Analyses 8X96  Main Challenge

The Twelfth of Never

Scores  by Richard Pavlicek

Never is a long, long time!

These six play problems were published on the Internet in August 2006 as a contest open to all bridge players. As declarer on each problem, all you had to do was choose your line of play from the choices offered.

Problem 1

2

3

4

5

6

Final Notes

Congratulations! The 21 perfect scores were sensational but created a problem with my prize distribution. Tinkerbell wouldn’t accept more than 12 on the trip to Never Never Land, and the Neverland Ranch is now closed (what a shame). This left nine persons ‘Never-less’ so I have to apologize. Nevertheless, I e-mailed Michael J., begging him to reopen the ranch; I even promised to name a cue-bid after him. Alas, came a mysterious reply, “We can fly, you know. We just don’t know how to think the right thoughts to levitate ourselves off the ground.”

I don’t know if that’s encouraging or not, but the flying part brought on a sudden craving for Peter Pan peanut butter and a Wendy’s hamburger — Fly me to the moon, and let me play among the stars. Take me away, Tink’, before I remember that I have to write up this contest.

Anthony Golding Wins!

Participation was up slightly from the last contest but only the sixth highest — somewhat disappointing with declarer play and slam contracts being big favorites. On the bright side, 21 perfect scores tied a record (December 2005), and the average score (43.51) is the best ever (496 persons scored 44 or higher to be listed). Further, four of the problems were aced by the consensus, which I think is a record; so the overall bridge standard seems to be improving — or maybe I’m getting easy.

In the overall rankings, Jonathan Mestel (England) held onto the top spot (60 never hurts) and upped his average to 59.25. Next in line are Rainer Herrmann (Germany), Leif-Erik Stabell (Zimbabwe) and Weidong Yang (China) with 58.75, followed by John Reardon (England) and Rob Stevens (California) with 58.50.

Overall stats from September 2000 through August 2006: 36 play contests; 26,626 entries; 5351 persons; 160 locations; 39.66 average score. Including 36 bidding polls: 72 events; 63,945 entries; 7187 persons; 166 locations; 43.41 average score. Thanks to all for the enjoyable run!

Several people mentioned that my title was also the title (in part) of the book Until the Twelfth of Never about the infamous murderess Betty Broderick. This was news to me, though I did see the TV movies A Woman Scorned and Her Final Fury. Sorry, Betty, but my theme came from the song. Don’t shoot! And if you ever get out of the slammer, remember that I live in Alaska.

Bidding is standard (except as noted) and you 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.

Problem 1

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

You win the A, cash the A (pitching 6) and ruff a spade as both follow low.

Your Next Play	Award	Votes	Percent
D. Ruff diamond, run Q	10	395	39
B. Ruff diamond, ruff spade, lead 5	8	207	21
A. Ruff diamond, ruff spade, win A	6	101	10
E. Win the A	5	127	13
C. Ruff diamond, run Q	4	85	8
F. Lead the 4	1	86	9

Despite somewhat random bidding, you landed in the par contract; 6 has excellent chances and would have been laydown with a heart lead, probably just as likely as the unhelpful diamond. Leading two rounds of spades (ace and a ruff) was basic technique to pursue the chance of establishing the suit but brought no providence ( K-J still outstanding). Now you face the moment of truth.

It is tempting to ruff another spade, either with or without leading a trump first. If you ruff a diamond then a spade, you have a lock if the K ruffs out simply by conceding a club (Line B) to ensure an entry to dummy.* Even if the K fails to fall, Line B is better than Line A, as you will always have a chance for the heart finesse, and West will be endplayed if he wins a blank K. Consider the following deal.

*Cashing the A would yield an overtrick if clubs are 1-1 but otherwise is fatal; whoever wins the K will have an easy exit in diamonds, and you’ll be forced to lose a heart, even with the K onside.

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

While Line B offers good chances, you can do even better with a simple trump finesse (Line D). In fact, this produces a lock if East follows in clubs; either the finesse will win, or it will lose to a blank king and leave West endplayed.* If East shows out, you will still run the queen to provide an entry for a last-resort heart finesse. Thus, the only time you will fail is if West has K-x and the K, making Line D over 90 percent by my calculation. In reality, it’s probably even better, since West might have acted on some hands with K-Q, K and K-x.

*With only two spades outstanding (K-J), West cannot lead a spade without establishing dummy’s suit; a heart return gives you a free finesse; and a diamond, a ruff-sluff.

Second place goes to Line B, which works if spades are 3-3*; or failing that, if the K is onside; or failing that, if West has a blank K — a total of about 83 percent.

*Assuming only the Q in West is known (ignoring dubious information from East’s 8 signal), the chance of K-x-x opposite J-x-x (either way) is 21.32 percent; and K-J-x-x opposite x-x (either way) is 19.38. All other spade holdings are impossible, so percentages must be reapportioned to a 100-percent total, which means spades will be 3-3 now 52.38 percent of the time.

Third place goes to cashing the A after ruffing a spade (Line A), which works if spades are 3-3*; or failing that, if clubs are 1-1 — a total of about 77 percent. Lines C and E are almost as good, always succeeding with clubs 1-1, but trading a favorable spade split for a heart finesse. Between them, the voting breaks the tie for fourth place.

*While unclarified in the problem, I assumed that if the K ruffs out, Line A would be abandoned for the 100-percent play of leading a low club. Hence, the A would be cashed only if dummy’s spades were not good.

Worst by far is to lead a low club immediately (Line F), as it is sure to lose a club, with no endplay possibility; then you’re forced to choose between the heart finesse and establishing spades, i.e., it’s the only play that doesn’t combine any chances.

Comments for D. Ruff diamond, run Q

Anthony Golding: If spades break 4-2, I need three more entries, which I don’t have. This way, if East follows to the Q, I let it run, winning or endplaying West. If East shows out, I let it run anyway, and use the last club as an entry for the heart finesse.

Toby Kenney: Routine elimination. This works whenever East follows; and if East shows out, I still have the heart finesse. Ruffing another spade works fine if I get overruffed but is problematic otherwise.

Jerry Fink: This automatically wins if clubs are 1-1 (52 percent), or if East holds K-2 (24 percent); and if West has K-2, there is still hope for a successful heart finesse (better than half of the remaining 24 percent, as West was silent with his minor-suit honors) — close to 90 percent. Nearest alternative is attempting to set up spades by another ruff (at this juncture spades rate to break 3-3 about 53 percent of the time); or if that fizzles, to catch West with the singleton K;…or as a last gasp, the heart finesse…for a grand total of 83 percent — better than most small slams I bid.

Grant Peacock: I just need East to have a club, or the K.

Rainer Herrmann: This loses only if West holds K-x and the K; and with that he might have overcalled. Anyway, chances of success are over 88 percent.

Radu Mihai: This wins if West doesn’t have both trumps; and even then, if the K is well-placed — 89 percent.

Bruce Neill: All other options [except Line F] give me two chances. This gives three: K onside, 2 onside or K onside.

Tim DeLaney: This combines many chances, and I make it around 88 percent. If West wins a singleton K, he is endplayed; if East shows out, I play low and try the heart finesse after West’s forced club return.

Jon Greiman: … Even if this loses [to a blank king], West has nothing to lead; red cards are obviously bad, and a spade sets up the suit…

David Kenward: I need East to hold at least one of the K, 2 and K — about an 88-percent chance. …

Leif-Erik Stabell: I make this line 88 percent, more than 5 percent better than Line B.

N. Scott Cardell: This is a problem of best odds, and Line D is a clear choice, succeeding unless West has three specific cards: K, K and 2. The a priori odds that East will have at least one of those cards is 89 percent; and the play so far has increased this to about 93 percent. Next best is Line B, which is about 84 percent at this point. Lines A, C and E are all around 75 percent, and Line F is worst of all.

Mauri Saastamoinen: This fails only when West has K-x and the K — should give me best odds.

Charles Blair: This works unless West has K, 2 and K. Line B works if spades are 3-3, or East has the K, or if West has a singleton K.

Julian Wightwick: If West wins a singleton K, he is endplayed.

Douglas Dunn: If East shows out, I’ll still let it run; West is forced to return his trump to the jack, then I’ll take the heart finesse.

Bill Powell: Making unless West has both clubs and the K.

Tong Xu: I only have trouble when West has K-2, but then I still have a chance with the heart finesse.

Rob Balas: [If East follows], this is 100 percent; if the hook wins, I’m home; if it loses to singleton king, West is endplayed…

John Reardon: This seems best, since West will be endplayed unless he has both clubs; and even then, I can take the heart finesse later.

Bernard Danloy: The key point is that it isn’t [necessary] to capture a singleton K offside — any return by West brings me home.

Dale Freeman: This is cold if the finesse loses to [a blank] K — a diamond gives me a ruff-sluff; a heart, a free finesse; and a spades sets up a spade trick.

Jim Munday: I lack entries to establish spades, unless they are 3-3. This gives me more chances: If East has the K, I’m home; and if West wins the stiff king, he will be endplayed. If West turns up with K-x, I will need the heart finesse to work.

Madhukar Bapu: … This only loses when West has K-2 and the K. (If East shows out, I will duck and later try the heart finesse.)

Erkki Malkamaki: This fails only if West has K-x and the K.

Thijs Veugen: Even if the finesse loses to the stiff king, West will be endplayed; I only fail if West has K-x and the K.

Daniel Korbel: I can’t see anything superior to playing for West not to have both K-x and the K — [better than normal odds] because West might have bid with 11-12 HCP…

David Ingham: If West wins a stiff king, he’s endplayed in three suits. If East shows out, I must duck in order to have an entry for the heart hook.

Nigel Guthrie: If East has a club void, I will fall back on the heart finesse.

Sebastien Louveaux: If the K is onside, this wins immediately; if the K is bare with West, he is endplayed. If West has K-x, I still can try the heart finesse…

John Lusky: This works whenever East has the K or K, or when West has a singleton K. No other line is this good.

Neelotpal Sahai: This line fails [compared to Line B] only when West has K-2, the K, and spades were 3-3 all along. …

Steve White: This makes if the K is onside or stiff offside, or if the heart hook wins.

Abby Chiu: This always makes when East has a trump; [else] it reserves the chance to finesse hearts.

Nikolay Demirev: Guided by the play so far, this is a lock; West will be endplayed [if he wins a stiff king]. Only problem is if East shows out; then I’ll need the K onside.

Jon Sorkin: If East follows, West will be endplayed [if he wins the king]; if East discards, I will duck and fall back on the heart finesse after a trump return.

Jean-Christophe Clement: If East has one or two clubs, contract is 100 percent, as West has no safe return if he wins a [blank] K. Otherwise, I hope the heart finesse will work.

Frans Buijsen: Even if the finesse loses to a bare king, West will be endplayed.

Wei Victor Zhang: If East follows low,…losing to a singleton K will leave West endplayed. If East shows out, I also play low to let West win the K, so I still can finesse hearts.

Gerald Cohen: Losing to a singleton king results in West being endplayed, so this only loses to K-2 offside — and then I still have the heart finesse.

Brad Theurer: Unless East has a club void, I’m a lock — either the Q will win, whereupon I will try the heart hook for an overtrick*; or West will win the K and be endplayed. If East has a club void, I pass the club to West, win the trump return, and take the heart hook.

