart before playing trumps in order to have one extra entry in hand.

Personally, I would never argue with anyone named for this contest.

Problem 2

Matchpoints	A 8 6 4 2			West	North	East	South
N-S vul	A J 9 2			LHO	Partner	RHO	You
	A J 8 2					Pass	1
	—			2 NT	4 1	Pass	4 NT
				Pass	5	Pass	7
Lead: Q		East plays 4		Pass	Pass	Pass
				1. splinter bid
	K Q 9 5 3
	K 8
	4
7 South	A K 7 5 2

Your Play	Award	Votes	Percent
C. Pitch heart (win A), K	10	130	18
A. Ruff club, win K	8	356	49
B. Ruff club, win A, ruff diamond	7	88	12
D. Pitch heart (win A), A, ruff diamond	5	72	10
E. Pitch diamond (win A), K	3	63	9
F. Pitch diamond (win A), A, ruff diamond	2	23	3

At first glance this looks like a claimer, but then you realize that a 3-0 trump break leaves you a trick short. West is marked for at least 5-5 in the minors from the unusual 2 NT, so a spade void is more likely than usual. Even so, there are several chances for a 13th trick: You might be able to ruff three clubs in dummy (or alternatively, three diamonds in hand); something good might happen in hearts or diamonds; or there might be a squeeze. Consider this layout:

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

The majority chose Line A (ruff club, win K) which gets a jump start on club ruffs to minimize the danger of an overruff. (Clearly, if you win the A first, you will never be able to ruff three clubs low.) This approach would work fine if East held three clubs (or if the Q fell), but as the cards lie it is destined to fail.*

*At double-dummy you can succeed against any layout. In the above case you could lead a heart to the eight (East cannot gain by splitting) or finesse the spade nine on the first round (then the third club could be ruffed high). Nonetheless, these plays would be silly at the table. Imagine having to bear the loss of a trump trick when trumps were 2-1 all the time. Ouch.

Another possibility is a dummy reversal. Instead of ruffing three clubs, perhaps you could ruff three diamonds in hand (overruffing East if needed). Almost. You can maneuver three ruffs, but you can’t return to dummy to draw East’s last trump. The impending club overruff comes back to haunt you again.

What about a squeeze? You have 12 sure tricks (counting two club ruffs), and it is obvious that only West can guard your long club. If West also has K-Q, he will be squeezed. Alas, this is unlikely because West would probably have led the K. But wait! West must have the long diamonds, so dummy’s fourth diamond will be a threat no matter how the honors divide.

This will not be an ordinary squeeze, but a ruffout squeeze. You must time the play so you can lead either minor suit at the moment West reduces one suit below its critical length. This means you must leave the A in dummy and have the lead in your hand after the squeeze. Further, you must not ruff a club early because you need two trumps in dummy after the squeeze to be able to establish diamonds.

The correct approach is Line C (show above). Draw East’s trumps and win the A to reach this position:

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

Next lead a heart to your king, and West is squeezed. You can establish the long card in whichever suit he pitches.

Line C is not foolproof. An expert West might foresee the ruffout squeeze and discard deceptively, e.g., abandoning his diamond stopper early (as if he held 0=2=6=5 shape) and pitching a surplus club at the moment of the squeeze. Nonetheless, this danger is inherent to most play problems and doesn’t detract from the correctness of the plan. Further, even an expert is unlikely to try this deception because the club layout is unclear, and shortening diamonds below four might surrender an unmakable contract.

Lines A and B are next best, with little to choose between them. Either line requires East to have three clubs (or something good to happen in hearts or diamonds). The edge goes to Line A per the voting.

Line D is considerably worse as you no longer can ruff three clubs, though you can succeed by a dummy reversal if East is 3-3 in the minors. (Note that Lines A and B work if East has only two diamonds.)

Lines E and F are the worst, as discarding a diamond from dummy also ruins the dummy reversal. Line E gets the edge by virtue of still allowing a ruffout squeeze if West has six diamonds (or K-Q), though it’s doubtful anyone chose it for this reason.

Comments for C. Pitch heart (win A), K

John Reardon: No problem unless spades are 3-0; then there is a ruffing squeeze on West.

Zahary Zahariev: When spades are 2-1, I have 13 easy tricks. Otherwise draw trumps (three rounds); then A, K, and West is squeezed.

Charles Blair: If trumps are 3-0, cashing A-K will squeeze West. I [may] have to guess the distribution, [but this should be easy] since West may not realize I have five clubs.

Rob Stevens: A [ruffout] squeeze, though some ambiguity. If West holds five diamonds and six clubs, he might beat me by discarding two diamonds; but East may already have exposed the position by signaling with a doubleton. If West has seven clubs or three hearts, I will get a perfect count.

Carsten Kofoed: The J is only a temptation. If West has at least 5-5 in the minors, he will be in trouble after three trumps, A and K.

Tim DeLaney: I will pull trumps (3-0, else there is no problem); A, K, and West is squeezed in the minors. I can establish the long card in whichever minor West [shortens].

Paulinho Brum: Cashing three trumps (if needed) and two hearts ending in hand is a sure thing if I can read the discards. …

Daniel Bertrand: If trumps are 2-1, pull trumps and claim. If trumps are 3-0, pull trumps and cash A, K to reach a seven-card ending: 8-6 J A-J-8-2 opposite 9-5 4 K-7-5-2. West is squeezed, though I might have to read the position correctly.

Hailong Ao: Then draw trumps (assume 3-0 for the worst) and win A, K (in that order) to squeeze West. Only thing is to read West’s six-card minor suit (if 0=3=5=5, there is no problem in reading).

Sivakumar Salem: If trumps break 2-1, there is no problem. If 3-0, I will pull trumps and win two hearts ending in hand, forcing West to come down to seven cards. I can [establish] whichever minor he shortens.

Pekka Viitasalo: If spades break, I claim. If not, I draw trumps and cash first the A then the K to squeeze West. Then I ruff out the suit West gave up. If West has 6-5 or greater shape, I have to guess the ending.

Neil Morgenstern: I don’t want to play or throw any diamonds yet because, if trumps are 3-0 with East, I have a diamond-club squeeze against West in mind… and I think I will need the A entry. Also, because dummy is short of entries I will need to preserve the club ruff for later; so Line C. …

Jinzhou Loo: Trumps must be 3-0 to cause a problem; so place West with 0=3=5=5. Now, I have to engineer a trump squeeze against West. Therefore, all the diamonds must be kept, and the club ruff kept as an option. I plan to draw three rounds of trumps and cash the A and K. Continuations will depend on how West defends. …

D.C. Lin: Reaching this seven-card ending: 8-6 J A-J-8-2 opposite 9-5 4 K-7-5-2, West will have a hard time finding a pitch in one of his minors.

Leif-Erik Stabell: Unless I misguess badly at the end, West will be caught in a trump squeeze. If West is 0=2=5=6, the trump squeeze is needed, since I cannot ruff three clubs in dummy.

Poon Hua: Trump squeeze against West.

Gabriel Nita-Saguna: Assuming West has at least five cards in each minor, this line will lead to a ruffing squeeze when trumps are 3-0 (very likely with West being void). In this case I will cash three spades and A-K, in that order, and West will be squeezed. If I don’t see three hearts from West, I will have to guess which minor he unguarded, but this is my best chance anyway.

