Analyses 7V48  Main Challenge

Dog Days of Summer

Scores  by Richard Pavlicek

These six play problems were published on the Internet in August 2001, and all bridge players were invited to submit their answers. As South on each problem, you are dealt a real “dog” yet fate has made you declarer.

Problem 1

2

3

4

5

6

Final Notes

Wojtek Siwiec Wins!

*And Boca Raton, Florida. I’m also pleased to say that Micki is one of my advanced students.

Among the rejected entries this month was one from Rin Tin Tin. Aww… a reminder of my childhood… “Yo! Rinty!” I enjoyed the laugh, but I can’t start a precedent to accept fake entries (politicians excluded). Doggone it!

Bidding is standard (except as noted) and your opponents use standard leads and signals.
For a reference see Standard American Bridge. Assume all players are experts.

Each problem offered six plausible lines of play. The merit of each is scored on a 1-to-10 scale, based on my judgment, so a perfect score would be 60. These problems were not easy, but the respondents did exceptionally well overall (the average score was the highest of all my play contests).

Problem 1

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

At trick two West leads the J, you win the king and East plays the 7.

Your Next Play	Award	Votes	Percent
B. Cash three diamonds, finesse Q	10	33	10
C. Win A, 3 to queen, finesse Q	9	13	4
D. Lead 3 to queen, finesse Q	7	44	13
A. Cash four diamonds, finesse Q	5	108	33
E. Win A, A, 3 to queen, lead to Q	4	86	26
F. Win A, lead 3 to queen, lead to Q	3	43	13

The bidding and early play mark West with exactly five spades, surely A-K-J-10-x. (The A demanded East to unblock or give count.) Assuming the K is onside from West’s opening bid, that finesse offers eight tricks, and the ninth should come from establishing the long club. The obvious problem is to do so without allowing East to gain the lead.

West is likely to have shorter clubs ( K-x) and, if given the chance, he will unblock the king to defeat your avoidance maneuver. Further, entry conditions allow only one club lead toward dummy (with two leads this would be a lot easier). Cashing the A first (Line E or F) is a vain attempt, as an expert West with K-x would surely see the light. No, you must take advantage of your one club lead from hand.

So, how many diamonds should you win first? The popular choice was to cash all four (Line A), but this would fail in many common layouts such as:

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

If you cash four diamonds, West would beam in glory to jettison the K, and your contract is history. This would be obvious too, since West can see you’d have at least nine tricks if you held the J. After winning the third diamond, you should follow Line B: Lead a club* to the queen (or unblock the 10 if West pops the king). Then, you must go with the odds and lead the 10 (note the need to waste the 10 to create a fourth-round entry to reach your last diamond).

*If diamonds did not split 3-3, it would be logical to cash the fourth diamond. If West had a doubleton diamond and failed to jettison the K, he surely has length in clubs. A few respondents noted (and didn’t like) that this created an obscurity in Lines A and B, however, I couldn’t tell you how diamonds break without spoiling the problem. The intended distinction was that in Line A you would always cash four diamonds. Sorry if you missed my drift.

Cashing even three rounds of diamonds might be wrong, e.g., if West held A-K-J-10-8 J-10-8-x x-x K-x, he would ditch the K on the third diamond. This suggests Line C, a strong contender. To decide which play is better, it is necessary to study the critical case when West has a doubleton diamond, hence six cards in hearts and clubs. If you assign West J-8* K (and East Q-7), that leaves seven missing cards ( 10-6-5 J-9-8-2) which means there are 35 ways (7C3 in combinatorial notation) to fill the West hand. Of these, nine contain K-x and nine contain K-x-x, which suggests a toss-up. No, three cases of K-x can be eliminated (West would never lead the J from J-8-6-5). Alas, six cases with K-x-x (when West holds J-8-6 or J-8-5) are tainted because West might not have led the jack (though it is certainly as good as leading low). So far, I would not be convinced either way, but there’s more: Line B also gains when West has four clubs. Further, when Line B fails you go down one, while Line C goes down two. This gives the edge to Line B.

*Note that I assume the 8 because East’s signal with the seven should deny that card.

Line D (cashing only one diamond) is clearly inferior to Line C because you would not discover when West has a singleton diamond. In that event it is clearly right to play West for club length (K-x-x) since he would have competed to 2 with 5-5 in the majors at the vulnerability.

Comments for B. Cash three diamonds, finesse Q

Prakasam Narasimhan: (1) If West follows to three diamonds: If West puts up K, duck; otherwise finesse Q then lead 10 placing West with K-x. This play gives a fourth-round club entry back to hand to cash fourth diamond. (2) If West does not follow to the third diamond, he is likely to be 5=3=2=3 with K-x-x or K-J-x. Then, low club to queen, cash A and concede a club. …

Michael Clark: This prevents West from being an absolute genius and chucking the K under your fourth diamond when he’s 5=3=3=2.

Rob Stevens: … It seems best to cash three diamonds first. This loses immediately when West holds 5=5=1=2 or 5=4=2=2 (barring K-J doubleton) but gains on 5=2=3=3 and 5=2=2=4. The latter two patterns are more likely than the former. If diamonds are 3-3, I will [lead clubs and] play West for 5=3=3=2 (losing the 10 to West’s king). … If West follows to two diamonds only…, I will cash the fourth diamond…

John Reardon: It looks as though West holds five spades and three hearts, and to succeed I must place West with the K and at least one more club, so he has at most three diamonds. If I cash too many diamonds, he may be able to throw the K from a doubleton, but there are also advantages in cashing three diamonds now. One bonus is when West has a singleton diamond and is 5=3=1=4. In this case I will cash the fourth diamond to force him to make a critical third discard, enabling me to establish my ninth trick. If he throws a heart, I will continue with the club finesse followed by A, A and another club. …

Gabriel Nita-Saguna: If West shows three or more diamonds, I will play him for K-x. … If he has less than three diamonds, I will play him for three clubs to the king (club to the queen, cash the ace and follow with the 10), provided he has not discarded the K on the third diamond (which he would do with 5=4=2=2, 6=4=1=2 or 5=5=1=2, but I think these are less likely than all the 5=3=2=3, 5=3=3=2 or 5=2=4=2 distributions; West probably would have bid again after 2 having 5-5 or 6-4 in the majors).