*Going for the overtrick is justified, but imagine if West had Q-x-x K-10-x-x-x-x-x K-Q-x -- and chose to stay out of the bidding with a bad suit at unfavorable vulnerability. Ouch! -RP

Jordi Sabate: I think this is about 88 percent, because I win whenever East has at least one club (76 percent); and if not, if he has the K (half of 24 percent). Other lines are worse.

Jyrki Lahtonen: Best combination play. I’ll make right away if the K is in the slot; or if West wins the stiff monarch, he is [endplayed]. Only if West has K-2…will I have to rely on the heart finesse.

Ronald Kuip: Taking two finesses, with the [extra] chance that West will be endplayed with a bare K.

Barry White: If East follows, I will finesse and claim; if East shows out, I will duck and take the heart finesse.

Murat Azizoglu: …I’ll make unless West has K-x and the K,…and also if West misdefends by not returning a trump when he wins with K.

Kevin Lane: If the club finesse loses to a singleton king, I am home, because West is endplayed…

Nigel Weeden: This wins with clubs 0-2 or 1-1 (if West has a blank K he is endplayed). If West has K-x, it allows the heart finesse chance.

Marek Malowidzki: If West holds K-x, I can still rely on the heart finesse; otherwise, I must win.

Ronald Michaels: This allows for both finesses, and also wins with the K singleton offside.

Leonard Helfgott: Losing only when West has both clubs and the K — a 12-percent chance. Other options are riskier.

Andrew de Sosa: This wins whenever East holds at least one club or the K. …

Joon Pahk: Endplaying West right away if he wins the stiff king; and if East shows out, I can duck, and West has to let me back in dummy to take the heart finesse. Not only is this an 88-percent line, but I can make an overtrick if both kings are onside.

Manuel Paulo: If the club finesse wins, I will try for an overtrick with the heart finesse; if West wins a singleton K, he is endplayed. On the other hand, if West holds J-x-x K-x-x-x K-Q-x-x K-2 (or K-x-x), my choice will be wrong, while Lines B and F would have [worked].

Subhransu Patnaik: This endplays West if he wins the bare K: A diamond return gives a ruff-discard; a heart gives a free finesse; and a spade sets up spades to pitch a losing heart.

Dmitri Shabes: This loses only to both trumps and the K offside — about an 88-percent chance. …

David Brooks: I finesse even if East fails to follow!

Barry Rigal: This seems to give me three shots ( K onside, singleton K offside, or the heart finesse). Everything else relies on only two chances [at most].

George Klemic: If East follows, this is 100 percent. If East shows out, I will need the heart finesse after a trump return. …

Jai Grama: This endplays West if he has a singleton K, and I can still take the heart finesse if he has K-2.

Sandy Barnes: This gives a slight extra chance, as West will be endplayed with a stiff K.

Albert Feasley: If West wins his stiff K, any return helps me.

Jim Wiitala: If East shows out, I’ll duck, win the club return, and finesse hearts; if East follows low, I’ll duck, and West is endplayed if he wins.

Tim McKay: If K-x is with West, it is quite likely the K is with East…

Problem 2

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

Note: West has three trumps.

After winning the A:

Your Next Play	Award	Votes	Percent
E. Win A, A, J, ruff club	10	374	37
F. Win A, J, lead 7	8	216	22
A. Win A, J, lead 7	7	156	16
D. Win A, A, J, lead 7	6	143	14
B. Win A, J-10, lead 10	4	65	6
C. Win A, J-10, finesse J	1	47	5

A twelfth-degree black belt couldn’t have bid to a better contract, but the obvious-singleton heart lead is cause for concern. You lack the transportation to ruff two clubs in dummy and return to hand to draw the last trump (assuming a 3-1 break), so perhaps you should lead a second heart from hand, allowing West to ruff in front of dummy. Consider a likely layout:

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

After winning the A, suppose you cash the A, cross to the J and lead a heart (Line F). West ruffs, and it’s twelve o’clock high! All you have to do is draw the remaining trump and claim. Oops, not so fast. A shrewd defender would realize that ruffing a loser can seldom gain; so he’d pitch, letting you win the K. You next lead a trump, discovering the 3-1 break, and now realize you’re in never land. There is no way to ruff two clubs and enjoy the good heart, so you need a lucky spade lie (e.g., East with K-x or Q-x). Not to be; down one.

The key to success is to apply pressure against East.

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

Ruffing just one club in dummy (Line E) gives you 11 sure tricks, then when trumps prove to be 3-1, draw trumps ending in hand to reach this position:

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

Note that East was obliged to keep equal heart length with dummy and chose to keep three spades (else you could establish a spade trick by force). Lead the 10 and pitch a spade from dummy, as East safely copies*; then the 8 and pitch the J, as East must copy again to prevent establishment of the long heart. Next cross to the K, cash the A, and lead the 2 to endplay East.

*If East still has a club, he would be forced down to a blank spade honor, then you must not lead the last trump but cash hearts for a club pitch, then establish spades with ace and another. Of course you must guess which path to take.

Second place is a toss-up among Lines A, D and F (leading the 7 while West has a trump or two). If followed up correctly, each allows success when East has K-x, Q-x or a blank honor. Rather than search for subtle differences (which may not exist) second through fourth place are ranked by the voting.

Lines B and C (drawing all of West’s trumps and leading a spade) are worse, requiring the same lucky spade lie, but forfeiting the chance that West might ruff the second heart. Line B at least caters to the more likely spade shortness in East; while Line C is counterintuitive, requiring West to have K-x or Q-x (or both honors which is arguably impossible after the choice of lead).

Comments for E. Win A, A, J, ruff club

Anthony Golding: I don’t have enough high trumps to ruff two clubs and draw trumps after leading a second heart, so I’ll play East for the K [or Q]. After the club ruff, I’ll draw the third trump and play a fourth, pitching a spade and reducing to six cards. East must keep four hearts, and I’ll have to guess if he’s bared his spade honor (then I pitch my club on the third heart and play ace and another spade) or voided himself in clubs…

Toby Kenney: Next play two more trumps to effect a trump winkle if East has five hearts and the K [or Q]…

Yes, that will rip East apart… Call it a Rip van Winkle.

Jerry Fink: One good hope I can see, assuming East has J-8-5-4-3, is to find East also with a [spade honor], with which he cannot [avoid] being endplayed.

Grant Peacock: I’m assuming the lead is a singleton. After two more rounds of trumps, I hope I can guess what East has come down to and play accordingly.

Rainer Herrmann: I cannot ruff both clubs. Instead, I’ll win two trumps and watch which black suit East gives up in the six-card ending.

Bruce Neill: When West has three diamonds, I don’t have entries to ruff two clubs. Unless West has made a tricky lead from J-10-8-6-5, I hope to squeeze-endplay East if hearts break 5-1.

Tim DeLaney: An expert West would be unlikely to lead a doubleton 10, so I assume a singleton. I haven’t the entries to ruff two clubs, so I’ll fall back on a squeeze and/or endplay against East… Line D looks inviting, but an expert West would refuse to ruff, and thereafter the contract is doomed.

Jon Greiman: If hearts are 4-2, even Fritz could make this. I’m not out of the woods yet, as I still need to diagnose the spade situation.

Leif-Erik Stabell: I’m home and dry if I can guess East’s distribution and number of spade honors.

N. Scott Cardell: There’s no problem unless hearts are 5-1, and if so, East surely five. With K-Q, West would probably have led the K, so East should have at least one spade honor, [in which case] he can be squeezed. …

Mauri Saastamoinen: This problem is really a headache! It seems like West already gave me a hint how to play. If East has all remaining hearts and at least one spade honor, he will soon be squeezed. (It is essential to save one heart entry.)

Charles Blair: This requires East to have a spade honor. When I am reduced to 3=1=1=1 shape, I must guess whether East started with five hearts and has discarded all his clubs.

Jonathan Mestel: West wouldn’t have led a stiff heart with K-Q, so I’m going to make this.

Douglas Dunn: I will run all trumps but one. If the 10 was a singleton, East will have to keep four hearts and two spades, possibly K-x, Q-x or K-Q. Then I’ll play the last trump, discarding the J…

Bill Powell: I believe the lead to be a singleton (the auction indicates an attacking lead so, presumably, West is playing East for a red ace). Two more trumps (pitching the 5) will squeeze East if he has a [spade honor].

Tong Xu: Next I play the last trump from dummy. If East has five hearts, he will [soon] be squeezed; and if I guess right, I can win the 9 or 10 as my 12th trick.

Rob Balas: Looks like a singleton lead, and with no spade lead I assume West [does not have K-Q]. … I will need to pressure East and strip his club exit cards or force a fatal reduction in spade or heart length… I will need to guess East’s distribution, as I must keep a diamond if East keeps a club and bares his spade honor…

John Reardon: If the lead is from shortage, East will soon feel the pressure.

Bernard Danloy: … When I next lead a trump, East has no solution if he has [at least] one spade honor… If he throws his last club, I will cash two more trumps, discarding dummy’s small spades; East must discard a heart or prepare himself to be thrown in.

Dale Freeman: I will lead all but one diamond, pitching the 5. Then [if I think East still has a club], I will lead a heart (setting up hearts if 4-2); and if East has five, cash the A to drop his [now-blank] honor. …

Rod Roark: It’s important to delay testing hearts for a while to put maximum pressure on East, if hearts are 5-1. Next I’ll cash all but the last trump, pitching a spade…

Jim Munday: It looks easy to ruff two clubs in dummy, but transportation is awkward. Given that the lead is almost surely a singleton, and East has one or both spade honors, there is a better way. After the club ruff, I will lead trumps; East will have to part with his clubs to keep a spade guard, then the final trump leaves A K-Q-9-2 in dummy, and East with no answer. A heart discard allows me to set up the long heart, and a spade will lead to a heart endplay. …

Rob Stevens: If East has five hearts, he will come under pressure. On the assumption that West would have led a spade with both honors, East will either be endplayed… or I will be able to establish the 10. …

Erkki Malkamaki: If East has a spade honor with five hearts, he will caught in rare trump-strip-throw-in squeeze — or whatever name it has. :) I next lead two trumps to leave A-J K-Q-9-2 in dummy. If East keeps K-x (or Q-x) J-8-5-4, I lead the last trump discarding the J… If East keeps a club, I will discard a club on hearts and make two spade tricks. Line F fails if West does not ruff the heart (it would succeed if South had the 7 instead of the 4).

David Ingham: Assuming East has five hearts (almost certain, given the lead), he can be pinched interestingly if he has one or both missing spade honors. The fourth round of trumps reduces East to six cards; he must keep four hearts, so he can have only two black cards. If he keeps a club and a spade honor, A-J establishes my 12th trick [after pitching a club on the third heart]. If he keeps two spades, I cash my last diamond, pitching the J…

Neelotpal Sahai: If hearts are breaking 4-2, this problem wouldn’t be here. The way to handle 3=5=1=4 distribution with East is through Line E, and it’s the only solution. If hearts are more routinely divided (4-2), I [may] fail; but I’ll take my chances.

Abby Chiu: Next I will lead a diamond to my hand. Assuming spade honors are split, East must keep three spades and four hearts; then I lead my last two trumps, as dummy holds the A and K-Q-9-2. East will be squeezed in the majors; if he discards down to one spade, I can endplay him in hearts after cashing the A.