Deniz Unlu: After three trumps (if West is void), I play a heart to the ace and come back to hand with the K. West has a discarding problem.

Toby Kenney: If spades are 2-1, I claim; if they are 3-0, I have a trump squeeze against West.

Neelotpal Sahai: If trumps break 2-1 or clubs break 5-3, this problem wouldn’t be featured here; so don’t count on it. It is likely West has 0=2=5=6… then a trump squeeze will materialize after winning three trumps and two hearts. So it is important not to discard any diamonds… and cashing the A will remove an entry to dummy prematurely.

Rainer Herrmann: West can be trump squeezed in the minors. West is likely to keep diamonds, so if he discards two diamonds and one club, I will assume 0=2=6=5 distribution. Should West be capable to discard this way from 0=2=5=6, he can beat the contract; but against the latter distribution, Line A fails without West needing to be clever.

Manuel Paulo: This prepares…for a trump squeeze against West in the minor suits…

Irina Levitina: Win three spades [if 3-0], A and K for a ruffing squeeze.

Perry Groot: If West has at least 5-5 in the minors and trumps split 0-3 (else no problem), I can squeeze West in the minors.

Ed Davis: Claim if trumps are 2-1. Otherwise, draw three rounds of trumps and cash the A, then K to squeeze West in the minors.

Sergey Kustarov: After three rounds of trumps (spades being 3-0), A and K, West is squeezed…

Bill Powell: If East has all the spades, draw them; then A, K will trump-squeeze West in the minors. There may be ambiguity if West is 6-5, but he’ll probably keep parity with dummy’s diamonds.

Brian Lee: Draw trumps, which I’m assuming split 3-0 (else there’s no problem), then cash the A-K and set up whichever minor West unguards.

Leonardo Feugas: Pull trumps if they are 3-0. Then A, K squeezes West, assuming he has at least 5-5 in the minors.

Anthony Golding: Three rounds of trumps followed by A, K finishes West. Ruffing the first club would leave me an entry short if he lets diamonds go.

Frances Hinden: After three spades and two hearts ending in hand, West must unguard one of the minors, which I can then ruff out. In real life, everyone followed to the K and I claimed.

Bruce Neill: If East has three trumps, cash three spades and two hearts ending in South. West is squeezed in the minors (assuming 2 NT showed at least 5-5). If West is 6-5, he will almost certainly keep four diamonds to cover dummy, so I should guess right. (Trying to take three ruffs will fail if West is 0=2=5=6.)

Rodolfo Cerreto: After drawing trumps (assume three rounds) I cash A and K… with seven remaining cards, West can’t avoid the establishment of either a diamond or a club.

Pratap Nair: I play to reach this end position: 8-6 J A-J-8-2 opposite 9-5 4 K-7-5-2 with South on lead. … West cannot hold on to both minors, and whichever suit he releases, I will establish the long card.

Ciaran Coyne: Draw trumps, then A and K. West must unguard a minor [ending described], and the long card can be ruffed good.

Marvin French: Then A, Q, A and K. West must hold four cards in each minor, but there are only seven cards left. So he unprotects one minor, which I establish with two ruffs.

Peter Franks: Since the contract is cold if spades are 2-1, I only consider 3-0 breaks. If West holds three trumps, he is presumably void in hearts, so a third heart trick can be built by leading a heart toward the K-8. But West is more likely to be void in trumps than to hold three, in which case a trump squeeze on West in the minors offers a much better chance. The timing for a trump squeeze would be destroyed if the club is ruffed at trick one, so pitch a heart.

Danny Kleinman: I win the A to preserve trumps in dummy as entries needed to ruff out diamonds if West comes down to three diamonds near the end. I pitch a heart because the fourth diamond is a threat card. I don’t start to ruff out diamonds early because I need [the A entry to dummy and] a diamond ruff as a hand entry later if West unguards clubs.

Problem 3

Matchpoints	—			West	North	East	South
E-W vul	A 7 5 2			LHO	Partner	RHO	You
	K J 10 9 8						3
	7 5 3 2			Dbl	5	6	Pass
				Pass	7	Dbl	Pass
Lead: K		East plays 3		Pass	Pass
	7 4
	Q J 3
	A Q 7 6 5 4 2
7 × South	10

You ruff and lead a club; East wins the A and leads the 3 won in dummy (West pitches 6).

Your Next Play	Award	Votes	Percent
A. Win the A	10	155	21
E. Ruff out all black cards	9	80	11
F. Ruff club, run the J	7	136	19
B. Lead the 2	5	46	6
D. Ruff club, spade, club, run trumps	4	277	38
C. Ruff club, ruff spade, run trumps	1	38	5

While partner’s sacrifice may have been a phantom (with the Q lead), it was a routine decision, so at matchpoints you should have plenty of company in 7 doubled. Obviously, you can’t make it*, so the object is to go down one, not two. Hence, the early club lead to rectify the count for a potential squeeze. Neat. It’s not every day that you deliberately give up a trick in a grand slam.

*On the actual deal from which this problem came, North’s hearts were A-8-6-2. Oops. This offered a legitimate play to make 7 (East with 10-9 doubleton) so I reduced the heart spots — at least I wanted to justify fully the club lead at trick two.

The takeout double and club discard suggest West’s shape is 4=4=0=5 (or maybe 3=5=0=5), which means that only West can guard the fourth club in dummy. If West also has the K, he is ripe for a squeeze. Consider this layout:

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

Only Line D allows the squeeze to function. After ruffing two clubs and your last spade, you will run trumps to reach this ending:

win 4	—		Trick	Lead	2nd	3rd	4th
	A 7 5		10. S	7!	?
	—			West is squeezed (down 1)
	7
—		A 10
K 10 9		8 4
—		—
K		—
	—
	Q J 3
	7
South leads	—

When you lead the last diamond, West must abandon his stopper in hearts or clubs; and you will discard the opposite suit from dummy to win the rest, aided by the heart finesse. Note that it was important not to lead hearts early; i.e., if you tried Line F, West could cover the J to remove dummy’s entry and kill the squeeze.

The above is certainly interesting, but it overlooks an important aspect about the defense. East could always defeat the squeeze by shifting to hearts, which would be a routine defense by any capable player. Certainly, the trump shift was useless — talk about vain attempts to cut down the ruffing power — so East is marked with the K. The actual deal might be something like this:

Matchpoints	—		Trick	Lead	2nd	3rd	4th
E-W vul	A 7 5 2		1. W	K	8	3	4
	K J 10 9 8		2. N	2	A	10	4
	7 5 3 2		3. E	3	2	6	9
A K J 2		Q 10 9 8 6 5 3	4. N	A!	?
10 9 8 6		K 4		Declarer might salvage down 1
—		3
K J 8 6 4		A Q 9
	7 4
	Q J 3
	A Q 7 6 5 4 2
7 × South	10

If you try for the aforementioned squeeze, not only will it fail but you will go down three (East would have a winning spade to cash when the heart finesse eventually lost). Ouch.

The correct play is Line A. Besides the remote chance of a stiff K, this seems to be conceding down two. Not necessarily. It will often gain against an expert East. Every trick counts at matchpoints, and East will foresee the elimination danger if he fails to unblock — imagine South with J-x-x — so I’d expect to see the K on the table. Thank you very much; down one.