N. Scott Cardell: … There are two basic ways to play the club suit: (1) Finesse the Q then lead the 10 (unblocking to reach your hand on the fourth round of clubs) hoping for K-x with West, or (2) Finesse the Q and cash the ace, hoping for K-x-x with West. … Line C and follow plan (1) [if West follows to two diamonds] gains when West is 5=4=2=2. … Line B gains when West is 5=3=2=3. … Also, Line C goes down two when it fails, while Line B never goes down more than one. …

David Breton: I want to lose a trick to West’s K. I can’t see a solution unless I’m playing double-dummy, so I will try playing very fast hoping for a penalty card.

Barry Rigal: If West has three diamonds, play him for K-x; if two diamonds, play him for three clubs. If you cash the fourth diamond, maybe West will pitch the K.

Comments for C. Win A, 3 to queen, finesse Q

Malcolm Ewashkiw: The problem, of course, is still not over. You must decide if West has 2 or 3+ clubs to the king. Line C protects against West being 5-4-2-2.

Stephen Tu: If West has two diamonds, I cater to him holding K-J-x or K-x by ducking if king appears, else play Q then 10, paying off to J-x offside. If West has only one diamond, I think odds are higher he is missing J (singleton can open with less points) and has three clubs, so I cash the ace next. … Playing more than two diamonds, or playing A, has too much risk of a jettison from K-x.

Tonci Tomic: Club ace is out of question because West can unblock with K-x. East (probably) encouraged with 7, which means that West has at least three hearts. That doesn’t leave room for lot of minors. … If West discards [on the second diamond] I will play him for K-x-x; otherwise, K-x.

Jonathan Weinstein: Assuming both players were honest in hearts, West is marked with J-10-8 and East with Q-7, with the six and five unknown (unless West has J-8 doubleton). This means the odds favor West having four hearts, so if he follows twice in diamonds I want to play for him to be 5=4=2=2.

Sid Ismail: The problem arises on the next club — A or 10. Was West [dealt] K-x-x or K-x?

Grant Peacock: I’ll play West for nine cards in the majors and four in the minors. So, I lead the 10 next, assuming he hasn’t shown out of diamonds.

Walter Lee: Do these “expert opponents” know they are defending a play contest?

Of course they do… I keep the little devils in a pickle jar between hands.

Walter Lee: Then next time, they should lead the 10 from J-10-8-6 and play the queen from Q-7-5.

Bob Boudreau: Next have to guess whether West has K-x or K-x-x; that’s why I played two rounds of diamonds.

Problem 2

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

After winning the K:

Your Next Play	Award	Votes	Percent
A. Win A, ruff club, lead J to queen	10	60	18
D. Win A, ruff club, lead 2 to nine	9	59	18
E. Win A, ruff club, win A	8	67	20
B. Win A, ruff club, lead J and let it ride	5	71	22
C. Win A, ruff club, lead 2 to queen	4	43	13
F. Lead the 3	2	27	8

Note: If you lead J or 2, West plays 4.

Your weak two-bid was not exactly a thing of beauty (or a joy forever), but you can’t expect to win on style points with all these dogs about. To succeed, you will need to establish the club suit (barring a miracle in spades), and it’s a matter of choosing the best technique. After the trump lead, the chance of a 3-2 trump break is much greater than usual (I would guess about 85 percent), so the main concerns are how the clubs will break and how to handle the spades.

First, let’s eliminate the weakest attempt. Line F (ducking a club) reduces your chance to about 50 percent — anytime the K is offside you are destined to fail after the obvious spade shift by West.

Line E (using dummy’s trump entry first) seems like the normal approach. It guarantees success when clubs are 3-3, but if clubs are 4-2 you will need the K onside. Putting this into ballpark math, the probability of success is 36 + 48 x .5, or about 60 percent. Not bad, but you can improve on this by retaining dummy’s ruffing control in diamonds.

So, how should you finesse spades? The main concern is to create two spade entries to dummy when the K is offside, so Lines B and C are seriously flawed. If you run the J, East can hold up the king; and if you lead low to the queen and king, the ace will be your only spade entry* to dummy. Both of these lines are inferior to the simpler Line E.

*Barring a doubleton 10. Note that if you attempt to finesse the 9 later, West will foil you by putting up the 10.

Lines A and D are both good. Essentially, either requires at least one spade honor onside and clubs 3-3 or 4-2, which amounts to 76 x 84, or about 64 percent. In these simplified calculations I did not consider the possibility of an enemy spade ruff (extremely far-fetched after a trump lead) or a 4-1 trump break.*

*If the possibility of 4-1 trumps is considered, the difference between Lines E and A/D diminishes. Using my 85-percent estimate for 3-2 trumps (based on the lead) and more accurate club-break percentages (3-3 = 42.31 and 4-2 = 57.69 since other breaks are eliminated) the results are remarkably close, but the same winner emerges. Line E = 42.31 + 57.69 x .5 x .85 = 66.83. Line A/D = 42.31 x .76 x .925 + 57.69 x .76 x .85 = 67.01. (The .925 factor is because with clubs 3-3 you succeed against 3-2 trumps and half the 4-1 breaks.)