Dean Pokorny: Trying to endplay East when he is 3=5=1=4 or 4=5=1=3 with at least one spade honor…

Lajos Linczmayer: I suppose the 10 is a singleton, and East has a spade honor. If East keeps three spades and four hearts, I cash two more trumps and throw him in with a heart at the end. If he keeps less the three spades (better defense), I must guess the position.

Frans Buijsen: Eventually, I may have to choose between playing West for a singleton heart or a doubleton. This keeps my options open as long as possible.

David Caprera: My table feel tells me the 10 is a singleton, given the speed it hit the table. :) Playing for a black-suit elimination and heart endplay against East will require some good card reading; but why play for the mundane when the spectacular can work? — a real New York Times sort of play.

Jordi Sabate: I cannot crossruff and remove West’s trumps (if 3-1) with hearts 1-5. I will ruff only one club and play for East to have at least one spade honor, trying to guess the ending and endplaying him if hearts are 1-5, else making two tricks in spades.

Len Vishnevsky: Next I win the K and 10 to reach A-J K-Q-9-2 opposite 10-7-2 7 4 9…

Barry White: If East has five hearts and a spade honor, as I suspect, a position will evolve in which I can squeeze East down to Q-x J-x-x-x, while dummy holds A-J K-Q-9-x. …

Robert Whitcher: Continuing by running all but one diamond to catch East in a two-loser squeeze in spades and hearts (if he has one or both spade honors). This opens the possibility of going down when hearts are 2-4, or if West has both spade honors,…but then I do not understand the lead. Oh well; partner will understand — not! …

Joon Pahk: I’ll play for spade honors to be split and East to have heart length; then he will have to come down to honor-doubleton in spades or discard his exit in clubs, subjecting himself to a strip squeeze.

Manuel Paulo: With two club ruffs, I can count 12 tricks, but transportation is trouble. If East holds a hand like Q-x-x J-8-5-4-3 x Q-J-x-x, I am bent on ruffing one club and drawing trumps to squeeze him.

Paulino Correa: The 10 smells like a singleton, so I’ll play for that. Next I’ll return to hand in trumps and play another trump, discarding the 5 from dummy. If East chooses to discard all his clubs, I’ll play my last trump discarding the J from dummy, as East reduces to one spade and four hearts; then K, A and 2 will throw him in to make the contract. If East chooses to keep a club (presumably an honor), I’ll keep my last trump and play K-Q to discard my last club and cash the A [dropping East’s honor], then my 10 will assure the contract.

Daniel de Lind van Wijngaarden: The lead is very likely to be a singleton. I draw two more rounds of trumps, discarding a spade from dummy. If East discards two spades and a club, I play a spade to the ace; if East drops an honor, I am home; otherwise I take the K and play a spade hoping East has a bare K left. If East discards two clubs, I play my last trump pitching the J; then [assuming East pitches a spade], A, A and 2, so East wins and has to play into Q-9.

Problem 3

IMPs	K			West	North	East	South
None vul	J 7 6 4			LHO	Partner	RHO	You
	A 6 4					4	5
	A 10 4 3 2			5	6	Pass	Pass
				Pass
Lead: 4		East plays A
	—
	A K Q 10 9 5 3 2
	K J 3
6 South	Q 9

You ruff with the 9 and cash the A (East pitches 5).

Your Next Play	Award	Votes	Percent
C. Win A, A	10	146	15
D. Win A, lead 2	9	188	19
E. Run the Q	6	234	23
F. Run the 9	5	95	9
A. Win J, lead 2 to queen	4	197	20
B. Win J, lead 2 to nine	3	141	14

This looks like an easy contract if there ever was one, as dummy has more than enough entries to set up the long club for a twelfth trick. But don’t forget Murphy’s Law! The obvious danger is a 5-1 club break (combined with a losing diamond finesse), but your club honors can be put to good advantage.

The instinctive play is to run the Q (Line E). If it loses, East will return a diamond, of course; so suppose you win the A* and cash the A — oops, East shows out, and you now need the diamond finesse (which also loses if there is any justice). Even after losing to the stiff king, you could have succeeded by finessing clubs again, but that would be double-dummy, as it loses when East has K-J. Running the 9 (Line F) is similar, paying off to a stiff jack.

*Alternatively, you could win the K in hand; then if West has five clubs and the Q, you can squeeze him. This is probably better once East turns up with the K, as East might have opened 1 with the Q as well.

What about starting clubs low from dummy (Line A or B)? No, a similar problem occurs if West wins cheaply and returns a club; you’ll win the ace (no fair finessing) and East may show out. From this point, you can still succeed against any distribution: If East has the Q, you can finesse; if West has it, he will be squeezed in the minors. Alas, you must guess which to play for, so your chances are not much better than 50 percent.

Aha! If you win the A first then exit with a club (Line D), West will be endplayed if he happens to have K-J-x-x-x-(x). He can’t return a club without establishing the 10, so he must lead a diamond into your K-J (else concede a ruff-sluff). Looks like 100 percent!

Well, not quite. It is barely possible that East has five clubs, but with a little foresight you can cater to this as well. Consider the following diabolical layout:

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

If you follow Line D, you will be defeated, as East will exit with a diamond. The key play is to cash the A (Line C) before leading a second club; then East will have no exit card in the above layout. Based on the bridge certainty that East has 7+ spades for his 4 opening, this is a sure-trick line against any distribution. Cashing the A costs nothing if West has five clubs (he is still endplayed); and if clubs break 4-2, dummy has three trump entries to establish and enjoy the long club.

Line D gets a close second, as the losing scenario is extremely unlikely, especially considering West’s choice to defend 6 (a 6 sacrifice seems obvious). Arguably it’s worth 9.99, but my policy is to score in whole numbers only.

Lines A, B, E and F will usually work in practice, as only some 5-1 club breaks and a losing diamond finesse (or losing minor-suit squeeze if chosen) will result in defeat. Even so, they’re all lazy and deserve to fail. Lines E and F warrant a higher ranking because they lose only to a specific blank club honor, while Lines A and B lose to any low singleton (four times as likely).* Rather than split hairs between Lines E and F, they are ranked by the voting; likewise for Lines A and B.

*Assuming West has five clubs, which is the only realistic concern.

This play problem actually occurred at the 1990 World Championship (Geneva) in the Rosenblum Cup semifinal. Amazingly, the given auction was replicated at all four tables. In real life, the play hardly mattered — perhaps because Switzerland’s neutral status dictated the friendly layout that follows.*

*For the problem, I swapped the 4 and 2, so that West’s lead would be consistent with four or five spades.

IMPs	K		Trick	Lead	2nd	3rd	4th
None vul	J 7 6 4		1. W	2	K	A	9
	A 6 4		2. S	A	8	4	3
	A 10 4 3 2		3. S	Q	5?	2	6
Q 7 6 2		A J 10 9 8 5 4 3		Inferior play makes 7
8		—
Q 10 7 5 2		9 8
K 7 5		J 8 6
	—
	A K Q 10 9 5 3 2
	K J 3
6 South	Q 9

The play record was given for only one table, and that declarer adopted Line E — sigh, making seven when West unwittingly failed to cover the queen. Justice was on vacation, as usual. I asked Eric Kokish, who was dummy at one table, if he could remember if any declarer found the sure-trick play (Line C) or the almost-as-good Line D; and to the best of his recollection, no one did. Thus, if you scored 9 or 10 here, you can consider yourself a deserving world champion.

I also used this deal in my United State Wins Swiss bidding poll (March 2006) regarding West’s choice to compete to 5 and not sacrifice in 6 — a decision that was upheld by the consensus.

Comments for C. Win A, A

Anthony Golding: The only problem arises if clubs are 5-1 (I have enough entries to set them up on a 4-2 break). If West has five clubs, he’ll be endplayed with the second club; but if East has the club length, I need to remove his hypothetical diamond exit to endplay him.

Toby Kenney: Next I lead a club. If clubs are 3-3 or 4-2, I can still ruff them out. If not, whoever has five will be endplayed (assuming East has 7+ spades).

Grant Peacock: Catering to East having 7=0=1=5 shape.

Rainer Herrmann: This is slightly better than Line D, should East be 7=0=1=5.

Radu Mihai: If clubs are worse than 4-2,…whoever wins the second club will have to give me the missing trick — assuming East would not open 4 with a hand like A-Q-J-10-x-x -- x-x K-J-x-x-x.

Bruce Neill: I aim to endplay whoever wins the second club. Cashing the A is necessary if East is 7=0=1=5.

Tim DeLaney: Next I play a club. If both follow, the fifth club will establish with two ruffs. If clubs are 5-1, whoever wins will be endplayed. It is necessary to cash the A when East has A-Q-x-x-x-x-x -- x K-J-x-x-x to remove his exit card.

Jon Greiman: Sneaky, Richard, omitting the important part of the answer. Next I play another club. If West has K-J-x-x-x, he has nothing good to lead. If East has K-J-x-x-x, he has only black cards to lead (unless he opened 4 on 6=0=2=5). If both follow, even my late grandmother could make it…

Are you sure about that? Grandmothers often ruff low.

David Kenward: I always have three trump entries to set up the long club on a 4-2 break. On a 5-1 break, either East or West is endplayed by the next club (unless East is 6=0=2=5).

Leif-Erik Stabell: Another club endplays whoever holds K-J-x-x-x. East cannot be 6=0=2=5, as West would not have led a spade with six.

N. Scott Cardell: I can set up my 12th trick in clubs unless clubs are 5-1 or 6-0… Either this or Line D will endplay West if he has five or six clubs. The danger is that East might have five clubs; but he surely has 7+ spades for his opening bid, so he has no more than one diamond.

Mauri Saastamoinen: I am playing this like all other dentists. Next I lead the 2. By the way, why didn’t our opponents bid 6 ?

Charles Blair: I cannot claim, since East could have 6=0=2=5 shape.

Julian Wightwick: Then the 2. If West has K-J-x-x-x, he is endplayed. If East started with 7=0=1=5 shape, he is endplayed. If East has only six spades, West would not have led a spade.

Douglas Dunn: There are lots of heart entries to set up clubs… This fails only if East has K-J-x-x-x and two diamonds.

Bill Powell: Then a club. This is basically the same endplay as Line D but allows for East being 7=0=1=5.

Tong Xu: Then continue clubs. Taking the A is to prepare for East having 7=0=1=5 shape.

John Reardon: This seems to be 100 percent if I can assume East has 7+ spades. Either I set up the long club, or the player with K-J-x-x-x-(x) is endplayed.

Dale Freeman: I have enough entries to set up clubs if 4-2 (I don’t need the A). Next I exit with a club and endplay probably West if he has K-J-x-x-x ; however, the reason to cash the A is to endplay East if he is 7=0=1=5 (unlikely but possible).

Jim Munday: If clubs are 4-2, I can set up the long club with ease. To cater to a 5-1 split, I must make the opponent who wins the second club regret it. If it is West, no problem, as he will be endplayed. If East, I must remove his diamond exit if he is 7=0=1=5. I will pay off to the unlikely 6=0=2=5.

Madhukar Bapu: This is a kind of dentist’s coup. By cashing the A before exiting with a second club, I ensure success in the event East has 7=0=1=5 shape, which is the only holding that threatens the contract…

Rob Stevens: This is 100 percent if East has 7+ spades.