Some people chose Line A for the wrong reason, citing that 7 would be a phantom save if West held the K. This possibility may affect the range of your matchpoints, but it has no bearing on the play. Your score (down one, two or three) is irrelevant in comparison to those defending 6 ; all that matters is how it compares to others in 7 doubled.

Line E (ruff out all black cards) is almost like Line A if followed by cashing the A*, so I felt obliged to give it a close second despite the fact that some who chose it had other ideas. Consider yourself lucky this time. Next time you’ll pay.

*Against strong opponents it is better to cash the A early, as East must commit before he has any information. If you ruff clubs first, West should play high clubs as suit preference for spades to warn East to guard hearts — effectively saying, do not unblock. If this seems subtle, look at the flip side: If West had good hearts (Q-J-x-x or Q-10-x-x), he would give suit preference for hearts to encourage the unblock. Against weak opponents Line E is better as East might never consider an unblock before the elimination was complete.

Against weak opponents, it helps to sing: Heavenly shades of night are falling… It’s endplay time.

My scoring awards are based on effectiveness, not elegance, so the problem was costly for those who went for the squeeze. Line D is pretty with the K onside but costs an extra undertrick in the probable layout. Even the give-up play of Line B (leading the 2) achieves a better result. Nonetheless, it’s still better than Line C (also down three) as failure to ruff a second club loses the squeeze chance as well.

Comments for A. Win the A

John Reardon: The choice seems to be between Lines A and D. In Line D, if West has K-x-x-x-(x) and at least five clubs, I will escape for one off by squeezing him in hearts and clubs. In Line A, I offer East a chance to unblock his K from K-x. [The bidding and defense suggest Line A.] Moreover, Line D may go down three (or four if East has the guts to bare his K) for a very poor result.

Zahary Zahariev: There is a squeeze for 12 tricks when West has 4=4=0=5 or 3=5=0=5 shape with the K, but a heart return from East could beat it. So the cards don’t lie thus. The best chance is a singleton K [or an unblock].

Salvador Assael: I could squeeze West with five clubs and K-x-x-x… but East could lead a heart to prevent West from being squeezed. Therefore, I hope East has a stiff K [or unblocks].

Charles Blair: Giving East full credit for (1) breaking up a squeeze if necessary and (2) avoiding a throw-in with K-x.

Rob Stevens: A heart return from East would have broken up a squeeze (or an endplay if West’s hearts were K-Q-9-x and South’s J-10-x). East didn’t do this because he holds the K, and the attempted squeeze will lead to down three (or four if East bares the K). Since East has no idea that your hearts are this strong, he’ll have to unblock his K under the A. He cannot defer this decision because South can ruff just two clubs and the spade before leading another heart. Interesting aside: If South were to start hearts by leading low from hand, how should West play to help partner? I suggest a low heart (or the top honor from anything sufficiently strong) should ask for an unblock, while the nine or 10 should say, “Keep your king.”

Carsten Kofoed: East is an expert and would realize the necessity of a heart shift unless he holds the K. When I start with the A, he will even be the unlucky expert when he unblocks the king. The squeeze is just another temptation.

Tim DeLaney: East didn’t shift to a heart to break up the club-heart squeeze. Why not? The only explanation is that he holds the K. If it’s singleton, I’ll drop it. If it’s doubleton, perhaps he can be induced to unblock it to avoid the (bogus) endplay. Is this “grand” larceny?

Franco Baseggio: A truly expert East would find a heart shift when in with A to break up a potential squeeze against West.

Paulinho Brum: If East is competent (ha-ha) and lacks the K, he would have returned a heart. So the best chance is to catch a singleton king [or tempt an unblock].

Daniel Bertrand: Trusting East. Why no heart shift, giving me squeeze possibilities? …

Hailong Ao: Line D might be right if West has five clubs and four or more hearts with the K, but I would hate to lose 800 when East had a singleton K…

Sivakumar Salem: … When I cash the A, an expert defender will think he may be endplayed; so with K-x, he might unblock the king, allowing me to escape for one down.

Jinzhou Loo: Assuming I am playing against top experts, I will give up on the club-heart squeeze. East had the chance to break it up by returning a heart. …

Poon Hua: Drop the singleton K since East failed to break the squeeze (if there is one); else settle for two down. …

Jos van Kan: [Based on the defense], cashing the A…is the only genuine chance to be down only one. …

Rainer Herrmann: Superficially, squeezing West in hearts and clubs looks best, but why did East not break up the squeeze by returning a heart? Maybe he knows that there is no squeeze; maybe he is staring at the K (possibly singleton); and if once guarded, will he not unblock? After all, West is much more likely to hold the Q than South.

Manuel Paulo: … If there were an impending heart-club squeeze against West (via Line D), East, an assumed expert, would have led a heart…at trick three. So, I’ll cash the A and go down one or two.

Leonardo Feugas: For a squeeze to work against West he must have four or more hearts to the king and five clubs; but in that case an expert East would break the squeeze by leading a heart… [Further], if I play for the squeeze I can be three down. …

Marcus Chiloarnus: Line D appeals but is too risky.

Bruce Neill: You promised East is an expert, so with 7=2=1=3 he should see the possible squeeze.

George Klemic: I expect a good score no matter how bad I play here. Four spades is a lock, and I’m not losing more than one more trick. Even 6 will be cold if hearts are 5-1 [or East has the king]. … Could East have the stiff king? …

Richard Morse: … The prospect of a 12th trick unless East has a stiff K seems remote. Ruffing out the blacks (partially or totally) just seems to help the defense count the hand. … I am going to cash the A, because I couldn’t live with the story of how I took a finesse and lost to the stiff king.

Jack Presser: … Running trumps will result in an extra undertrick. Play for a singleton K [or an unblock].

Comments for E. Ruff out all black cards

Teymur Tahseen: Hope for the unblock on the pseudo endplay.

George W. Bush: I have no quarrel with these East-West opponents, but their regime must be brought to an end. Bids of mass destruction like East’s 6 have no place in the game today. It’s sad that we must sacrifice in 7 but a small price to pay. Of course I ruff black cards — no red cards to ruff — and when my ruffs are all gone, I’ll try that squeezamajig my daddy taught me.

Problem 4

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

Note: West is void in hearts.

Your Play	Award	Votes	Percent
B. Win A, A-K-Q, K	10	140	19
E. Win K, A-K-Q, K	9	151	21
D. Win K, A-K-Q, A, K	7	117	16
F. Win K, A-K-Q, K	6	98	13
A. Win A, A-K-Q, K	5	47	6
C. Win A, A-K-Q, finesse J	2	179	24

With 12 top tricks, the obvious chance for 13 is the club finesse through East. Normally, a finesse through the non-preemptor would be a favorite, but here it’s doubtful* since West’s diamond suit alone does not justify a vulnerable 3 bid; hence, odds are good he has an outside queen or two. Forget the J; it’s mostly a mirage. The contract can be made on a squeeze with proper technique.

*Even more ignominious about the club finesse is that you will be down two whenever it loses. If you follow Line C, West will return a diamond for East to ruff; and if you postpone it with Line E, West can knock out dummy’s side entry before clubs are unblocked.