Here is a typical layout that shows the advantage of leading spades early:

IMPs	A Q 9		Trick	Lead	2nd	3rd	4th
E-W vul	A K		1. W	9	K	2	4
	4 3		2. N	A!	8	2	10
	A 7 6 5 4 3		3. N	3	9	5	K
10 7 6 4		K 8 5	4. S	J!	4	Q!	K
9 8 7		3 2	5. E	2	J	Q	3
A Q 9 7		K 10 6 2	6. W	A	4	6	5
K 10		Q J 9 8	7. W	7	A	10	8
	J 3 2		8. N	4	Q	10	6
	Q J 10 6 5 4		9. S	Q	7	5	3
	J 8 5		10. S	J	8	6	5
4 South	2		11. S	2	7	9!	8

Let’s follow Line A. At trick four you lead the J to the queen (key play) and king. What can East do? Nothing. You still have control of diamonds with dummy’s A, and three entries to dummy to establish and use the clubs. In fact, East had better shift to diamonds to cash out, else you’ll win an overtrick. Line D would accomplish the same thing.

Another subtle factor that supports Line A/D over Line E is the matter of undertricks. For example, suppose East holds K-x-x 8-7-3-2 K-x-x-x Q-x, where you will always fail. With Line E, you will go down two or three (you may even lose your A if you take the finesse late), while Line A/D goes down only one (after winning the K East will probably return a trump to prevent a possible diamond ruff, then when you ruff a club and discover it is hopeless, you can draw trumps and win two spades).

Are Lines A and D equal? Not quite. One possible advantage for Line D is when West has both the K-10 and trumps are 4-1; you could then win 10 tricks on power. Unfortunately, to capitalize on this against most distributions you must abandon your primary chance of establishing the clubs; i.e., when the 9 holds, you must follow a different path — cash the A so you can draw trumps, or ruff a club and hope to cash your spades immediately (or possibly pitch a diamond on the third club) — any of which would fail in the above layout. The point to bear is that when the 9 holds it proves only that West has the 10; East might be holding off with the king. Nonetheless, there are a few distributions* (e.g., if West has K-10-x 9-8-7-3 A-Q-x K-10-9) where you will still survive after your main chance fails, and this is an advantage for Line D.

*Thanks to N. Scott Cardell for noting this.

On the other hand, I can see three advantages for Line A: (1) You will succeed against a singleton 10 with East, (2) you will win an overtrick (or two) when West has the K and East the 10, and (3) the lie of the spade suit will be a mystery to West. To clarify the last advantage, suppose East in fact holds K-10. If you lost the 9 to the 10, it would be an open book for West to lead another spade as soon as he gained the lead in diamonds. But when you lead the J to the queen and king, West does not know where the 10 is (you could easily have J-10-x). Hence, if West held x-x-x-x 9-8 A-Q-x-x K-10-x, he might conclude that his best defense is to tap dummy with a third diamond, hoping partner has J-x-x.

Comments for A. Win A, ruff club, lead J to queen

Prakasam Narasimhan: This creates two entries to dummy required to set up clubs when they divide 4-2, assuming K-10 are divided (or both with West). The playing of jack is to prevent West, holding 10-x-x, from frustrating the efforts by playing the 10 later to deny a second entry to dummy.

Stephen Tu: I think Line A is better by a microscopic smidgen over Line D (singleton 10 offside, followed by two diamonds and a spade ruff). All that’s needed is the 10 or K onside, with a 4-2 club split. …

Neil Morgenstern: If clubs are 4-2, I need an extra entry to dummy, and this is the best way to create one. Of course, I could look silly if clubs are 3-3 all along, but this is against the odds. …

Leonard Helfgott: If the spade finesse is on, everything works when clubs are 4-2. Line B fails if East ducks, and Line C fails when West plays the 10 on second round. Line E relinquishes control of the third round of diamonds (when K is offside), and Line F loses when West wins, cashes two diamonds and leads a spade. The nonintuitive Line A allows for a second spade entry when the king is offside.

Tonci Tomic: Lines B and C work when the K is onside or clubs are 3-3 (about 68 percent). Lines A and D work when the K or 10 is onside (about 75 percent). … Line A is slightly better than Line D. …

Gareth Birdsall: Lines A and D maximize the chances of two entries to dummy. Line A is preferable because losing the lead would increase chances of a trump promotion.

Herbert Wilton: Why lose to a possible 10 by adopting Line D, which is basically equivalent?

Tommy Cho: To gain [an extra entry] on the chance of West holding either K or 10.

George Klemic: Line F can’t be right; West wins and plays spade. Line B looks wrong too; if K is offside, a holdup will eat your entry… Line C messes up the second entry when the K is offside. Line D is premature, [losing] an overtrick when K is working. Line E works if either 3-3 clubs or K onside, but Line A works also when 10 is onside. Looks like the winner to me.

Branko Vlajnic: This provides the necessary entries; whereas in Line C West could insert 10 on second round.

Colin Smith: Close with Line D, but I would prefer to get over there now if possible. Line B misses the point, and East should find it easy to hold up, while Line C [loses] when East wins.

Nigel Guthrie: If West has K or 10, you can establish clubs when they are 4-2. (If instead you run the J, a cunning East ducks.)

Andrew de Sosa: Play for split spade honors, if necessary. I need to risk K-10 offside to gain the extra entry necessary to set up clubs when they split 4-2, as expected.

Darrell Gibson: I don’t see much difference between Lines A and D; both create a second finesse to reach dummy a second time in spades. I think A is slightly superior because of the improved chances for playing safe (and overtrick possibilities) if the K is onside.

James Hudson: Leaving a heart in dummy to take care of diamond plays; trying to maximize my chances for two dummy entries in spades.

Mark Rishavy: This gives the best chance of having two entries to dummy in spades, which I will need if clubs are 4-2. Low to the queen allows West to put in the 10 on the second round to hold the entries to one. …

Robin Burns: Any of the other options leave open the chance of West making a clever play of rising with the 10, thereby denying dummy the vital extra entry if clubs are 4-2. West has to hold either the K or 10 for the contract to make.

Bob Boudreau: If it wins, I have an extra entry to ruff clubs; if it loses, I might have to take a second finesse in spades to get the extra entry.

Sandy Barnes: I need to set up clubs, and I need two spade entries if the clubs are 4-2.