Erkki Malkamaki: Then the 2, in case East is 7=0=1=5 with both club honors.

Thijs Veugen: No problems when clubs are 3-3 or 4-2; otherwise, the player with long clubs will be endplayed.

Daniel Korbel: A sure-trick play, as long as East has 7+ spades.

David Grainger: This makes unless East has only six spades (with x-x K-J-x-x-x), as whoever has five clubs will be endplayed; or clubs easily [establish] if 4-2 or 3-3.

Nigel Guthrie: This loses only when East is operating with 6=0=2=5 shape.

Sebastien Louveaux: Clubs can be established if 4-2 or 3-3 (dummy has three heart entries, so the A is unnecessary). If West has 5+ clubs, he will be endplayed. If East has five clubs, he will also be endplayed, as he won’t have a diamond left. …

John Lusky: I will next play a low club as in Line D, but this protects against 7=0=1=5 pattern with East. If clubs are 4-2, my three heart entries will let me set up and cash a club winner.

Neelotpal Sahai: I thought I had a foolproof solution in Line D but then realized that East might have opened 4 with 7=0=1=5 distribution, then only Line C works. Of course, I play the 2 next. (Richard often omits the correct follow-ups, else the solution is too easy.)

Steve White: Cashing the A is unlikely to matter; but East could be 7=0=1=5, and it takes his exit card.

Rossen Georgiev: Then a club to endplay either defender who has 5+ clubs. Cashing the A protects against 7=0=1=5 distribution in East.

Dean Pokorny: The only problem arises when clubs are 5-1 or 6-0. Line D works when West has 5+ clubs, but this is even better, because it wins against 7=0=1=5 distribution with East by removing his only safe exit card.

Jon Sorkin: This protects against K-J-x-x-x with East (he is endplayed with 7=0=1=5 shape) or [West].

Jean-Christophe Clement: And then a club. If clubs are 4-2, no problem; if West has five clubs, he has no return; and if East has five clubs, he won’t have a diamond (key play was to cash the A).

Gerald Cohen: The only problem is when East is 7-5, so cashing the A will endplay him (just as West) when I lead another club. If clubs split 4-2 or 3-3, no endplay is needed.

Carsten Kofoed: Either the fifth club will be a trick, or someone will feel bad.

Brad Theurer: Contract is easy if clubs are no worse than 4-2… If West has K-J-x-x-x-(x), ace and a club will endplay him; but if East has K-J-x-x-x, I need to remove his diamond exit (he should have seven spades, so only one diamond)…

David Caprera: Cashing the A protects against the only [layout] that can hurt me (East 7=0=1=5).

Jordi Sabate: Then I will lead a club — 100 percent if East has 7+ spades… Only 6=0=2=5 shape in East will beat the contract.

Jyrki Lahtonen: Line D is almost good enough but fails if East is 7=0=1=5. Line C caters for this shape by removing East’s exit card in diamonds before endplaying him with a second club. Of course, if clubs break no worse than 4-2, I will have a non-cerebral path to 12 tricks by the carefully retained trump entries.

Len Vishnevsky: I only have to worry if clubs break 5-1 or 6-0. If I play A and a club, I can claim…if West has 5+ clubs (he’s endplayed); but if East has five clubs, he has a safe diamond exit, so I need to cash the A first. East has to have 7+ spades — not just for his opening, but for West selling out [and leading a spade] — so if he has five clubs, he won’t have more than one diamond.

Barry White: Next a low club, which should endplay whoever has five clubs. (If clubs are 4-2, I can set up the long club.) I cash the A in case East holds 7-5 in the black suits.

Frank Mulder: And then a small club of course. Cashing the A is essential if East is 7=0=1=5.

Kevin Lane: Kind of like Line D (I’m playing a low club next) but protecting against 7=0=1=5 distribution in East by removing a safe exit. If West has K-J-x-x-x-(x), he’s still endplayed; and I have plenty of entries [to set up clubs if 4-2 or 3-3].

Nigel Weeden: Ace and another club will work almost all the time (West at least two clubs); but cashing the A allows for the unlikely case that East is 7=0=1=5, at no cost.

Chuck Lamprey: Unless East opened 4 on 6=0=2=5, I should be able to claim.

Robert Teesdale: Then the 2. This only fails when East has 6=0=2=5 shape (including K-J)… Otherwise, clubs have broken and a winner can be established, or [whoever] has 5+ clubs is endplayed.

Skafti Jonsson: Then the 2 finishes East-West. [Cashing the A] caters for 7=0=1=5 East.

Amnon Harel: Tightening the endplay, in case East has 7=0=1=5 shape.

Ronald Michaels: This caters to a 5-1 club split either way.

Pontus Silow: Then a low club. If clubs split 3-3 or 4-2, I will get a discard on my fifth club. If West has five or six clubs, he cannot continue clubs without giving me a diamond discard on the 10, and he cannot play on spades or diamonds. If East has five or six clubs, he will have only spades and clubs left to play…

Leonard Helfgott: Assuming East has at least seven spades, the contract is assured. Only danger is K-J-x-x-x-(x) in either hand (dummy entries can handle all 4-2 club breaks, and the club position will be revealed after a second club lead). Cashing the A is necessary to remove a safe exit if East is 7=0=1=5…

Robert Whitcher: Then a club — and pay off if East opened 4 on 6=0=2=5 (unlikely) but otherwise chalk it up. …

Michael Dimich: The only distribution to cause a problem is East with 7=0=1=5 shape, but cashing the A before exiting with a club solves that.

Andrew de Sosa: This protects against K-J-x-x-x in East — the only layout that can hurt me — by eliminating his potential safe exit in diamonds.

Joon Pahk: Then a club. This is 100 percent, as long as East has at least seven spades — and surely West would not have led a spade with six-card support. …

David Stern: Assuming East has at least seven spades, he has at most six minor cards. If he has two diamonds and four clubs, I can establish clubs. If he has one diamond and five clubs, cashing the A will endplay him.

Manuel Paulo: If East holds A-Q-x-x-x-x-x — x K-J-x-x-x, I apply the dentist’s coup then throw him in. …

Paulino Correa: I continue with a small club. If West has K-J-x-x-x-(x), he’ll [be endplayed]. If both opponents follow to the second club, I’ll have time and entries to [establish] dummy’s fifth club. … If East has K-J-x-x-x, he is 7=0=1=5 (or 8=0=0=5) and will have to lead from his J or give me a ruff and discard.

Subhransu Patnaik: A problem only occurs if clubs are 5-1 [or 6-0]. Cashing the A before leading the 2 is a precaution to take care of five clubs with East (with 7=0=1=5 shape he will be endplayed on winning the K).

Richard Stein: Then a club. I have three trump entries to dummy, so I’m home if all follow. If East should have five clubs, he’ll almost surely be 7=0=1=5 — and endplayed when he wins the K. …

Ed Barnes: Then a small club. Only way this can lose is if East holds K-J-x-x-x and two diamonds.

Junyi Zhu: I will continue with the 2. If anyone has K-J-x-x-x, he will be endplayed. If no one has five clubs, I can then establish the last club.

Dmitri Shabes: This loses only to East having less than seven spades, K-J-x-x-x, two diamonds and no Q. Even then, West with six-card trump support and a five-card side suit might have bid 6 [and would never lead a spade].

David Brooks: I must cash the A if East is 7-5 in the blacks.

George Klemic: I wrote a nice long paragraph about how Line D works except against East holding 7=0=1=5 but now realize that Line C covers this case as well. With multiple trump entries, I don’t need the A, so I steal East’s exit card [just in case]. …

Alon Amsel: I have enough entries to establish clubs if they’re no worse than 4-2… This makes sure East will be endplayed if he has 7=0=1=5 shape.

Daniel de Lind van Wijngaarden: If clubs are 4-2 or 3-3, I can [establish clubs] to pitch a diamond. If West started with five or six clubs, he is endplayed after winning K. If East started with five clubs, he will have only one diamond (7=0=1=5) and also be endplayed.

Problem 4

IMPs	10 9 8			West	North	East	South
None vul	2			LHO	Partner	RHO	You
	A K Q 6 4				1	Pass	1
	A 8 6 3			Pass	2	Pass	4 NT
				Pass	5	Pass	6
Lead: 3		East plays 2		Pass	Pass	Pass
	A K Q J
	A K 3
	5 2
6 South	Q 7 4 2

After winning the J:

Your Next Play	Award	Votes	Percent
C. Win A, ruff heart, lead 4	10	400	40
A. Win A, ruff heart, draw trumps	9	234	23
D. Win A, ruff heart, lead 3	7	88	9
E. Win A, lead 3	5	33	3
B. Win A, ruff heart, win A-K	4	79	8
F. Duck a diamond	2	167	17

Holding four top trump honors in hand, dummy’s appearance with only three trumps is quite a surprise; though it’s hardly a Twelfth Street Rag. Indeed, the Moysian slam is excellent, with better chances than 6 or 6 NT. Translation: You’d better make it.

With 10 top tricks in high cards, and an easy heart ruff, you need only a twelfth trick (so what else is new?). Straightforward play seems to be to ruff your heart (saving a top heart for control), draw trumps, and play on diamonds. If diamonds split 4-2, you can give up a diamond; and if they split 5-1, you might be able to do something with clubs. Alas, this makes an interesting story, but it has a dire communication trap. Consider a plausible layout:

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

If you follow Line A, you must lead all your trumps to draw West’s, so you pitch clubs from dummy to keep five diamonds, as East pitches a heart and a club. This leaves the following position:

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

You cannot afford to cash the K, so you play diamonds from the top hoping for a 3-3 split or the defender with four to hold the K (he would be endplayed). No luck; down 1.

The problem was timing. With expected breaks (diamonds and spades 4-2) you have to lose a diamond, and you must do so while you have communication and control. At Trick 4 duck a diamond (Line C) and the rest is easy. You win four spades, four diamonds, three hearts (counting the ruff) and the A. I estimate the chances to be over 80 percent, considering that West would not lead a singleton trump and would probably lead a singleton diamond; hence only East could have a singleton spade or diamond.

Despite failing in the above scenario, second place goes to Line A, which certainly has good chances — about 68 percent by my ballpark math. Generously, I made it a close second because friendly breaks would produce an overtrick.

Line D (leading to the Q early) gets third place. Assuming a club return if the queen loses (removing dummy’s entry) and the added risk of a club ruff, I’d estimate about 58 percent.

Fourth place goes to Line E ( A then leading to the Q) which is clearly inferior to Line D, because a trump return prevents you from ruffing a heart, unless you play all out for 3-3 trumps.

Line B (ruff heart, win A-K) is hard to appraise, because much depends on what you do next. Arguably this might deserve third or fourth place, but choosing an inferior start does not suggest accurate play nor clairvoyance later, so it will settle for a close fifth.

Last and clearly worst is Line F (duck a diamond immediately), as a trump return stamps paid on all your chances — well, except a stiff K. You need a heart ruff for a twelfth trick, and to obtain it means being locked in dummy. I would have awarded it 1, but 167 votes drew some sympathy.

Comments for C. Win A, ruff heart, lead 4

Anthony Golding: Playing for 4-2 diamonds seems the best bet. I need to take the heart ruff before ducking a diamond, else a second trump ruins my communication.