North’s diamond threat behind West is the key to suggest a squeeze. The presence of threats in two other suits (spades and clubs) plus an abundance of entries makes a squeeze unstoppable in theory, though you may have to guess West’s pattern to succeed in practice. If West has stoppers in both black suits (likely with a heart void), this will be a compound squeeze; you must first force West to abandon one of the black suits, then a double squeeze will follow if you retain the necessary entries. Consider this layout:

Matchpoints	A 9 7 6		Trick	Lead	2nd	3rd	4th
Both vul	A K Q		1. W	Q	4?	3	K
	A 8 4		2. S	4	2	A	2
	A 6 2		3. N	K	3	6	6
Q 10 2		J 8 3	4. N	Q	5	8	7
—		7 5 3 2	5. N	2	3	K	5
Q J 10 9 7 6 2		3	6. S	J	9	6	7
10 9 5		Q 8 7 4 3		continued below…
	K 5 4
	J 10 9 8 6 4
	K 5
7 South	K J

Suppose you win the K, which seems like the natural play to keep an entry with the diamond threat. Next cash A-K-Q and cross to the K (Line F) to draw East’s last trump. This leaves:

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

On the next heart, West pitches a club, and you pitch a spade from dummy. It seems like you should have a double squeeze — West stops diamonds, East stops clubs and both stop spades — but it’s a dead end. If you lead the last heart, dummy will be squeezed first; and if you win the A, you can’t return to your hand without wasting the K, a crucial entry.

Line D suffers a similar fate. The bottom line: You need an extra entry to hand, which means winning the A at Trick 1. You then follow Line B ( A-K-Q, cross to K) then draw the last trump to reach this ending:

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

On the next heart, West pitches a club, and you pitch a spade from dummy. Careful now! You must cross to the A, return to the K, and then lead your last trump: West must pitch a spade to keep the J, pitch the 8 from dummy, and East is squeezed in the black suits. Note how the twin entry in spades was crucial to the squeeze mechanics.

If West instead abandoned spades on the next-to-last trump, the play is less demanding. You could (1) Lead your last trump to pitch another spade, cross to the blank A, return to the K squeezing East of a club stopper, then the K squeezes West in the minors; or (2) Cash the A, K and K, then lead the last trump for a simultaneous double squeeze. In fact Option 2 would work even if you led the last trump before the K or K.

Curiously, Line E ( K, A-K-Q, K) also lets you succeed against any distribution, but you must guess which defender has the Q. This is the ending you will reach:

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

Lead the 10, pitching a spade from dummy, and West’s best defense is to pitch a club.* On the last heart he must pitch another club, as you let go the 8. Then if West has the Q it must drop under the king (giving you three club tricks); or if East has it, you have two entries ( A, A) to finesse the J, cash the K, and enjoy the A. Would you guess it? Probably, so I was generous scoring Line E as 9.

*If West pitches a spade, you have a double squeeze (no need to guess Q): Win the A, A and K, then lead the last heart.

Lines A, D and F are effectively the same, requiring East to have the spade stopper or, alternatively, West to have the Q; but you must decide which to play for. They are ranked by the voting.

Line C is the worst. Besides the early committal, you will go down two whenever the finesse loses (diamond ruff) — and you won’t need any fingers to count those matchpoints.

Comments for B. Win A, A-K-Q, K

John Reardon: A compound squeeze. I need the K as a late entry to operate the squeeze.

Zahary Zahariev: There is a standard [compound] squeeze, and the K is a key entry.

Charles Blair: This is a clash squeeze, not a [typical] compound squeeze. After cashing all the hearts, the J may have forced West to unguard spades; win the A, then the K squeezes East, and the K squeezes West.

Rob Stevens: A potential compound squeeze but ambiguous in the ending. I should probably play West for four or five clubs (not 3=0=7=3) since his preempt is pretty weak.

Carsten Kofoed: The odds for a successful club finesse are [8-to-6], but the possibility of a “tuxedo squeeze” is too tempting. This plan also preserves my [options] until I have seen the opponents’ discards.

I missed the lesson on “tuxedo squeezes”… But I know of Tennessee Tuxedo. Does that count?

Franco Baseggio: Compound squeeze. I can’t have three threats in dummy, so the spade threat must be in South and the K must be preserved. In the ending, if West unguards clubs, I will need to win the A before the final squeeze card, so the K must be saved as a late entry.

Paulinho Brum: Oh, theory. This line ensures the contract on several different squeezes (I think) if I can read the distribution. Not so easy this time. Oh well.

Daniel Bertrand: Compound squeeze. Next cash two hearts to come down to: A-9 8-4 A-6 opposite K-5-4 9 K J. West can only keep four black cards. If West keeps three spades, cash A, K and 9 to force him to pitch a spade; then pitch the 8, and East is squeezed in the blacks. If West keeps two clubs, cash A, K, K and 9 to force West to pitch a club; then pitch the 8 and East is squeezed in the blacks.

Hailong Ao: On the fifth heart (dummy pitches two spades) West will have to give up one black suit. Then I cash the top honor(s) in that suit and get back with the K to play the last trump.

Sivakumar Salem: I need to prepare for a compound squeeze, so I preserve the entry to hand and keep spades open.

Pekka Viitasalo: Good news: This is 100 percent on a compound squeeze. Bad news: I have to guess the suit West still protects when he discards a club on the fifth trump. Does it come from 3=0=7=3 or 2=0=7=4?

Neil Morgenstern: … I don’t want to rely on the club finesse. In fact, I could replace the J with a small club and still make it. I must retain a top spade in both hands, so that only leaves Lines B and F. I need the K entry later to lead [the last] trump, so I’d better play the ace now.

D.C. Lin: A compound squeeze. In the six-card ending with A-x x-x A-x opposite K-x-x 9 K J, West may do his best to unguard clubs. I would then have to win the A, come back to the K and play the 9 to inflict a double squeeze. The  K is a critical late entry.

Leif-Erik Stabell: Even if West has stoppers in both black suits (3=0=7=3), five rounds of hearts will be too much. Best defense is to give up clubs; but a club to the ace, diamond to the king, and the last trump will finish them off (dummy having discarded two spades).

Gabriel Nita-Saguna: This is the only line that gives me the necessary communication to convert the compound squeeze into a certain type of double squeeze… depending on the black suit West chooses to unguard when I cash the fifth heart. However, similarly to problem two, I have to guess West’s initial distribution. But this is better than other lines, [which allow] West to foil my squeeze by pure technical means.

Toby Kenney: Draw the last trump then play another trump. West is squeezed and forced to unguard one of the black suits. Cash all top winners in that suit, then cross to the K and cash the last trump for a double squeeze.

Rainer Herrmann: A classic compound squeeze, where entries to the South hand have to be preserved. Nevertheless, it is doubtful whether the squeeze of the restricted variety is much better than the finesse, which is at least 57 percent to succeed. But who could resist temptation? I will see only one black discard from West, and should he hold a black four-card side suit, I am likely to go wrong if he discards from that suit.

Grant Peacock: Then J-10, and now I have to read the shape correctly. But an educated guess is always better than a finesse, right?