Rosalind Hengeveld: A toss-up versus Line D (spade to nine); this line may win a mere IMP. But I’m a Dutch girl, and Dutch girls have been known to win a world championship by half an IMP.

Phil Clayton: Best play to get an extra entry in case clubs are 4-2. Letting the J ride gets foiled by East holding up. Leading low to the Q allows West to play the 10 as a blocking play [on the second round]. …

Daniel Korbel: … This way I make whenever either spade honor is onside, assuming clubs are 4-2 or better.

Problem 3

IMPs	Q J			West	North	East	South
None vul	10 4			LHO	Partner	RHO	You
	A K J 9 4 2			Pass	1	Pass	2 1
	A K J			Pass	2 NT2	Pass	4
				Pass	Pass	Pass
Lead: Q		East plays K
				1. weak
				2. artificial force
	A 10 9 8 7 5
	8 6 5
	7
4 South	10 9 8

At trick two East leads the 2, ducked to dummy’s jack (West plays 3).

Your Next Play	Award	Votes	Percent
C. Lead the 10	10	61	19
E. Win A-K (no honor drops) to pitch heart, ruff diamond	8	142	43
A. Lead Q to the ace	7	22	7
D. Win A-K (no honor drops) to pitch heart, run Q	5	51	16
F. Win A-K (no honor drops) to pitch club, ruff diamond	3	42	13
B. Lead Q and let it ride	1	9	3

The contract is excellent, so your first thoughts might be along the lines of Murphy’s Law: If something can go wrong, it will go wrong. Yes, the spade finesse worked once, but we all know that proves nothing. But even with the K offside, there are good prospects of establishing the diamond suit, and a last-resort club finesse to boot. Line E was the popular choice, as it pursued these two chances in a direct manner. Alas, Line E abandons the additional chance of ruffing a heart in dummy.

The crux of the problem is to realize there’s no hurry to start diamonds. The threat of an easy heart ruff forces the opponents to lead trumps twice, and this can be put to your advantage when trumps are 4-1. Consider this ominous layout:

IMPs	Q J		Trick	Lead	2nd	3rd	4th
None vul	10 4		1. W	Q	4	K	5
	A K J 9 4 2		2. E	2	5	3	J
	A K J		3. N	10!	2	6	J
K 6 4 3		2	4. W	4	Q	3	7
Q J 9 3		A K 7 2	5. N	A	3	7	5
6 5		Q 10 8 3	6. N	K	8	8	6
5 4 2		Q 7 6 3	7. N	2	10	8	2
	A 10 9 8 7 5		8. S	A	6	4!	6
	8 6 5		9. S	8	4	A	7
	7		10. N	9	Q	9	5
4 South	10 9 8		11. S	9

The key play is to lead dummy’s remaining heart at Trick 3. For the defense to have any chance, West must win and return a low spade. This spoils your heart ruff but gains a precious tempo in the pursuit of your primary goal — call it a “delayed Line E.” When you ruff the third diamond, West will pitch a club (best). Next cash the A and pitch a diamond from dummy — not a club, as West could then beat you with a timely ruff. Finally, lead a club to the king, ruff a diamond, and lead a club. West is helpless to win anything but his K.

If you pursued the straightforward Line E, you would soon discover the impasse. West will pitch a club as you ruff the third diamond, then you cannot manage both drawing trumps and establishing diamonds. (If you lead trumps, West will win and force you with a heart.)

Note that West’s duck of the first spade was a necessary defensive maneuver; if he won the king, you would have an easy time regardless of the return.

In the event East were able to lead a second trump after you lost the 10, you would rise with the ace and be no worse off in your plan to set up diamonds. If trumps are 3-2, the play is routine. If East turns up with four trumps, you need diamonds to establish with one ruff, else a club finesse (or if West has long diamonds, a show-up squeeze).

Comments for C. Lead the 10

Prakasam Narasimhan: If East wins and returns a spade, go up with the ace then: (1) If trumps are 3-2, enter dummy with a diamond, ditch a heart on the K, ruff a diamond and concede a spade to the king. … (2) If trumps are 4-1, you will lose control if you try to set up diamonds when 4-2, so [in that event] concede to the K, and later take a club finesse after drawing the outstanding trump.

Radu Mihai: They have to play a trump back, and I win and make if trumps are 3-2, or with four trumps West, or with four trumps East if the diamonds are 3-3 or the club finesse works. This line fails if East has four trumps and the Q and diamonds are 4-2. But it is hard to believe that East, having K-x-x-x, some hearts with A-K, probably a doubleton diamond and the Q finds nothing to say over 1 . So, assuming diamonds are no worse than 4-2, this line is nearly 100 percent.

Rob Stevens: Barring 5-1 diamonds, I will always make on 3-2 trumps. If trumps are 4-1 then, paradoxically, I am in better shape if they are offside! … Nothing is lost by leading a second heart. … The big advantage comes when spades are 4-1 offside. Now West will have to win the second heart and lead another spade from his king, which neutralizes the effect of his low trump. …

John Reardon: The only defense to trouble me now is when East wins the A and leads another low spade. I will win with the A, cash A-K discarding my last heart, then ruff a diamond. If spades were 4-1 and the Q is still out, I will exit with a trump. East must exit with a heart to trouble me, and even then I will make unless East has the guarded Q since there is a show-up squeeze in clubs and diamonds (assuming West has the diamond guard). If East has the diamond guard I would just take the club finesse, which is odds-on since East would already have shown up with 12 points.

Malcolm Ewashkiw: Just because the J won doesn’t mean the finesse is working. Line C is the clear winner because it forces the opponents to play trumps, [then] you can take advantage of the 4-2 diamond break. If they choose to play clubs through dummy instead, you can arrange to ruff a heart in dummy after all.

Gabriel Nita-Saguna: I can make the game in either of the following cases: (1) spades are 3-2, regardless of who has the king; (2) West has four spades; or (3) East has four spades, and either diamonds are 3-3 or West has the Q.