Toby Kenney: This preserves communications and works whenever spades and diamonds are each no worse than 4-2.

Jerry Fink: I need spades and diamonds each to break no worse than 4-2 — 84 x 84 = 70.6 percent. Next best is to ruff a heart and draw trumps (if possible), hoping for something good to happen in diamonds and/or clubs — around 65 percent.

Grant Peacock: Doing everything in the right order.

Rainer Herrmann: Only this keeps control of suits and [preserves] entries to both hands.

Radu Mihai: Best chance is hope spades and diamonds are each no worse than 4-2. This keeps everything under control.

Bruce Neill: A control problem. I can’t draw trumps early in case they are 4-2, and I must ruff a heart before ducking a diamond in case another trump is led.

Tim DeLaney: This brings in 6 , as long as diamonds and spades are each no worse than 4-2. The point is that I must maintain communication with the South hand to be able to cash the K after trumps are drawn.

Jon Greiman: Communication problems much? At least this way, I’ll make if neither pointy suit is 5-1.

Leif-Erik Stabell: This is fine, as long as spades and diamonds each break 4-2 or 3-3.

N. Scott Cardell: If each pointed suit breaks 4-2, this is the only way to set up diamonds, get a heart ruff and be able to cash the K safely.

Mauri Saastamoinen: Playing this way, I will have enough entries to enjoy my diamonds and the K.

Julian Wightwick: This works, so long as spades and diamonds are each no worse than 4-2.

Jonathan Mestel: The trump lead is a bit suspicious, but not enough to deter me from this natural line.

Douglas Dunn: I have to delay pulling trumps to avoid being stranded from the K.

Bill Powell: Making when each pointed suit breaks 4-2 or 3-3.

Rob Balas: Lines A and C are both good. Line A works better if trumps are 3-3 (I can play on clubs if diamonds are 5-1), or if trumps are 4-2 and diamonds 3-3 (or if the person with four diamonds has the K, I can endplay him). Line C works better if trumps are 4-2, because I [succeed] on any 4-2 or better diamond split. Based on the lead, trumps appear to be 4-2 (either way), since the lowest card first [suggests] an even number…

John Reardon: This wins with reasonable breaks: diamonds and spades each no worse than 4-2.

Bernard Danloy: A nice hand, where communication is the main issue. I won’t waste my time; diamonds [offer] the best prospect, and I have to duck a trick as soon as possible. Then I can safely pitch three clubs on high cards from my hand, and cross back to dummy to get home.

Jim Munday: Maintaining communication between hands, when spades and diamonds are 4-2.

Madhukar Bapu: Even if diamonds are 4-2, I must play carefully due to the lack of entries. Best option is to duck a diamond after ruffing a heart. If diamonds are 5-1, I hope East has a singleton J [so no ruff is possible], and West…has the K [so he can be squeezed].

Rob Stevens: Bringing in 3-3 or 4-2 diamonds, and making sure I don’t get cut off from my last heart winner.

David Grainger: This works whenever trumps and diamonds are each 4-2 or 3-3. A trump return after Line F would remove my hand entry.

David Ingham: It looks simple: Ruff a heart, draw trumps, and expect diamonds to split no worse than 4-2, with some chances even if they’re 5-1. But no! If [spades] and diamonds are each 4-2, and the K isn’t stiff or [favorably placed], I’ll be cut off from my heart winner. Ducking a diamond immediately doesn’t work, either — a second spade makes my communication kaput. Only a heart ruff followed by a diamond duck [works] when each pointed suit splits 4-2.

Nigel Guthrie: Duck soup for a simple soul. …

Sebastien Louveaux: This simply requires spades and diamonds each to be no worse than 4-2. Line A requires spades or diamonds to be 3-3, otherwise there is no entry to cash the K. Lines B and F do not improve Line C. Lines D and E run the risk of an immediate club ruff (and I’m not home if that doesn’t happen).

John Lusky: This makes if diamonds and spades are each no worse than 4-2, unless an opponent ruffs the first club [or third heart]. I don’t think I can test clubs without losing better chances in the diamond suit.

Steve White: I can win any return, draw trumps, and hope dummy’s fifth diamond is good.

Abby Chiu: This preserves entries for both drawing trumps and running diamonds.

Dean Pokorny: This is best, because it fails only when spades or diamonds are worse than 4-2 (29.4 percent). If a diamond is ducked before a heart is ruffed, opponents can ruin my communication with a trump return.

Nikolay Demirev: Line A is superior with spades 3-3, but there is an entry problem when they are 4-2. I won’t bother to calculate percentages, but Line C is practical and overall seems best.

Jon Sorkin: If I duck a diamond before ruffing a heart, a trump return prevents ruffing a heart and drawing trumps.

Lajos Linczmayer: This is required if spades and diamonds are each 4-2.

Jean-Christophe Clement: Hoping diamonds are not 5-1 or 6-0. All other options ruin my communication.

Frans Buijsen: This wins if diamonds [and spades] are each no worse than 4-2, which is the best chance I can get.

Gerald Cohen: Other lines have entry problems, like getting locked in dummy at an inopportune time.

Carsten Kofoed: I must retain a sure entry to reach the K.

Brad Theurer: A classic case of keeping control, to guard against each pointed suit breaking 4-2. No return can hurt me — barring 5-0 clubs [or 7-2 hearts].

David Caprera: Maintaining communication. Other lines could prevent me from cashing my easy tricks.

Gregory Gorshkov: This works if spades and diamonds are each no worse then 4-2; or in [rare] cases if five diamonds are with the K, and a [blank J prevents] a ruff. All other choices seem to suffer communication problems, e.g., in Line A, if [spades and] diamonds are 4-2, I cannot cash the K; or in Line F, a trump return [prevents] me from ruffing a heart and returning to hand to draw trumps.

Jordi Sabate: The only way to make the contract if spades and diamonds are each 4-2. It doesn’t matter who has the K.

Ronald Kuip: With silent opponents and so many hearts missing, a 5-1 diamond break looks unlikely.

Len Vishnevsky: If a heart or club is returned, I’ll be able to throw in a Vienna coup, but that would play for a singleton J [and] an error… Line A looks good,…but I may get cut off from the K! If I duck a diamond [immediately], I won’t be able to negotiate a heart ruff.

Barry White: This should make unless spades or diamonds split 5-1.

Murat Azizoglu: It’s tempting to duck a diamond first, but transportation does not work if another trump is led.

Dick Yuen: As long as diamonds or trumps do not split 5-1, I am home free.

Mark Chen: I will play for 4-2 trumps and 4-2 diamonds.

Marek Malowidzki: To preserve communication in spades.

Ronald Michaels: This wins as long as spades and diamonds are each no worse than 4-2.

Pontus Silow: [This should produce] five spades [counting the ruff], two hearts, four diamonds and one club…

Andrew de Sosa: This works whenever spades and diamonds are each worst-case 4-2. I can’t afford to test for 5-1 spades to see if I must rely on 3-3 diamonds and 6-3 hearts.

Audrey Kueh: As long as spades and diamonds are each no worse than 4-2, I’ll have communication to draw trumps and cash the K, leaving dummy high.

Joon Pahk: I have to keep an entry back to hand for the K after losing a [diamond].

Manuel Paulo: To keep control and [guard against] a West hand, such as x-x-x-x x-x-x-x x-x K-J-x. After any return, I count four spades, three hearts (with the ruff), four diamonds and one club.

Ken Cohen: This guarantees the contract anytime spades and diamonds are each no worse than 4-2 — and there is no surprise club ruff [or heart ruff].

Paulino Correa: Plan is to expect spades and diamonds each not worse than 4-2… If I start by ducking a diamond, another trump lead [is fatal]; so I must ruff a heart immediately.

Richard Stein: I don’t see another line that sees me home against normal breaks (spades and diamonds 4-2, K offside). On other plays, something or other [may] be stranded.

Ed Barnes: This should make when trumps and diamonds are each not worse than 4-2, with small extras if a defender has a stiff J and no K.

Dmitri Shabes: No reason to get fancy. I’ll just handle all 3-3 and 4-2 distributions in the pointed suits, which only this option does.

David Brooks: Diamonds 3-3 or 4-2 is 84 percent. Playing on clubs requires the K onside or diamonds 3-3, reducing my chances to 68 percent.

Alon Amsel: Keeping a crucial [trump] entry to my hand.

J.J. Gass: My plan is to win any return,…draw trumps, cash the K if I still have it, and cross to whichever of dummy’s aces is still there…

Adrian Petculescu: This is the only line that ensures, on any return, being able to draw trumps, cash the K and win four diamonds — assuming trumps and diamonds are each no worse than 4-2, else it’s [probably] a lost cause.

Problem 5

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

After winning the A:

Your Next Play	Award	Votes	Percent
F. Win A-Q, K, run hearts	10	269	27
C. Win A, overtake Q, run hearts	8	101	10
D. Win A-Q, A, run hearts	7	229	23
E. Win A-Q, finesse 10	6	190	19
A. Lead Q (king-ace), A-Q, finesse 10	3	70	7
B. Lead Q (covered) and duck	2	142	14

Six hearts might have been easier with the ability to ruff a diamond, but 5-2 fits are elusive slams. In notrump, you have 11 top tricks with the marked spade finesse, but prospects for a twelfth are bleak. Considering the bidding and lead, playing for 3-3 clubs is a long shot, and hoping to score the 10 is even worse.

But wait! Placements are right for a double squeeze: East obviously protects spades, West almost surely has 4+ clubs, and both probably protect diamonds. Unfortunately, the count is not rectified, so you must lose a trick early to prepare. But how? You can’t give West a club without being set. If you give East a spade, a spade return removes a vital entry to your hand. Finessing the 10 (or ducking a diamond) will work if East has longer diamonds*; but West is likely to be longer, then a rattlesnake (diamond back) breaks up any squeeze.

*East alone is later squeezed in spades and diamonds.

When in doubt, a good general principle is to lead your solid suit! Running hearts early will still squeeze East if he happens to have 4+ diamonds, and forcing enemy discards will sometimes enable other opportunities, even against perfect defense. Consider the following layout, which is typical for the bidding and lead:

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

After winning the A, cross to the A and lead the Q. Should you overtake? No. Line C works as the cards lie, but there is no need to risk heartbreak from a 5-1 heart break; just play low. Next comes the key play: Cross to dummy with a club (Line F) to run hearts. This is the position before the last heart is led:

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

The 10 now squeezes East. If he pitches a spade, you lead the Q, ducking as he perforce covers, to establish the 7 as your twelfth trick. If East instead pitches a diamond, forcing West to guard diamonds, you then pitch a spade; now the spade duck rectifies the count, and West is later squeezed in the minors. Note the importance of not winning a top diamond early (or pitching a diamond from hand) else a diamond return would ruin the final squeeze.

A double squeeze without the count is a rare bird — and I believe impossible without an extended threat of some kind. Here, the ability to establish a long spade supplies the crucial element, forcing East to abandon his diamond stopper prematurely, thus fating West to a minor-suit squeeze.

Second place goes to overtaking the Q (Line C). This offers no advantage with a normal heart break, because the K must be cashed before the last heart, else you will have to commit before East. Also note that if hearts are 5-1*, you cannot benefit from 3-3 clubs against accurate defense — East can deny you two hand entries by refusing to cover the Q (or playing the K if you lead low).