Manuel Paulo: Line B develops a compound squeeze or a [double] squeeze played as a compound; other lines can’t win or need to risk the club finesse.

Irina Levitina: Compound squeeze. After five trumps, if West keeps three spades and one club: A, K, trump. If he keeps two spades and two clubs: A-K, K, trump.

Perry Groot: It seems you can make the hand on a compound squeeze, and this line ensures all necessary entries.

Ed Davis: It seems as if the J is an illusion (I guess I should say a grand illusion). I make the contract by reading West’s discards correctly. [Play described].

Sergey Kustarov: A restricted compound squeeze. After five rounds of hearts (pitching two spades), I need to guess which black suit West stops. Then the K entry [provides the necessary communication].

Bill Powell: West will have to unguard a black suit on the fifth heart. East’s pitch may help decide which it was.

Nigel Guthrie: Clyde would “Love” this 3-2 mutate compound squeeze. Discard a spade on the penultimate heart. [Play described].

Gareth Birdsall: If I read the position correctly, I can always make. Prettiest is the compound squeeze if West was 3=0=7=3, which requires me to keep the K as a late entry in case West discards clubs.

N. Scott Cardell: [Play described]. Double-dummy, where I know which black suit West can’t stop, this is 100 percent; but single-dummy against inscrutable experts, just running trumps and discarding spades is [optimal] because it always works when West has two or fewer spades or the Q — the combined chance being greater than the simple club finesse. …

Brian Lee: Hope I can guess West’s pattern. Cash two more trumps, then cash the top card(s) in whichever black suit West unguards. The  K and last trump complete the double squeeze.

Leonardo Feugas: Compound squeeze. On the fifth heart West is squeezed, and I need the K in hand if he unguards clubs. Then win the A, K and last heart for a double squeeze. …

Daniel Korbel: This is a 100-percent position [if I guess the distribution]. I will run all but one trump, catching West in a compound squeeze…

Anthony Golding: West is more likely to be 2=0=7=4 than 3=0=7=3, so I’ll probably end up playing for the basic double squeeze; but this keeps things flexible.

Nikolay Demirev: It’s a pity if the A gets ruffed at matchpoints and a spade is returned, but this line prepares the matrix for a compound squeeze: West in three suits; East in two. …

Bruce Neill: Compound squeeze, as long as West has six or more diamonds, but I may need to guess which black suit West guards. For example, if he throws four diamonds and a club on the first five hearts, was he 2=0=7=4 or 3=0=7=3? …

Rodolfo Cerreto: In this ending: A-9 8-4 A-6 opposite K-5-4 9 K J, West can’t guard spades, diamonds and clubs. If he keeps spades: A, K, last trump. If he keeps clubs: A, K, K, last trump.

Bill Daly: Assuming West’s preempt is legitimate, I have a guaranteed compound (or double) squeeze… but I’ll have to guess West’s distribution — but that’s more likely than the club finesse. [Play described].

Patrick Bocken: This only loses if West is 3-3 in the black suits without the Q. If West has the Q, he will be obliged to throw it away when the last trump is played; if he chooses a spade instead, the K [entry] will allow me to unblock [spades] and squeeze East in the black suits.

George Klemic: … The crucial decision at trick one boils down to keeping the K entry in hand. … Darn it. Missed 7 NT again!

Jeff Goldsmith: Nice compound squeeze. Be careful not to cash the K too early; it is needed as a hand reentry if West unguards clubs the first time he is squeezed.

Joerg Wensch: A double squeeze develops when West abandons either spades or clubs at trick seven. If he keeps spades, I must cash the A and return to hand with the K…

Anil Upadhyay: As only West can protect the third diamond, there is basic threat over him, and he will be squeezed on the next-to-last winner, producing a double squeeze. …

Robert Lipton: West should have a 2=0=7=4 hand, [which provides] a double squeeze with clubs as the pivot suit. Might as well go down in a big way.

Ciaran Coyne: Playing to reach A-9 8-4 A-6 opposite K-5-4 9 K J. I may need to read the distribution, but I cannot be stopped from making. If West comes down to 3=0=2=1, play club, diamond, trump… If 2=0=2=2, play A, K, trump…

Daniela Tonti: I can suppose West has 3=0=7=3, so I need the K as a supplementary entry in hand to preserve the K for the double squeeze workings.

Marvin French: On the next-to-last heart West must unguard a black suit. Of course I guess which one, cash its high card(s), then lead the last heart for a double squeeze. I save the K to return to hand if the A must be cashed, since both high spades are needed for that double squeeze.

Leonard Helfgott: Since West is likely to be 3=0=7=3 or 2=0=7=4 (rarely 4=0=7=2 or only six diamonds), the club finesse is only around 60 percent. If I play West for 3=0=7=3 or believe I can read the distribution from discards, I need to keep the K in hand…to preserve the compound squeeze on West. [Play described].

Pieter Geerkens: Retain South’s K has “an additional entry in one of North’s threat suits.”

Gerald Cohen: Compound squeeze, but I had better watch the tricks carefully. I run five hearts and throw two spades from dummy. … If West abandons spades, then A, K, K and the last heart. … If West abandons clubs, then A, K and the last heart.

Comments for E. Win K, A-K-Q, K

Dale Freeman: The club finesse is too final. I can go for the double squeeze if only East guards spades, or the simple squeeze if only West guards spades. The key situation is when West has sH-x-x Q-x-x; maybe he will pitch a spade. I’ll play for the double squeeze unless it appears otherwise. …

J. Michael Andresen: If I can tell enough of the distribution to play for a squeeze, I’ll do that. Otherwise, I’ll try the club finesse.

Tim McKay: Allows the A to be played later, and if it looks like there’s no squeeze, I can still take the club finesse and get back to dummy.

Problem 5

Matchpoints	A J 9			West	North	East	South
N-S vul	A 10			LHO	Partner	RHO	You
	A K Q 5				2	Pass	2 NT
	K Q 9 2			Pass	4 NT	Pass	7 NT
				Pass	Pass	Pass
Lead: 4
	K 7
	K Q J 9
	4 3 2
7 NT South	A 10 4 3

Note: If you play the 9 or J, East covers cheaply.

Your Play	Award	Votes	Percent
B. Win A, A-K-Q, run hearts	10	108	15
F. Win K, A-K-Q, A, run hearts	7	269	37
E. Win K, A-K-Q, run hearts	6	252	34
C. Win K, A, run hearts	4	12	2
D. Win K, run hearts	3	71	10
A. Win A, run hearts	1	20	3

You have certainly reached an excellent contract with many chances: clubs 3-2 (or 5-0, stiff jack or guessing J-x-x-x); diamonds 3-3; West with the Q or 10 (help from the lead); plus various squeeze possibilities. Your first decision comes at Trick 1; West is more likely to lead from a 10 than a queen, so playing the 9 is better than the J. You are told that this doesn’t help, else it wouldn’t be a problem.