Manuel Paulo: I think that Line C is the only winning line when West has something like K-6-4-3 Q-J-x-x x-x x-x-x, the upset being that my expert opponent did not choose a low black card on the lead. Against other hands, Line C seems to be as good as [or] better than any other.

Tonci Tomic: If spades are 3-2 and diamonds no worse than 4-2, I’m home. Leading the 10 also works when West has four spades and two diamonds.

Gareth Birdsall: This is better than Line A or E since it also allows us to make against K-x-x-x offside (since they are forced to play trumps again to prevent a heart ruff). Line F may go down if I am overruffed on the fourth diamond and put back in dummy.

Charles Blair: The only problem arises if East wins and leads a spade. I play the ace. If West shows out, the bidding and play both make a club finesse (after testing diamonds) a good bet.

Grant Peacock: Line A needs a 3-2 spade split or a 3-3 diamond split or a club hook. That is above 90 percent, but Line C offers one extra chance: If East is out of spades he must duck, and West must lead another spade away from his king. Now declarer is in control.

Walter Lee: Playing for a show-up squeeze when East psychs with K-x-x-x A-K-x-x-x x-x Q-x.

Andrew de Sosa: East does not necessarily have the K. Assuming East wins and returns a spade, will play the A, followed by A-K (pitch heart), diamond ruff. If East started with four spades and diamonds aren’t 3-3, I may have to revert to the club finesse. If West started with four spades, however, I will either get to ruff a heart in dummy, or West will have to win the second heart to return a trump, but this gives up a valuable defensive tempo.

Anne Bell: If trumps split 3-2, the contract is safe provided a heart is pitched at the right time. To have a chance of defeating the contract, the defense must return a trump, thus revealing the 4-1 split. If East wins the heart lead, then declarer wins the A, crosses to dummy with a diamond, pitches the heart, and ruffs a diamond. If diamonds split 4-2, then the suit must be abandoned; clear trumps and try the club finesse.

Rick Kelly: Lets see how spades are breaking before committing to a line of play. I can always pitch a heart on a diamond later…

Noer Imanzal Kartamadjana: … The problem here is when West started with K-x-x-x.

Franco Baseggio: Basic plan is to play A and try to ruff out diamonds. Threatening to ruff a heart can gain a key tempo if West has four spades, though. The only layouts where you can go down on this line are those in which East might have acted, e.g., K-x-x-x A-K-x-x x-x Q-x-x.

Marcos Paiva: If they can play spades, I’ll try to establish diamonds; if this fails, I must win the club finesse; and if this fails, I’ll cry.

And if crying also fails… start breakin’ some tables.

Daniel Korbel: This will force the defense to lead another round of trumps, then you can win the ace, cash the A-K pitching your heart, and ruff a diamond. Two board entries remain to set up diamonds.

Bruce Cook: I don’t trust West. I think he has the K (probably four long).

Problem 4

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

After winning the A:

Your Next Play	Award	Votes	Percent
C. Duck a diamond	10	144	44
F. Win K, heart to king, duck a diamond	9	102	31
D. Win K, heart to king, lead a heart	8	28	9
E. Win K, heart to king, win A-K	5	14	4
A. Win A-K, give up a diamond	3	27	8
B. Win A, duck a diamond	1	12	4

Five clubs is a sound contract, especially with the A surely onside. Assuming a 3-2 diamond break, which you’ll probably always need, there are 10 tricks in view, and an 11th can come from a spade ruff or the K. Almost any sensible play will work if trumps split, but the fierce enemy bidding vulnerable is an omen to the contrary. Consider this layout:

Matchpoints	A		Trick	Lead	2nd	3rd	4th
Both vul	K 8 7 2		1. W	J	A	9	2
	A K 8 6 3		2. N	2	6	K	10
	A 5 2		3. S	3	6	K	5
K J 10 7 5		Q 9 4 3	4. N	2	J	4	9
A 10 9 6		Q J 5	5. E	Q	3	A	7
Q J 5		10 9	6. S	2!	5	A	9
10		9 8 7 6	7. N	K	10	4	J
	8 6 2		8. N	8!	7	Q	10
	4 3		9. S	7!	Q	3	3
	7 4 2			Declarer succeeds w/dubious line
5 South	K Q J 4 3

Line B can be quickly dismissed as inferior, probably yielding an easy diamond ruff. Line A is better but leaves an insoluble problem with a spade return — you’re dead in the water having to lead from dummy at trick six. Line E (then give up a diamond) may be better yet, as the opponents must cash their heart immediately. In short, none of these lines gives any real chance against 4-1 trumps with best defense.

Line D works like a charm. Win the K and lead a heart to the king as West ducks (best), then give up a heart. If the defense returns a trump, simply win the ace and duck a diamond. If instead they return a spade, ruff; A-K; heart ruff; spade ruff; then the last heart, pitching a diamond if East ruffs. If they return a third heart, ruff; A-K; then ruff (or overruff) the last heart and concede a diamond.

If you duck a diamond at trick two (Line C), a diamond return is pretty obvious, giving you no further chance. If you draw trumps and run diamonds to pitch your spades, dummy is endplayed in hearts. Or if you lead a heart early, West will hop and give East a diamond ruff.

Line F ( K, K, diamond duck) also fails, as a spade return locks you in dummy. There is no way to return to hand to draw trumps, so the opponents will either win a spade trick or force dummy to ruff with the A.

While the above layout is realistic, it is certainly not the only one to consider. On other distributions Line C or Line F fares better, so finding the true winner took some effort.

First, I had to determine the probability of various distributions. Rather than go through a difficult calculation, I did a computer simulation: I gave West K-J-10-7-5* A (East Q-9-4-3) and randomly dealt the remaining cards, accepting only those deals in which West had a minimum-range opening. The computer tallied the West distributions for a million appropriate deals to find the percent chance of each.