*Several people noted that I did not state whether East follows to two hearts, as 5-1 hearts might dictate a different path. As usual with incomplete information, you should assume the ordinary (East follows) as I would have to tell you if he showed out and it were significant to the problem.

Third place goes to Line D (crossing to the A) which works if West’s singleton spade is the 10, 9 or 8 (close to 50 percent) or if East has both diamond honors. After running hearts and the K, East must keep four spades to prevent routine suit establishment, hence only one diamond. Next lead the Q; king, ace, dropping the 10/9/8 (hopefully); cross to the K and lead a spade (unless the 10 is good) then duck East’s intermediate to leave him endplayed.*

*Thanks to Lief-Erik Stabell (Zimbabwe) for this variation. Originally, I had overlooked the value of the 7 and awarded Line D only 5 (fourth place).

Fourth place goes to Line E (finessing the 10) which fails in the diagram but works when East has longer diamonds, or if West has both diamond honors.*

*Some would argue that East must have a diamond honor for his weak two-bid. Probably, yes, but I wouldn’t bank on it. Tournament players take great liberties at favorable vulnerability, and some desperadoes might not even have the K.

Lines A and B are worst, as breaching the spade suit early allows East to lead a second spade to kill any squeeze chance. The only hope then is a miracle in diamonds. The edge goes to Line A, as a successful diamond finesse would produce the same double squeeze for an overtrick — call it the thirteenth of never.

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

Anthony Golding: Playing East for only two clubs. On the hearts, I’ll pitch two clubs and a spade [assuming East keeps four spades] then lead the Q, ducking if covered. The heart run should have taken out East’s diamond guard (else spades run), and two more rounds of spades will see off West.

Toby Kenney: Assuming East has the K for his bid, I can always succeed; unfortunately, I need to guess the position. If East started with two clubs, [after running hearts] I lead the Q and duck… If he started with three or four clubs, I need to concede a club or play a guard squeeze. If I duck a spade early, East can return a spade to cut my communication. The position is unlikely to be easier to read if I keep the K, and overtaking the Q runs the unnecessary risk of a 5-1 heart break.

Jerry Fink: If East shows out on the second heart, I shall have to make a hard choice between the double squeeze (diamonds being the “both” suit), or simply playing for clubs 3-3.

Three-three breaks make bridge solemn. Double squeezes make the bridge column.

Grant Peacock: Just your everyday two-loser compound squeeze.

Radu Mihai: I discard a club on the first big heart and then have to decide if clubs are 3-3 (play is obvious) or West is longer (more probable). In the second case, I cash another heart discarding a club, then on the last heart East will be forced to keep four spades and thus only two diamonds; so I discard a spade, play the Q and duck East’s king, then squeeze West in the minors.

Tim DeLaney: The main line is a nonsimultaneous double squeeze with diamonds as the common threat. The spade position allows me to delay rectifying the count until after East is squeezed out of his diamond guard. If East has three clubs (unlikely), I will have to read the position accurately and lead a third round of that suit.

Jon Greiman: Assuming East has kept four spades, he cannot guard diamonds (I am hoping he doesn’t have three clubs). After leading the Q and ducking East’s king, I have a simple squeeze on West in the minors.

David Kenward: I first throw two clubs, which forces East to keep four spades; so he comes down to two diamonds, as I throw a spade on the last heart. Next I lead the Q and duck East’s king, then squeeze West in the minors. I just hope clubs aren’t 3-3.

Leif-Erik Stabell: Basically, I’m playing for West to have the sole club guard, since he might not have led a club from Q-J-10 bare; but if discards indicate clubs are 3-3, I might still have a chance to switch plans.

N. Scott Cardell: East [should] have the Q for his 2 bid (5 HCP minimum), and likely only one or two clubs from the bidding and opening lead. (Given six spades and the Q opposite one spade and Q-J-10 or Q-J-9, chances are about 94 percent that West has at least four clubs.) If so, there is a double squeeze (or a simple squeeze against East if he has Q-J both). Due to limited hand entries, I must run hearts before rectifying the count. When I lead the last heart, my hand will be A-J-7-2 5-3 8. If East comes down to three spades, I discard the 3 and set up my 12th trick in spades. If East keeps four spades, he can’t stop diamonds, so I discard the 2 and lead the Q, ducking East’s king to rectify the count to squeeze West in the minors.

Mauri Saastamoinen: East could easily have something like K-10-9-x-x-x x Q-x-x-x x-x. After running hearts, I will be able to take three spade tricks [if East kept less than four] else squeeze West in the minors; [in either case] I lead the Q and duck East’s king.

Charles Blair: If East has six spades and at most two clubs, no further guessing is needed.

Julian Wightwick: I pitch two clubs on hearts; then on the last heart, East must keep four spades,…so I pitch a spade. East can keep just two minor cards, and I hope he would have pitched a club [if he had three] to protect the diamond finesse. Next I lead the Q and duck the king, ending up with a minor-suit squeeze on West.

Jonathan Mestel: If East has [one or two] clubs, I can rectify the count by leading the Q and ducking — without having my diamond entry mangled.

Douglas Dunn: If East has fewer than three clubs, he will be squeezed without the count in spades and diamonds. If East holds on to K-x-x-x, I [pitch a spade] then lead the Q and duck East’s king to later squeeze West in diamonds and clubs. Even if East had three clubs, he may have to discard one; e.g., with K-10-x-x-x-x x Q-J-x 9-x-x.

Bill Powell: East is more likely to have two clubs than three. Therefore, he will have to relinquish diamonds to keep spades; then after leading the Q and ducking East’s king, West will be squeezed in diamonds and clubs.

Tong Xu: I only need West to have four or more clubs (or East to discard a club if 3-3); then he will be squeezed in the minors [after East unguards diamonds to protect spades].

Rob Balas: This is best, because the Q lead is likely from length, and [keeping A-K prevents] a squeeze against West being killed by a diamond return after ducking a spade. Running hearts will squeeze East in spades and diamonds in preparation to squeeze West in the minors. …

John Reardon: It is usually best to rumble your winners. This hand is no exception.

Bernard Danloy: If I assume the lead shows at least four clubs, the slam is made with a compound squeeze. On the last heart, East must keep four spades, so I pitch a spade; next I concede the Q to the king, then A-J squeezes West in clubs and diamonds.

Dale Freeman: I will pitch two clubs on the third and fourth heart; and on fifth heart, East must give up diamond control to keep four spades, so I pitch a spade. Now I lead the Q, East covers, and I duck to rectify the count; later I squeeze West in clubs and diamonds. If clubs are 3-3, I will probably go down. Ouch!

Rod Roark: Looks like this can always make double-dummy, but I’ll have to guess East’s pattern by the fourth round of hearts to do the right thing. If East keeps four spades and three diamonds, I’ll cash the last heart; East must unguard diamonds, then I pitch a spade, coming down to A-J-7 5-3 8. Then I play the Q and duck East’s king to rectify the count to squeeze West.

Jim Munday: Communication is limited, but I do have the material for a squeeze. West is likely to have the sole guard in clubs, while East certainly does in spades; so I can arrange a simple or double squeeze depending on how diamonds break. I can’t afford to lose a trick early, as the defense can damage communication. This line will squeeze East out of his diamond guard (if he has one), while I discard a spade; then the Q forces a cover and I duck, subsequently squeezing West in the minors.

Madhukar Bapu: … If East shows out on the second heart, I’ll play him for 6=1=3=3 and set up a club trick. If East follows to the second heart,…a squeeze comes into effect. Running hearts [forces East to unguard diamonds], then West can be squeezed in the minors after leading the Q and ducking East’s king.

Rob Stevens: Planning on a double squeeze. I am not going to guess a 3-3 club break, so I might as well avoid the risk of a 5-1 heart break.

Thijs Veugen: Then lead the Q and duck the K. Assuming East has at most two clubs, I have a double squeeze with diamonds the central suit.

Daniel Korbel: Not clear, but this will make for sure if East has only one or two clubs.

David Ingham: Looks like an easy double squeeze: Lose a pointed-suit trick, run winners, and gin — but it won’t work, as the same suit will be returned to foul my communication. Rather than a straight double squeeze, this has elements of a delayed-duck, compound and guard squeeze. The key is my fourth spade, which forces East to keep four spades (lest I establish a trick by ducking), so he is pinched down to two diamonds… Then I can duck a spade and squeeze West in the minors — as long as East doesn’t have a club left. …

John Lusky: The basic plan is to surrender a spade trick to East after squeezing him out of a potential diamond guard, then squeeze West in the minors. For this to work, East must be unable to break my communication in diamonds, so Lines D and E are out. For the initial squeeze to operate against East, I have to cash the second club before the last heart; so I might as well adopt Line F and not worry about hearts being 5-1.

Steve White: If I can guess Easts distribution, I am cold. Most likely, [running hearts] will force East to keep exactly two diamonds; next I lead the Q, ducking, then later squeeze West in the minors.

Abby Chiu: Playing for West to have — x-x-x-x-x J-x-x-x Q-J-10-x (or the like). Cashing the K and all hearts will first squeeze out East’s diamond guard; then after ducking a spade to East, West will be squeezed in the minors.

Rossen Georgiev: A double squeeze will be 100 percent if I can determine East’s shape… It’s easy if only two spades are discarded (I will throw a spade and squeeze West after leading the Q and ducking). Problematic is the discard of three spades. Did East start with seven spades? Or did he drop his [double] stopper with six? …

Dean Pokorny: Playing for a nonsimultaneous double squeeze. First, East is squeezed down to four spades and two diamonds; so I [pitch a spade] and lead the Q, ducking the king, then West will be squeezed in diamonds and clubs.

Nikolay Demirev: Practical and technical. On the last heart, East is squeezed in three suits if he remains with K-10-9 Q-J-x x;…but if he has one or two clubs as the lead suggests, he has to come down to K-10-9-x Q-x; then I lead the Q, covered and ducked, after which West will squeezed in the minors.

Lajos Linczmayer: I make the contract if West has longer clubs, which is likely the basis of…his opening lead. As East must keep four spades, he cannot keep more than two diamonds. After giving East a spade trick, I will squeeze West in the minors.

Jean-Christophe Clement: I hope East has two clubs or less. On the last heart, East must keep four spades, so only two diamonds; then the Q, covered and ducked, will lead to a minor squeeze on West.

Wei Victor Zhang: Planning to squeeze West in the minors. After running hearts, I’ll play the Q to duck, and later cash A-J to squeeze West.

Gerald Cohen: I hope East has no more than two clubs; then after five hearts, I can lead the Q and duck…

Carsten Kofoed: The lead suggests that West is loaded in clubs. First, I squeeze East in spades and diamonds; then I’ll lead the Q and duck to correct the tempo; and at last put pressure on West.

Ronald Kuip: It looks as if Line B (lead Q and duck when covered) is the essential move to make, but it should be executed after Line F, when East is reduced to K-x-x-x and two diamonds. I assume, of course, East has at most two clubs.

Frank Mulder: On the hearts, East is squeezed in spades and diamonds (assuming he has the Q or J) or has to reveal that clubs are 3-3. His last discard will determine what is going to be my 12th trick.