A common strategy in cases like this is to find out which opponent stops one suit (diamonds), then play your second suit (clubs) to either squeeze that opponent or finesse his partner. If West stops diamonds, this works fine: Cash winners to leave 5 K-Q-9 opp. A-10-4-3; then if clubs are 4-1, either West will have been squeezed or East will be finessed. Unfortunately, this will not work if East stops diamonds, because testing clubs for a finesse against West will ruin your entries for the squeeze. Consider this unfriendly layout:

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

Suppose you follow Line F (above) to reach:

NT win 6	J		Trick	Lead	2nd	3rd	4th
	—		8. S	Q	6	5	10
	5		9. S	J	8	J	Q
	K Q 9 2		10. S	3	5	K	6
8 6 5		Q		Declarer can succeed w/guess
8 6		—
—		10
5		J 8 7 6
	—
	Q J
	—
South leads	A 10 4 3

On the Q you can pitch a club from dummy and succeed easily, but you’d fail if West held J-x-x-x. Suppose you pitch the diamond, as does East. The same problem arises on the last heart, so suppose you pitch the spade as East copies again. Next you lead a club to the king and both follow. Who’s got the button?

The truth is you can’t tell. The only clue is that West led the 4 and played the 3, but this could be a doubleton. Note that East’s discard of the Q could easily be a falsecard holding all the remaining spades. If you knew just one card in either hand, you’d have a lock since that opponent could not stop clubs.

Therein lies the key; you must preserve the K as your last non-club winner, so it can be cashed while East still has a diamond. Only Line B allows this: Win the A, test diamonds and cash four hearts (pitching spades) to reach this ending:

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

Next cash the K and pitch the diamond. East will also pitch his diamond, but now you know East has all clubs left. If East followed to the K, he would still be known to hold a diamond, so only West could have four clubs. In short, you have a guarantee against any distribution. Dummy’s J-9 were immaterial, or red herrings; you’d have the same lock to make 7 NT if they were low spades.

It would be equally good (100 percent) to cash one top ( K or Q) early. (I didn’t offer this option to simplify description of the choices.) In practice it would definitely be better, because a blank J or show-out would end the play immediately. Time is money!*

*Or at least it used to be. Mabel often kids me about the time I “waste” on my web site, “Why don’t you write a book or do something profitable?” Hah! She doesn’t realize the big bucks I pull in. RPbridge is just a front for smuggling rare birds out of Cuba.

One wise guy suggested another “foolproof” line: Play the J at trick one; queen, king; A-K-Q (assume East has the stopper, else no problem); K; A (assume East has the stopper, else finesse clubs); Q. Now run hearts, and East will be triple squeezed on the third round, since I told you East has the 10. Cage please!

Lines E and F are good, combining a variety of chances, and indeed drew the great majority of votes. Line F gets the edge for cashing the extra winner (might drop the Q) since it makes little sense to reserve a finesse that’s almost sure to lose. While either line will work over 95 percent of the time, I couldn’t justify a higher award than 7 for missing the sure-trick play.

Lines A, C and D are poor because you must discard twice from dummy before knowing how diamonds split. Line C seems the best of the group for the same reason that Line F outranks Line E (cashing the extra winner). Line A is surely the worst as it abandons the chance that West has led from the 10 with no benefit in return.

Comments for B. Win A, A-K-Q, run hearts

John Reardon: Easy if West has three or more diamonds; I either have 13 top tricks or West must keep his diamond and clubs will come in. Otherwise, I will obtain a sufficient count on East’s hand after throwing J-9 on the hearts then cashing the K (throwing the now-useless diamond) to know how to play clubs. …

Zahary Zahariev: Run hearts and pitch spades. If West stops diamonds, cash the K (pitch club), then K-Q. If East stops diamonds, cash the K and pitch the diamond; now East’s hand must be counted. Either he keeps his diamond and can’t hold four clubs, or he pitches his diamond and must hold all clubs…

Charles Blair: If East has four diamonds and three hearts, he will have to discard a spade on the last heart, since dummy keeps the 5. Then the K, discarding the diamond, will tell me whether East has [or cannot have] four clubs. …

Rob Stevens: … The opponents are forced to reveal which, if either, can hold four clubs.

Carsten Kofoed: I discard two spades on the hearts then play the K (pitching a diamond). I will then know if East or West has [or cannot have] four clubs.

Tim DeLaney: This is 100 percent. The K is cashed at trick nine, and I will know at that point who can hold four clubs.

Franco Baseggio: This is a sure-trick line. Pitch spades on the hearts; next play the K pitching the 5 (unless it’s good). The only way no one holds a diamond at this point is if East pitches it on the K, in which case I have a full count.

Pekka Viitasalo: … I will run hearts pitching spades from dummy… If the 5 is high, I claim; if not, I cash the K and discard the 5. There are some variations on wild major-suit distributions, but the general idea is that I will know now for sure who may have four clubs.

Walter Lee: The person who guards diamonds is forced to reveal whether he can have four clubs.

Neil Morgenstern: For now, it’s a count of the hand I’m looking for, not a squeeze. I throw dummy’s spades on the hearts and then lead the K…

D.C. Lin: Run hearts, pitching J-9 from dummy. When West has four diamonds, sooner or later he cannot keep four clubs, so either a finesse through East or a squeeze against West will succeed. When East has four diamonds, I can read his shape and know for sure whether he has four clubs or not.

Leif-Erik Stabell: If West has diamonds stopped, no problem. If East has diamonds stopped, he will be void in spades after I have finished playing hearts if he also holds four clubs. The  K (with a diamond discard in dummy) will then tell me how to play clubs.

Dale Freeman: Find out who has the diamond stopper, run hearts pitching the J-9, then cash the K. If there is J-x-x-x anywhere, it should be evident.

Gabriel Nita-Saguna: This problem has the most unexpected solution of this set because the Q is not a relevant card as one might have thought. If West started with four diamonds and four clubs as well, he will be squeezed… or a simple club finesse against East will bring me the 13th trick. If East had four diamonds initially, I will cash all the hearts discarding the two spades… Then, when I cash the K, discarding the diamond, East will have to reveal if he can have four clubs or not…

Deniz Unlu: On the last two hearts I discard dummy’s two spades, then the K will reveal who might hold four clubs.

Neelotpal Sahai: On the run of hearts, discard two spades from dummy (crucial to keep length in both diamonds and clubs). Now, when the K is played… [Logic explained].

Grant Peacock: Neat play. I guess if dummy’s spades were A-3-2, it would be a little easier to find. You need more booby answers. If  A, K, A had been a choice, I might not have looked any further, even though I’ve seen this play in Michael Rosenberg’s book in Favorite Hand #4: A-Q-9-2 A-J-9-2 A-10-7-3 2 in dummy facing K-10-7-6 K-10 K-Q-5 A-K-Q-J (7 NT on a club lead).

Irina Levitina: Pitching two spades, then K pitching a diamond. If the opponent with the fourth diamond follows, then he cannot have four clubs; if he pitches the diamond, he must have four clubs.

Ed Davis: Pitch spades on the hearts… then cash the K pitching dummy’s last diamond, ending with four clubs in each hand. The defender with four diamonds will either show out on the K (revealing his exact distribution) or follow, thus [proving] he cannot hold four clubs…

Sergey Kustarov: A 100-percent line [to reveal] the count [whoever] holds diamonds. I pitch two spades on hearts, then the K pitching the diamond…

Nigel Guthrie: Classic sure-trick count squeeze. Run the hearts throwing spades then, assuming the diamond is not good, cash the K and throw the diamond, willy-nilly. If an opponent shows out on the K, I have a complete count; otherwise, the opponent with the last diamond has room for at most three clubs.