*In theory, West’s spades could be J-10-x-x-x, but this is far-fetched — not only from the fact that West opened the bidding but also because of his choice of leads (I would lead a spade spot, if only to guard against a blank queen in dummy and A-9-8 in declarer’s hand). Also, there’s a good argument that East might not jump raise with Q-9-x-x and out, but the LOTT assures us an endless supply of daredevils.

In order to verify which Line (C, D, F) works against each distribution, it was necessary to define the lines further. For Line C, I assumed a diamond return, after which there are two reasonable plays: (C1) Win the K, ruff a spade high and draw trumps hoping for a 3-2 trump break, or (C2) Win the A-K and lead a heart. For Line D, I assumed a heart return forcing South to ruff; then declarer wins the A-K and leads the last heart (the winning sequence in the diagram). For Line F, I assumed a spade return (best) which forces declarer to rely on 3-2 trumps. The results are shown in the following table:

Case	West’s Pattern	Percent	Winning Line
1	5=5=2=1	11.24	C2
2	5=4=3=1	13.36	D
3	5=4=2=2	17.04*	C1 C2 D F
4	5=3=3=2	11.73	C1 F
5	5=3=2=3	2.72	C1 C2 F
6	5=2=3=3	2.91	C1 C2
7	5=2=2=4	0.85	None
8	5=1=3=4	0.44	C2

*This percentage is inflated from real life because it gives East 4=3=3=3, and even devout LOTT followers might draw the line on some of those hands. Fortunately, it doesn’t affect the comparison since all lines work.

I did not list distributions with diamonds 4-1 (or either minor 5-0) since it was obvious none of the lines would work. Totaling percentages for winning cases shows Line C1 (34.40 percent) to be best by a whisker (or should I say, a dog hair) over Line C2 (34.35 percent). Line F (31.49 percent) was next, followed by Line D (30.40 percent). So be it, and so go the awards. I would have thought otherwise.

This problem was adapted from a deal played by Michael Arnowitt and posted on the rec.games.bridge newsgroup. In the actual deal South held Q-x-x, but I changed it to three low spades (1) to make the enemy bidding more realistic, (2) to simplify the analysis (sigh, that didn’t work), but most important (3) to give South more of dog!

Comments for C. Duck a diamond

Radu Mihai: I need diamonds 3-2 (no line wins without this). If they return a diamond, club to the king, spade ruff high, and club to hand; this will make anytime trumps are 3-2. Line A (they’ll play a spade) and Line B (they’ll probably make a ruff) are the worst. If I play a club to hand and a heart, West may take immediately his ace and lead a spade. Now, if I try to make two heart ruffs in hand (or to discard a diamond on the last heart), I can make with trumps 4-1 (when East is 4=3=2=4) but, more often, I’ll be the subject of an uppercut when trumps are 3-2. If I duck a diamond, they’ll play back another spade and I’ll need trumps 3-2, still risking a promotion. …

Rob Stevens: I must find both minors 3-2 in order to make. Since it is matchpoints, there is a case for finding a line that is safer for down one, but no clear line exists that doesn’t lead to extra possibilities for failure when both minors are 3-2. Therefore, it is best is to duck a diamond immediately. Leading a club to hand and a heart toward dummy, the only reasonable alternative, fails when West holds 5=2=3=3. He can rise ace and force dummy with a spade. Now I will have no way to get diamonds going without conceding a trump promotion.

Malcolm Ewashkiw: A 4-1 diamond break spells doom, but you can handle some 4-1 club breaks. Line C makes any time trumps are 3-2, and also if trumps are 4-1 unless West (with A) has three diamonds. Lines A and E subject you to a spade tap on dummy. Line B risks a diamond ruff when they are 3-2. My notes tell me that Line D risks defeat with a heart ruff, but those notes were made long ago and I’m not sure at this very moment why that is so! Line F will work if trumps are 3-2, but risks defeat when trumps are 4-1. So, Line C it is.

Neil Morgenstern: If diamonds are 3-2, and either West has the A or can’t get in because diamonds are blocked, I am now in control. … I’ll also need clubs 3-2.

Leonard Helfgott: Lines D, E, and F fail when West rises with A and forces dummy with a spade (and repeats on a diamond duck) when clubs are 4-1. Also, Lines A and B fail when clubs are 4-1 and diamond communication is destroyed. Line C appears to cover more bases.

Manuel Paulo: To win with any line, I need diamonds breaking well, thus it’s logical to duck a diamond. … Line D is the only winning line against 5=4=3=1 West distribution; on the other hand, Line C wins against 5=1=3=4, 5=2=3=3 and 5=5=2=1, and the joint probability of these distributions is bigger than the other.

Tonci Tomic: Don’t want to go down if diamonds and clubs are 3-2. The problem with Line F is that West can have A doubleton; he will not duck the heart in that case.

Gareth Birdsall: With so few top losers it’s disappointing to only offer a line of play requiring two suits to split 3-2.

Bob Simkins: This contract is almost impossible to make if diamonds are 4-1, but I [may be able to] handle a 4-1 club break if I am careful.

Walter Lee: My plan is to induce East to lose the singleton he has during the bidding. I will play as few cards as possible and then pray really hard.

Frans Buijsen: This wins if diamonds are 3-2. I have the feeling all the others can’t really deal with clubs 4-1 even if they try, but I’m probably wrong again.

Mark Rishavy: On Line A (or B if they play a third diamond) I will lose the link to dummy and have problems ruffing a spade, drawing trump and still using the diamonds. The  K as an entry won’t work because they can cash a spade after I draw trump. I think that Lines D through F will fail if trumps are 4-1. …

Rainer Herrmann: Assume diamonds to break evenly, otherwise there seems little chance. Best defense requires clubs to break evenly as well, however, Line C requires a diamond return from the defense, which may be difficult if clubs are 4-1. Line F requires only to continue spades and force dummy, not too difficult if looking at four clubs.

Arian Lasocki: Preserve communication in diamonds, less threat of a diamond ruff, and maintain spade control.

Barry Rigal: Most lines need diamonds 3-2, so I might as well assume the A is onside — as it should be.