Nigel Weeden: West had a safe [spade or] heart lead, so I trust his lead is from Q-J-10-x-(x); so I plan to squeeze East in spades and diamonds, then West in clubs and diamonds. East is squeezed at trick seven and has to throw a diamond; count is rectified next by leading the Q, covered and ducked; then whether East returns a spade or diamond, West will be squeezed on the third spade.

Chuck Lamprey: I hate this hand. I’m going to take the position that West has club length, and I may have to take another later on the spade distribution.

Marek Malowidzki: Given the bidding [and lead], West should have 4+ clubs, so I’ll prepare for a double squeeze…

Robert Whitcher: Pitching two clubs, then a spade on the last heart after squeezing a diamond stopper out of East (obviously I keep the spade if East pitches down to three spades). Then the Q, ducking when East covers; win the spade or diamond return, and squeeze West in the minors. Of course, I will laugh hysterically if East can produce a third club.

Gerald Murphy: Next lead the Q and duck when East covers. [If East kept a double spade stopper], I retained two diamonds and a club,…so my two remaining spades will squeeze West in the minor suits.

Audrey Kueh: Assuming East has at most two clubs, the hearts squeeze East, who must retain four spades. Then I can rectify the count by lead the Q and ducking, later squeezing West in the minors.

Joon Pahk: I’ll play for East to have short clubs (or to discard from x-x-x during the heart run), so I can safely duck a spade to rectify the count and maintain entries…

Manuel Paulo: East may have a 6=3=3=1 distribution. On the last heart (South having pitched two clubs), East must discard from K-10-x-x Q-x-x (or J-x-x). If a spade, I win three spade tricks. If a diamond, I lead the Q, covered and ducked, to rectify the count for a minor-suit squeeze against West.

Ken Cohen: [If East keeps four spades], I come down to A-J-x x-x x then play the Q and duck to rectify the count. Anytime West started with four or more clubs, A-J will then squeeze him in the minors.

Paulino Correa: [If] East has Q-J, a [decent chance] after his bid, running hearts will reduce him to K-10-9 Q-J-x. Then the Q, covered and ducked, gives me three spade tricks.

Jeff Lesser: I plan on ducking the Q, when covered, eventually to squeeze West in the minors. East had to [unguard] diamonds to keep a [double] spade guard.

Subhransu Patnaik: Clubs are likely 4-2 or 5-1. On the run of hearts, I [expect] a spade-diamond squeeze on East; then [after losing a spade], a club-diamond squeeze on West. …

Dmitri Shabes: Always making double-dummy. :) After discarding two clubs and a spade (if East kept four spades), I now try to guess East’s two unknown cards (if a diamond honor was discarded, I can cash one diamond to reduce the guess further). If I think East has two diamonds, I lead the Q (covered) and duck. If I suspect East has at least one club left (unlikely after the lead, but maybe East showed up with a heart singleton or void), I must guess if his remaining diamond is an honor or not. Most defenders would give away the position by hesitation and/or sequence of discards.

Sandy Barnes: I must delay the spade duck until after hearts are run. If East reduces to three spades and three diamonds, [my long spade establishes]. If he comes down to four spades and two diamonds, A-J will squeeze West.

Problem 6

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

Note: West has two trumps. Both follow low on spade leads.

After winning the A:

Your Next Play	Award	Votes	Percent
B. Win A-K, ruff spade with 10	10	178	18
D. Draw trumps, win A-K, run J	9	275	27
E. Draw trumps, win A-K, ruff spade	8	432	43
C. Win A-K, ruff spade with 6	6	20	2
F. Draw trumps, win A, finesse J	3	55	5
A. Win A-K, ruff spade with K	1	41	4

Without a heart lead, this would be a twelfth-night comedy, needing only to decide how to start trumps; but now it’s serious business. With the A removed, you must obtain a discard for your heart loser, and entries are a concern. Should you draw trumps first? Or start spades at the risk of a ruff or overruff?

Suppose you draw trumps* and discover West has two trumps as stipulated.** Clearly, finessing the J (Line F) is inferior, as it loses to a doubleton queen in East, while the ruffing finesse is as good as the straight finesse. Therefore, you cash both top spades and lead the J. When all follow low, you face the critical decision: Pitch a heart for a ruffing finesse (Line D) or ruff and hope the queen falls (Line E). If you ruff and West shows out, you lack the entries to establish spades; so you must guess right.

*Cashing the K first is better because if West were void in clubs, he would likely have bid. An overcall after a 2-over-1 response doesn’t require much, so a club void would be a great incentive to bid 2 with K-Q-10 (if 5+ cards) as a lead-director, even without the A. Conversely, East would rarely bid over 1 with a club void and at most the J and A.

**Distributional information given in my problems is not a precondition but only describes what happens as you play. Thus, it becomes authorized only when it would be known at the table.

In general, it is better to hope the queen ruffs out (Line E beats Line D) per the vacant-space principle*, however, this situation is skewed by known factors. West’s opening lead indicated K-Q, which some would think gives West two known cards; but the proper deduction is one. West had to lead something, so the chosen K cannot be considered known for odds purposes, but the Q is.** Further, drawing trumps reveals that West has two; so West has three known cards, and East only one. Thus, East has two more vacant spaces, or one more at crunch time, which makes the ruffing finesse (Line D) superior.

*At the moment of truth, West has one more card than East, so he is more likely to hold the queen.

**Ignoring for practical purposes the slim chance that West might have led from K-x.

What about East’s 9 at trick one? As with the opening lead, a chosen card has virtually no bearing — unless it gives information about other cards. If it’s an honest signal (likely), East shows the J and denies the 10; i.e., one known card for East, and one more for West, effectively canceling each other out. Thus, the previous deduction that East has two more vacant spaces still holds.

Among Lines A, B and C (leading spades first), it must be best to ruff the third spade with the 10 to minimize the risk of an overruff. Ruffing with the king is super safe for that trick but then requires a trump finesse if the Q falls (or a blank Q with East if West shows out). Ruffing low can never gain, as saving the 10 only helps to pick up three trumps in East; but in that event, you are destined to fail anyway after ruffing a spade. The following deal shows the advantage of ruffing with the 10:

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

It is obvious that drawing trumps followed by a ruffing spade finesse (Line D) works; but so does Line B. After ruffing the third spade with the 10, cross to the A (felling the queen), ruff a spade high, and draw West’s last trump with the J. Ruffing with the K would also work (miraculously); but imagine how silly you’d look if West had Q-x-x.

Now it only remains to compare ruffing a spade early (Line B) with drawing trumps (Line D) to find the winner. Argh! A cursory look shows this to be extremely close, with no compelling evidence either way, so I had to do a detailed calculation. In order to compare fairly, Line D must be allowed to change if trumps break differently; e.g., if East has two trumps, vacant spaces become equal, so you should ruff the third spade rather than take a ruffing finesse. Further, I assumed the K is cashed first; then if East is void, the proper play is to draw trumps and lead a spade to the 10.*

*A first-round finesse is necessary, because you lack entries for a ruffing finesse, and East is far more likely to hold the Q. After the 10 wins (hopefully), you will cash the A, cross to dummy with a fourth trump, pitch a heart on the K, and lead the J. If the J is taken by the ace, your K-Q makes 12 tricks; if not, you will revert to spades.

Line B also has a deviation to consider: If the Q drops from East on the first or second round, should you play trumps differently based on new information that East is short in spades? I say no, because an expert East with Q-x-x and a club void would realize his queen would ruff out easily, so he’d drop it to lure you into playing trumps wrong. Therefore, considering the compelling prior evidence that a club void is more likely in East than West, you must stick to your original plan to maximize chances.

Using my Dual Suit Break Analyzer, with 11 spaces West, 12 spaces East, and ruling a spade void East as impossible (no Lightner double), I made the following table of West holdings that allow 6 to be made with proper play (not double-dummy). Columns for Line B and Line D show the percent chance of each holding that works for that line.

Case	West Clubs	West Spades	Line B	Line D
1	Q-x-x	x-x-x-x-x	0.0270	0.0270
2	Q-x-x	x-x-x-x	0.3718	0.3718
3	Q-x-x	Q-x-x	1.4875	—
4	Q-x-x	x-x-x	1.4875	1.4875
5	Q-x-x	Q-x	1.1156	—
6	Q-x-x	x-x	—	2.2312
7	Q-x-x	Q	0.2550	—
8	Q-x-x	x	—	1.2750
9	Q-x-x	—	—	0.2231
10	Q-x or x-x	x-x-x-x-x	0.2231	0.2231
11	Q-x or x-x	x-x-x-x	2.2312	2.2312
12	Q-x or x-x	Q-x-x	6.6937	—
13	Q-x or x-x	x-x-x	6.6937	6.6937
14	Q-x or x-x	Q-x	3.8249	3.8249
15	Q-x or x-x	Q	0.6693	0.6693
16	Q-x or x-x	x	—	3.3468
17	Q-x or x-x	—	—	0.4462
18	Q-x	Q-x-x-x	2.9749	—
19	Q-x	x-x	—	5.0999
20	x-x	x-x	2.5499	2.5499
21	Q or x	x-x-x-x-x	0.4462	0.4462
22	Q or x	x-x-x-x	3.3468	3.3468
23	Q or x	Q-x-x or x-x-x	15.2999	15.2999
24	Q or x	Q-x	3.3468	3.3468
25	Q or x	Q	0.4462	0.4462
26	Q or x	x	—	2.2312
27	Q or x	—	—	0.2231
28	Q	Q-x-x-x	2.2312	—
Total chance of success			55.72	56.04

A photo! Line D appears to be the winner by less than half a percent. But wait! West is likely to have bid on hands with 11+ red cards — almost surely with the A and often without it. Therefore, Cases 17, 26 and 27 must be attenuated (also Case 25 but it affects both lines). Just how much is subjective, but any fair amount changes the outcome. Cutting them in half reduces Line D to 54.59, giving Line B over a 1-percent edge. Further, cases with 10 red cards West are exaggerated, of which Cases 9 and 16 favor Line D, so Line B is a clear winner.

A close second goes to Line D, not only from the preceding battle, but also because most failures mean down only one. Line B is more apt to go down two, e.g., if you get overruffed with the Q. Indeed, this factor could be enough to make Line D better; but it’s arguable pro and con, and I always resolve doubtful issues in favor of making the contract.

Third place goes to Line E, which is easy to calculate relative to Line D, as it gains in Case 12 and loses in Cases 19 and 20 for a net loss of 0.96, or 53.63 percent. I made this a close third, because West would be more inclined to bid with x-x than Q-x-x — a factor that could hardly make up the difference but surely closes the gap between Lines D and E.

A not-so-close fourth goes to Line C, which is clearly inferior, losing a big chunk to Line B in Case 20.

I won’t waste time calculating the obviously weaker Lines A and F, but common sense dictates Line A as worst (bordering on ludicrous) though it might draw a huge roar from the spectators if it works.

Thanks to Karen Walker (Champaign, Illinois) for this problem, which was posted on rec.games.bridge. No auction was given, so I created a plausible one. On the actual deal, North held K-J-8-7-3, and West played the nine on the first round — effectively meaningless because a falsecard would be routine — but I altered the spades to simplify presentation. Alas, this all-nighter was anything but simple.