N. Scott Cardell: … There are a host of squeeze possibilities and finesses… however, only Line B is 100 percent… [Play described].

Brian Lee: This is 100 percent, assuming I can count to 13. Hmm. Make that 90 percent.

Leonardo Feugas: If West has four diamonds, he will be squeezed if he has four clubs… If East has four diamonds, I have a complete count when I play hearts and discard spades from dummy… then the K discarding a diamond…

Daniel Korbel: If East has the diamond guard, four rounds of hearts (pitching spades from dummy) forces him to pitch spades, at which point the [ K will reveal] the defenders’ shapes. …

Kyoko Ohno: Then cash the K and pitch dummy’s diamond [if not good]. Whether the defender with the good diamond follows or discards, [I will know how to play clubs].

Douglas Dunn: Throw spades on the hearts and the last diamond on the K. This will identify which defender can possibly hold four clubs, then play clubs accordingly.

Problem 6

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

You next win the Q (both follow) and lead the J (East plays 10).

Your Next Play	Award	Votes	Percent
F. Win J, K	10	197	27
E. Win J, ruff diamond	7	217	30
D. Win J, K, ruff diamond	6	102	14
B. Win J, A, K, K	5	139	19
C. Win J, A, K	4	38	5
A. Overtake with K	3	39	5

Despite only 12 sure tricks, 7 is a fine contract with three obvious chances: (1) a 3-3 club break, (2) the J falling singleton or doubleton, or (3) a club-heart squeeze if the player with longer clubs also holds the K. It takes proper technique, however, to combine them all.

The popular choice was Line E (win J, ruff a diamond) no doubt because it involves no risk of an enemy ruff. (The diamond is ruffed high if trumps are 3-2, else low with safety if West is out of trumps.) Let’s see if it works:

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

After ruffing the diamond, you can safely lead all your trumps (pitching hearts from dummy); then lead a club to the queen and cash the K to reach this ending:

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

You now can succeed, of course, by winning the K to drop the jack; then cash the 10, and dummy is good. But what if the remaining cards were:

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

To succeed here, without taking the club finesse (no fair peeking), you must cash the A to drop the king. Note that East was squeezed down to a blank K to keep his club stopper. In other words, Line E does not cater to all the original chances.

To keep all your chances alive, you must leave a low diamond in dummy as a means to return to hand, and you must not cash the A prematurely. This eliminates Lines B, C and D as well. The proper technique is to cross to the K (Line F) and lead all but one trump to reach this ending:

win 6	—		Trick	Lead	2nd	3rd	4th
	A		8. S	4!	9	Q	7
	K 3		9. N	K	Q	4	9
	A Q 6		10. N	A	8	6	3
—		—	11. N	3!	?
J 10 3		K 8		East is squeezed (no guess)
10 9		Q
9		J 8 7
	6
	Q 6 4
	—
South leads	10 4

Next cross to the Q to see if the jack drops. When it doesn’t, cash the K and A, then ruff the diamond to squeeze East in the process.

Lines B through E are pretty close, as they each give up one of the original chances. The edge goes to Line E because it involves no risk of an enemy ruff. Line D is next with only negligible risk. Lines B and C involve further risks in cashing winners with a trump out, plus they’re committal; i.e., you no longer can cater to J-x with dummy’s heart entry gone.

What about Line A? This also caters to all the original chances, but it incurs an additional risk. Don’t trust that East dude! The  10 could be a falsecard from 10-9-7-x just to lure you into overtaking. At least that’s far more likely than a club void, the only risk in Line F. There’s no doubt that Line F is best, but I’m left with a scoring problem: Is Line A better than Lines B through E? It is in theory if followed up perfectly; but can I really assume a perfect follow-up from someone who chose this play in trumps? I think not, so it gets the basement.

Comments for F. Win J, K

John Reardon: Keep the A as an entry to North in case the J is doubleton, and keep the diamond ruff as an entry to South in case a squeeze is needed.

Zahary Zahariev: Then draw trumps (pitch hearts), followed by a club to the ace. If the J falls, I have the A entry. Otherwise, cash the A, K and ruff a diamond, eventually squeezing an opponent with the K and four clubs.

Salvador Assael: To allow testing for J doubleton and [to retain squeeze chances].

Charles Blair: If I knew West had three spades and six diamonds, I would want to keep the option of finessing the 10; however, with 9-x-x West might have led a trump instead of giving me distributional information. Maybe he didn’t lead a trump because he has a singleton. …

Rob Stevens: I need to keep open the chances of a doubleton J and entries to play the A (Vienna coup) in preparation for a heart-club squeeze against either opponent.

Carsten Kofoed: [Should I pay off] to 6-0 clubs or to East deceiving me?

Tim DeLaney: This retains all the options: clubs 3-3, J singleton or doubleton, K singleton, or a club-heart squeeze. …

Franco Baseggio: Draw trumps, then fish for J-x; then A, K and a diamond ruff, hoping for 3-3 clubs or the K and four clubs together. I need to preserve the A in case the J falls, and I need to preserve the small diamond for a late reentry if the J doesn’t fall.

Paulinho Brum: This seems best for keeping the chance of a doubleton J. After drawing trumps, I can play a club, cash the A and K, then come back to hand with a diamond ruff for the heart-club squeeze.

Daniel Bertrand: I cannot…cash the A to retain the extra chance of a defender having a doubleton J. Overtaking with the K is tempting, but spades are more likely to be 4-1 than clubs 6-0. I will play three more high trumps, than cash the A… If no J appears, unblock the A (Vienna coup), cash the K and ruff a diamond…

Hailong Ao: This covers spades 4-1, J doubleton, clubs 3-3, or 4+ clubs with the K. Ruffing a diamond early may result in entry problems.

Sivakumar Salem: …This takes the small precaution that the J may fall in two rounds… Else I can still fall back on the automatic squeeze by cashing the A (and K)…

David Johnson: This guards against a tricky East with four spades and allows for J-x, while preserving the Vienna coup.

Pekka Viitasalo: I make if the J is doubleton or singleton; K singleton; clubs 3-3; or the K and 4+ clubs in the same hand. I draw trumps pitching hearts and play a club to the ace. If the J does not drop, I cash the K, A and ruff a diamond to complete the Vienna-coup squeeze.

Neil Morgenstern: Firstly, overtaking is stupid as East may be falsecarding from a four-card holding. I want to combine my chances the best way possible. The club finesse can’t really enter the equation, but I should include the chances of the J falling doubleton…and J-x-x-x in the same hand as the K, as well as a 3-3 club break. [Play described]. I couldn’t afford to ruff a diamond earlier as I needed the entry to hand… nor could I afford to cash the A as I needed the entry to dummy if the J fell doubleton.

D.C. Lin: To cater for the possibility of J-x, I need to keep the 3 as a late entry.

Leif-Erik Stabell: This preserves the main squeeze chance (four clubs with the K) and also maintains communication to take care of J-x.

Poon Hua: This caters to J-x; else a simple squeeze in hearts and clubs or a 3-3 club break.