Franco Baseggio: They have to come back a diamond; now play A-K, heart and hope East didn’t start with two diamonds and three clubs.

Pete Jackson: Give up the loser while dummy’s clubs control the spades. The K should win later.

Arvind Ranasaria: I need diamonds to break 3-2. … If I play the A and duck a diamond, I risk a diamond ruff. If I play A-K and another diamond, a spade will be returned to force dummy to ruff, then after drawing trumps when I lead a heart, West will hop up with the ace and cash a spade. All this is avoided with a simple diamond duck at trick two.

Jojo Sarkar: Everything seems equal. I have no clue what’s going on!

Neither do I, really… But I quote a lot of percentages to sound smart.

Arpan Banerjee: … The A is well-placed from the bidding. A diamond needs to be ducked immediately, planning next to ruff a spade and take out trumps…

Bruce Cook: It looks like you need the A onside and reasonable splits in the minors. Lose your sure losers early.

Problem 5

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

After winning the A:

Your Next Play	Award	Votes	Percent
C. Win A-K (pitch club), A, ruff heart	10	127	39
A. Lead the 3	8	43	13
D. Win A, A, ruff heart, K, give up a club	7	58	18
B. Win A-K (pitch spade), A, ruff heart	6	44	13
F. Duck a club	3	37	11
E. Win A-K, give up a club	1	18	6

The respondents were right on target again. To make 5 you almost surely need a 3-2 club break, but you do not need a 3-2 trump break. West’s trump lead was a valiant attempt to foil the crossruff evident from the bidding. Here’s a typical layout to consider:

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

If the defense started with two rounds of spades, a successful crossruff would be easy. With the trump lead, however, only Line C will succeed. After the first heart ruff, you will return to dummy with a club and ruff the last heart to reach this ending:

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

You now simply exit with your last club to pose a dual threat and render the defense helpless. If West leads another trump, you can draw trumps and score the good club. If West instead leads spades to tap dummy, you can ruff the last club in your hand.

This deal actually occurred in a knockout team event. Well, almost. As South, I really had two jacks (blank J and J-4-3-2) and made six. (When the Q fell doubleton, I could ruff the last heart and draw trumps; diamonds were 3-2 so I had 12 tricks.) At the time I was proud to have chosen diamonds (preferring the suit with texture over a lousy jack) as only 11 tricks were available in clubs. My partner, however, was more concerned about how we could bid the slam.

Comments for C. Win A-K (pitch club), A, ruff heart

Prakasam Narasimhan: This play assumes a 3-2 break in clubs is necessary to make the contract, even if diamonds are 4-1. Enter dummy with the K and ruff the last heart, then give up a club. If the defense punches dummy with a spade, a club ruff can be taken; if the defense returns a trump, the fourth club in dummy can be cashed after drawing trumps.

Radu Mihai: I have to make two heart ruffs and three club tricks. So, A-K (pitch a club), A, heart ruff, K, heart ruff and lead my last club; they have no answer. Of course, I take the risk that East, having less than five cards in clubs and hearts together, will make a ruff. But this risk is present (and even bigger) on the other lines, too. …

Rob Stevens: I need clubs to break, but can stand a 4-1 diamond break. I will use the twin threat of either ruffing two hearts and a club in the South hand, or, should the opponents lead a second diamond after conceding the third club, draw all the trumps and score the fourth club.

John Reardon: The danger is when East has something like: K-Q-J-10-6-3 Q-8-5 3 Q-J-9. I will continue with a club to the king, ruff the last heart and exit with a club.

Malcolm Ewashkiw: In the likelihood of a 4-1 trump division, you must play to establish the dummy. … Line C continues with a club to the king, ruff the last heart and lead a third club. Now, if the opponents play a second trump, dummy is good, and if they tap dummy, I can ruff the fourth club in hand. Bingo! I don’t believe you can make this contract if clubs are 4-1…

Gabriel Nita-Saguna: I need clubs to be 3-2. This is better than Line B because it brings 11 tricks, even when trumps are 4-1, by ruffing the last club from dummy with the last trump from my hand — in case they play two rounds of spades to shorten dummy’s trumps [and prevent drawing trumps].

Michael Scanlon: Then K, [ruff the last heart] and give up a club. If nothing nasty happens, I can survive a 4-1 trump break; the defense can choose to let me draw trumps or crossruff, but I will make 11 tricks either way.

Neil Morgenstern: Then a club to the king, ruff a heart and lead a club. … If they force dummy in spades, I can ruff the last club. And if West gets in to lead a trump, I draw them all and win the last club.

Leonard Helfgott: Lines A, D, E, F appear to be jeopardized by 4-1 diamonds. Line C beats Line B because it allows for ruffing the good club in hand, if necessary, since they can’t force dummy in spades and lead a second trump simultaneously.

N. Scott Cardell: … This makes so long as clubs are 3-2 and the hand with the doubleton club can’t sluff it on the third round of hearts. After ruffing the heart, return to the K; when both follow you can claim 11 tricks. … All the other lines are likely to fail if diamonds are 4-1.

Manuel Paulo: To win with any line, I need clubs breaking well… Line A is the only winning line against 2=6=2=3 West distribution; on the other hand, Line C wins against 2=4=4=3 and 2=5=4=2, and the joint probability of these distributions is more than twice bigger than the other. Line C also wins against 2=7=2=2 West distribution, when East can ruff the K or pitch a club with no profit in every case.

Gareth Birdsall: With only four outside winners and the defense able to reduce me to a maximum of six trumps tricks, it’s clear I need clubs 3-2. I can succeed against 4-1 trumps with Line C. After ruffing two hearts in hand and losing the third round of clubs, if trumps are 4-1 then the defense must force me with spades (else I can draw trumps); but then I can counter by ruffing the fourth club in hand.

Steve White: Pitch a club so you can ruff the fourth round if they force dummy after you give up a club.