Comments for B. Win A-K, ruff spade with 10

Anthony Golding: It appears to be a choice between Lines B and D. Line B wins on any 3-3 spade break, Q doubleton or singleton, West with Q-x-x-x and Q-(x), or East with Q-x-x-x and a [blank] Q. Line D wins on Q doubleton or singleton, or any length with East. Based on my extremely rudimentary probability analysis,…I’ll go with Line B.

Toby Kenney: This succeeds if spades are 3-3, or if they are 4-2 and the Q is singleton (and not with West if East has four spades). If I draw trumps first, I won’t have entries to ruff out a 4-2 spade split. …

Jerry Fink: Any 3-3 spade break, or 4-2 with the queen dropping, or a singleton queen, or 4-2 with West who also holds the Q, or 4-2 with East who also holds a blank Q, totals 70.5 percent. … Even if I do not take into account the information given about West holding exactly two clubs, odds favor Line B over Line E…

Grant Peacock: Line D is essentially 50 percent; but Line B works if spades split, or if West has Q-x-x-x and Q-x, or if East has Q-x-x-x and a stiff Q. I think this has to be an improvement.

Rainer Herrmann: This wins over Line E if East holds Q-x-x-x plus a singleton Q, or if West holds Q-x-x-x plus the Q singleton or doubleton. In the absence of a Lightner double, Line E wins over Line B if East holds five or six spades, but this is a lesser chance. … If my calculations are correct, a priori chances for Line B are roughly 55 percent…

Radu Mihai: If spades are 3-3, I’m home; if West has Q-x-x-x, best chance is to establish spades via a club finesse;…if East has Q-x-x-x, I win only if he has a singleton Q…

Bruce Neill: If spades are 4-2 the wrong way (length in East), I must hope East has a singleton Q. I don’t have communication to combine chances any other way.

Tim DeLaney: Line B, like Line E, hopes to find spades 3-3, but has two significant extra chances: (1) East might have Q-x-x-x with a singleton Q, and (2) East might have x-x with one or two low clubs. In both cases, I can ruff out the Q and get back to dummy, while a trump still remains in my hand.

Jon Greiman: This wins with 3-3 spades, or Q-x-x-x East with a stiff Q.

David Kenward: Besides a 3-3 spade break, this gives an extra chance of East holding Q-x-x-x and a stiff Q. If East shows out on the third spade, best chance is a club to the jack.

Leif-Erik Stabell: This gains over Line E when East has Q-x-x-x and a bare Q, as well as when West has Q-x-x-x and the Q [singleton or doubleton]. This loses out to 6-0 spades (either way) or Q-x-x-x-x with East; but in many of those cases, opponents would have bid.

N. Scott Cardell: If spades are 3-3, I’m home; or if the Q had dropped, I would have drawn trump and claimed. If East discards, I must try finessing the J… If West discards, I hope East has a singleton Q…

Mauri Saastamoinen: Difficult. [Several] lines seem to be equally good at first glance, but I think I should take into account all passes around the table. It seems that 5-1 and 6-0 spade distributions are less likely than normal, knowing opponents have nine cards in an unbid major. Thinking this way, Line B seems to give me a slim extra chance when East has Q-x-x-x and a singleton Q, or West has Q-x-x-x and Q or Q-x.

Charles Blair: If spades don’t split, I will know what kind of good luck I need in clubs. I wonder whether there are any cases in which an opponent should falsecard with the Q. Perhaps South should have bid 4 NT rather than 6 , in case North has followed South’s example in cue-bidding a king-queen; or could he have K-Q-J-x-x x J-x A-Q-J-x-x?

Julian Wightwick: The main chance is 3-3 spades or short Q. If East shows out on the third spade, I’ll ruff cheaply and finesse the J. If West shows out and cannot overruff the 10, I’ll need East to hold a singleton Q.

Jonathan Mestel: Gaining if East has a stiff Q. Is this a ruffing finesse?

Douglas Dunn: This seems the best percentage play, gaining when spades are 3-3 (36 percent), or a doubleton queen (16 percent); and also if West has Q-x-x-x and the Q,…I can finesse to gain an entry; or if East has Q-x-x-x and a singleton Q…

Bill Powell: Silent opposition suggests a 3-3 spade break will be more likely than a priori probability suggests. Of Lines A, B and C, this caters to more 4-2 spade breaks.

Rob Balas: I need to allow for West having x-x and 9-x,…or Q-x-x-x and Q-x (or a stiff queen)… If the 10 holds and West shows out, I cross to the A, ruff with the K, and return to the J. If East shows out, I ruff and hook the J.

Bernard Danloy: … Communication needs [suggest] not drawing trumps early… Line B always works with spades 3-3, and [has extra chances] of finding the Q with Q-x-x-x (where I need it to enter dummy twice without losing trump trick)…

Dale Freeman: Two situations with spades 4-2 are keys: (1) If West has Q-x-x-x, I will ruff and finesse the J to ruff again, then use the A to enjoy the fifth spade; and (2) if East has Q-x-x-x…and a singleton Q, ruffing with the 10 is a winner…

Rod Roark: If West discards when I ruff the spade, I still make if East has a stiff Q — better than other choices, which seem close to 50-50.

Thijs Veugen: This wins when (1) spades are 3-3, (2) the Q is [singleton or] doubleton, (3) East has Q-x-x-x and a stiff Q, or (4) West has Q-x-x-x and Q-x or a stiff Q.

Daniel Korbel: My initial instinct was Line D or E, but this gains against a significant percentage of 4-2 breaks while losing only to a spade void West (East could have doubled for a spade ruff if void) and most 5-1 breaks. Extra chances against Q-x-x-x add a lot of play [barring] 3-0 trumps.

David Grainger: Of Lines D, E and F, Line E is best a priori. Line B wins in all cases Line E wins, unless East has Q-x-x-x-x or spades are 6-0. To compensate, Line B gains if West has Q-x-x-x and Q-(x),…or if East has Q-x-x-x and a singleton Q.

Nigel Guthrie: Playing for (1) the Q to drop in three rounds, or (2) West to have Q-x-x-x and Q-x [or a stiff Q], or (3) West to have x-x and 9-4.

Sebastien Louveaux: If the Q falls or spades are 3-3, this is plain sailing (Lines D and F are minor variations, close to Line E in percentage). If spades are 4-2, I need two spade ruffs and two club reentries; if West has Q-x-x-x, I can finesse in clubs; if East has Q-x-x-x, the Q must be bare.

John Lusky: The virtue of Line B is that I can vary my play in trumps according to how many entries I need to establish and cash a spade. If spades are 3-3 or the Q drops doubleton, I will next play the K; if East has x-x, I will play a club to the jack; and if East has Q-x-x-x but West can’t overruff the 10, I will play a club to the ace hoping to drop the stiff queen.

Nikolay Demirev: Barring Q-x-x-x-x-(x) in East, this line gives a little edge when spades are 4-2. If East has Q-x-x-x, I need a singleton Q in East; if West has Q-x-x-x, I need Q-x or a singleton Q in West. Otherwise, there is a little tiny problem that after I set up the long spade and pitch a heart, I will be out of trumps.

Lajos Linczmayer: … Playing spades first is better, [gaining] when East has Q-x-x-x and a bare Q, or West has Q-x-x-x and Q or Q-x (finessing the J).

Brad Theurer: If spades are 3-3, or either opponent holds a doubleton queen, it doesn’t matter if I draw trump first or not. Critical cases are when one opponent holds Q-x-x-x; if West, I must delay drawing trump due to entry considerations; if East, it appears I need to draw trumps if I intend to play for that holding,…but [Line B still works] if he has a singleton Q…

Murat Azizoglu: I cannot afford to pull trumps first, since I run out of transportation to dummy if spades are 4-2. I don’t give much thought to ruffing with the K and finessing clubs… If West has only two spades and the Q, I’ll go down…

Chuck Lamprey: On the surface, Line E looks best; but I think this gives me some additional chances. If East shows out on the third spade, I can try a first-round club finesse; while if West shows out (without overruffing), I can try to drop the singleton Q.

Robert Teesdale: This loses [compared to Line D] only when West has short spades (without the Q) and the Q (overruff).

Marek Malowidzki: This still leaves some chance when spades divide 4-2.

Leonard Helfgott: Normally Line E would be superior to Line D by 11-to-10; but with clubs 2-1, they are mathematically equal [ignoring inferences from the lead]. Line E loses to Q-x-x-x in [either hand] with any club holding, while Line B [has chances].

Ken Cohen: This works when spades are 3-3, or East has Q-x-x-x and a stiff Q with the clue that West [couldn’t overruff].*

*Ken’s comment, like some others, is based on my given information that “both follow low on spade leads.” Hence, he omits (but is surely aware of) the case of Q-x-x-x West with a blank or finessable Q. -RP

David Brooks: If the Q does not drop, there is a chance the Q is singleton in East, allowing me to ruff the fourth spade with the K.

Barry Rigal: This makes against 3-3 spades, and also when East has a stiff Q. Maybe I can do better, but I can’t see how!

Carlos Dabezies: This wins if spades are 3-3, or East has a [blank] Q. Because of entries, Line E requires a 3-3 spade split; Line F is only fractionally better than 50 percent; Line D is better than E or F because Q-x-x-x East is more likely than Q-x-x West [given the lead and club break]. Line B offers fewer losing possibilities than Line A or C.

Daniel de Lind van Wijngaarden: I win whenever spades are 3-3. If East has Q-x-x-x, I win if he also has Q bare, as I next play a club to the ace. If West has Q-x-x-x, I play a club to the jack next, winning whenever West has Q-x (or a stiff Q). … Conditions of this problem are awkward, as a priori chances (not knowing West has two trumps and both follow on spade leads) differ from the given situation. A complete analysis, accounting for 3-0 trumps and 6-0 or 5-1 spades, might show Line D is best.

Final Notes

I hope you enjoyed the contest, and recollection of the haunting renditions of “The Twelfth of Never” by Johnny Mathis, Elvis Presley, and others. Thanks to all who participated, especially those who offered kind remarks and personal wishes. I only wish I had time to reply individually to all the wonderful people out there. I will bid you adieu for a spell, but like General MacArthur, I shall return.

Comments are selected from those scoring 50 or higher (top 209) or in the overall Top 200 prior to this contest, and on each problem only those supporting the winning play. This may seem biased, but I feel it’s the best way to ensure solid content and avoid potential embarrassment in 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.

Finally, let’s rectify the count by tricking a few ducks:

Bill Cubley: I have no chance! There’s no Twelfth Street in San Leandro where I live; and there’s no longer a Twelfth Street in Detroit where I was born (it was renamed Rosa Parks Blvd. if you need to know).

Charles Blair: “With all those aces and trumps, it shouldn’t be too difficult.” -Rueful Rabbit

Kevin Conway: Your quizzes show how complex bridge can be, whether it’s bidding, leading, defending or declaring. All that’s missing was a “You Are Dummy” quiz. Couldn’t you have found some hands where an irregularity occurred and dummy had options?

Mary Marx: Why do I get the feeling that no matter how carefully I plot these out, nothing works?

No idea, Mary, but it would be Duck Soup for your brothers.

Analyses 8X96 Main Challenge

Scores Top The Twelfth of Never

Acknowledgments to Jerry Livingston, composer of title song
© 2006 Richard Pavlicek