Gabriel Nita-Saguna: … This allows me to test all the realistic chances: (1) J doubleton, (2) simple squeeze in clubs and hearts against either opponent, which involves a Vienna coup, and (3) clubs splitting 3-3. …

Toby Kenney: Then A, K and A; and if the J hasn’t dropped, cash K, A, ruff a diamond and lead the last trump for a heart-club squeeze.

Neelotpal Sahai: Even though the safest return to hand is a diamond ruff, it is important to come via the K to preserve an entry should the J fall doubleton ( J-x is much more likely than a 6-0 club break). …

Grant Peacock: Seems like this combines the most chances; then A-K-8 pitching hearts, A, K, A, and a diamond ruff… So along the way I tried for J on the short side, 3-3 clubs or a club-heart squeeze — or maybe some bizarre defensive accident.

Perry Groot: This wins whenever clubs are 3-3, the K is together with 4+ clubs, or J-x. Line A loses with trumps 4-1, and other lines can’t cope with [all chances].

Ed Davis: My best chance is a club-heart squeeze against either opponent if the J does not fall doubleton or singleton. [Play described]. This line makes if the J is third or less (54 percent) or if the K is with the long clubs… about 74 percent total.

Bill Powell: Making when the J is accompanied by the K or less than three other clubs.

Jean-Christophe Clement: This will allow for a heart-club squeeze, with the extra chance to catch the J doubleton. The only danger is a 6-0 club break.

Gareth Birdsall: The problem is I would like to play the A as a Vienna coup, but I must keep it as an entry in case someone holds J-x. Hence, I must keep the third diamond in dummy as a late entry back to hand; so use the K now.

N. Scott Cardell: I must combine my chances: clubs 3-3, J singleton or doubleton, or a club-heart squeeze. There is no good reason to risk a trump loser should East have falsecarded from 10-9-x-x, so I [reject Line A]. [Play described].

Brian Lee: This wins if clubs are 3-3, J doubleton, or long clubs with the K.

Leonardo Feugas: Best chance. [Play described]. This wins when the J falls, clubs are 3-3, or squeezing an opponent in hearts and clubs. I need the Vienna coup if East has the K and clubs, after which I reenter my hand with a diamond ruff…

Daniel Korbel: I want to make this whenever the J falls doubleton or tripleton, or I can squeeze someone in hearts and clubs, so I better keep that 3 for communication.

Anthony Golding: Overtaking should score minus 10. I want to test for J-x, then fall back on clubs 3-3 or a club-heart squeeze after cashing the A. Ruffing a diamond to get back to hand to draw trumps looks marginally safer…but takes out an entry to hand prematurely. [Play described]. I can’t cash the A early, as I may need that entry if the J drops.

Nikolay Demirev: [Play described]. This allows me to combine all my chances: J, J-x or J-x-x; K stiff or together with 4+ clubs… not so bad a grand. :)

Alex Dov: Preserves chance of J doubleton. Then win A-K and A… if no J falls, A (Vienna coup), K and diamond ruff.

Frances Hinden: This makes on any of clubs 3-3, J-x, or J-x-x-x with the K. … Line A is silly if trumps are 4-1.

Kyoko Ohno: Then draw trumps, pitching two hearts from dummy, then win the A (OK if J drops); else, K, A (Vienna coup), diamond ruff, and lead the last spade.

Bill Daly: There are three chances: 3-3 clubs, singleton or doubleton J, or a heart-club squeeze. I have a slight entry problem, which is why I should use K entry to draw trumps. [Play described]. Line A is unnecessarily risky, since a 4-1 spade break is more likely than 6-0 clubs. …

Thijs Veugen: I succeed when the J is doubleton or singleton, clubs are 3-3, or when the K is with the long clubs.

Douglas Dunn: Pull trumps, then play to the A hoping for J-x; else rely on 3-3 clubs or a squeeze (after taking the A).

Patrick Bocken: Best line by far. Clubs 3-3, J doubleton, or J-x-x-x with the K makes this a reasonable grand…

Joerg Wensch: Combines three chances: J doubleton, clubs 3-3, or a club-heart squeeze… Next draw trumps, win the A (test for J-x), A, K, ruff a diamond and finish trumps.

Anil Upadhyay: After drawing trumps, win the A to see if the jack drops. If not, win the A (Vienna coup), K and ruff a diamond for reentry…

Dale Rudrum: No point in giving away my distribution, or in taking unnecessary chances with the spades. I give up the chance of a club finesse, as I cannot think of a situation where I would take it…

Marvin French: Then all spades but one, throwing hearts from dummy, and Q. No J? Then A (Vienna coup), K and a diamond ruff…squeezes whoever holds two clubs and the K.

Bernard Danloy: I must care about a 4-1 trump break and combine my chances in clubs: J doubleton or third, or a squeeze in hearts and clubs after a Vienna coup.

Leonard Helfgott: The Vienna coup succeeds whenever the K is with three or more clubs, and this is clearly better than saving the A entry [to cater to] J-x. However, Line F affords both options. [Play described]

Andrew de Sosa: Playing for a possible J doubleton in addition to the heart-club squeeze against either opponent… I need to keep the A as an entry to the fourth club if the J is doubleton. Otherwise, I need to keep the small diamond as an entry back to hand after unblocking the A…

Pieter Geerkens: This picks up any of J-x in either hand, clubs 3-3, or club length in the same hand as the K, without risking a 4-1 trump split (provided there is no club void in the hand with three trumps). It is true that restricted choice ( 10 is more likely to be forced than a choice from 10-9-x-x) knocks down the odds of East having four trumps; but why risk it? The odds of a club void are lower still.

Frans Buijsen: … This saves communication to allow playing all chances: clubs 3-3, J doubleton or the heart-club squeeze.

Venkatesh Ramaratnam: Overtaking the J is an unnecessary risk. If clubs don’t break, I need to cater to both a club-heart squeeze and J doubleton. [Play described].

Gerald Cohen: … A doubleton J is more likely than a club void… If the K wins, draw trumps throwing two hearts, then a club to the queen… If the J doesn’t drop, cash A, K and ruff a diamond; then lead the last spade…

“If the K wins?” Don’t worry! If it doesn’t, the paramedics will arrive with a stretcher.

John Haslegrave: Basic plan is that clubs split 3-3 or the long clubs are with the K. Just in case the J drops doubleton, I’ll deal with the red suits later.

Final Notes

Thanks to all who responded, and especially those who offered kind remarks about my web site.

Comments are selected from those above average (top 326 in this edition) and on each problem only those supporting the correct solution or close seconds. 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 flawed. On this basis, I included over 70 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, aided by the comments received, has determined the best solutions in theory, but oversights are possible. Feedback is always welcome.

Well, it’s been a grand month! For the grand finale, I’ll leave you with some grandiloquent remarks:

Michael Jinks: What? Doesn’t anybody lead trumps against grand slams these days?

Or Shoham: Where can I hire your dealer? I haven’t seen a hand like these in years, much less six of them.

Ian Coombs: Sorry for wasting everyone’s time. I must sleep now.

Anthony Golding: Thou swell, thou witty, thou grand!

Bill Jacobs: Since I specialize in endplays, this quiz is most unfair. I hope the next quiz features six 1 contracts.

Don’t give me ideas.

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© 2003 Richard Pavlicek