Bob Simkins: I will usually go down when clubs don’t break; so I need to worry about a bad diamond break. If I ruff two hearts (pitching a spade) and then sell a club, I will go down when diamonds are 4-1 because the defense will force dummy to ruff a spade. [Line C] counters this, as I can crossruff the rest. This also makes against the only 4-1 club break I can handle: when the hand with a stiff club also has a stiff diamond.

Charles Blair: I plan to continue K, heart ruff, club.

Venkatesh Ramaratnam: This succeeds even when diamonds are 4-1 provided clubs break 3-2 and hearts are benign.

Grant Peacock: [Then continue with] K, heart ruff, club. If East is 6=2=3=2, this will fail, as compared to Line G: A, A, heart ruff, K, heart ruff, draw trumps — but that can’t be right since it’s not listed.

Show me a man who votes for Line G… And I’ll show you a man with courage (or a stupid bot).

Branko Vlajnic: [This will succeed] against a 4-1 trump break.

Colin Smith: … Aiming to present the opponents with the choice of letting me ruff the fourth club or make it naturally.

Nigel Guthrie: Then a club towards the king, ruff a heart and concede a club. … If opponents exit in trumps, draw trumps; if they exit in a major, ruff the last club.

Gowniyan Vaideeshwar: [Later] if the opponents force you to ruff a spade, you can ruff the last club.

Rainer Herrmann: I assume clubs to break evenly to have a chance. Line C requires East to have five cards in clubs and hearts, but makes even if diamonds are 4-1.

Bill Cubley: A high crossruff should do it if the aces and kings cash.

Bill Powell: This will let me make when trumps misbehave (they won’t be able to draw trumps and force dummy in spades).

Arvind Ranasaria: This way I just need clubs 3-2 and can cater to a 4-1 diamond break. …

Stefano Biciocchi: Can’t win with clubs 4-1, but must with diamonds 4-1: [continuing] K, heart ruff, duck club; then I can draw trumps or crossruff. Cashing the A at trick four may save an undertrick if clubs are 4-1.

Problem 6

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

Note: Trumps split 2-2.

Your Play	Award	Votes	Percent
E. Duck, ruff second club, lead J	10	104	32
F. Duck, ruff second club, win A-K, A-K	9	54	16
D. Duck, win A (pitch diamond), A-K, lead trumps	6	46	14
B. Win A, ruff club, A, ruff club	4	78	24
A. Win A, A-K, ruff club, lead J	3	36	11
C. Duck, win A (pitch spade), A-K, lead trumps	2	10	3

OK, 6 is an overbid, but prospects are better than it might seem. With the spade finesse marked, you have 11 top tricks.

One possibility is an elimination and throw-in against West, as instigated by Line B. After ruffing out clubs and drawing trumps, the plan is to cash A-K and exit with a diamond. This might work, but it takes a miracle: West must have a doubleton (or singleton) K and be obliged to win the third diamond, e.g., K-x J-x Q-J-10-9 K-Q-J-10-x. Note that if West had three spades, he could simply exit with a low spade; or if he were not solid in diamonds, he could unblock to avoid the endplay.

Forget that long shot. Chances are much better if you try for a squeeze. In fact, in the likely event that West has five or more clubs you can always succeed, though you might have to guess his pattern. This will not be an ordinary squeeze but a compound type involving threats in three suits. Consider this typical layout:

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

To rectify the count you duck the first club, and then you must decide whether to win the ace next or ruff. You must ruff because you cannot afford to discard from your hand (the spade and diamond threats in South may be necessary later).

Let’s follow Line E first. West should cover the J, else you will have a simple positional squeeze against West. After winning the A, you draw three rounds of trumps ending in your hand to reach this position:

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

When you lead the 9, West is triple squeezed as you discard a spade from dummy. West obviously must keep his club stopper, and your continuation depends on which other suit he abandons: (1) If he pitches a spade, do not cash your last heart yet; win the A; A (pitch a diamond); Q; then lead the last heart to complete a simultaneous double squeeze. (2) If he pitches a diamond, lead your last trump and pitch a diamond from dummy; then A-K squeezes West out of his spade stopper, and the A squeezes East in spades and diamonds.

Line F also works. After cashing A-K in both red suits, you will lead another trump to reach:

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

On the 9 everyone pitches a diamond (West is obliged to pitch the Q sooner or later since he cannot afford to blank the K). On the 5 West must pitch a spade; you pitch a club from dummy, and East discards a club. Next comes the J (West must cover else his king falls on air) to the ace, then the A squeezes East as before.

So which is better? Both lines have the built-in frailty that you might misguess the distribution, but there are two cases where only one of the lines has a chance. If West is 4=3=1=5 or 3=3=1=6, Line F will suffer a diamond ruff — ouch. Yes, I told you trumps were 2-2, but this was just to answer a question you would soon discover; you would not know this at trick three when the two lines diverge. Hence, the top award goes to Line E.

Albeit far-fetched, it is interesting to note that if West shifts to a diamond at trick two, Line E will no longer work. (The extra diamond entry is crucial in the variation where West abandons spades.) Instead you must reach the ending of Line F, but you don’t need to risk a diamond ruff. Because a club ruff is now available to return to hand, you can draw three rounds of trumps before cashing the second diamond.

As you might expect, it takes an original diamond lead to beat the contract.

Comments for E. Duck, ruff second club, lead J

Prakasam Narasimhan: From the bidding West is clearly marked with the K. If West ducks the J, he can later be brought under a club-spade squeeze. If West covers the J, a double squeeze can be developed by watching carefully his discards; [the sequence] depends on whether he unguards spades or diamonds.

Radu Mihai: Clubs seem to be 5-3 (looking at East’s five), and anyway this is my best chance. … If West covers the J, win the A and four trumps discarding a spade from dummy. At this moment only East can guard both spades and diamonds. I have to read correctly the situation. If East is the only one to keep diamonds, win the last trump and discard a diamond; A-K squeezing West; A squeezing East. If East is the only one to keep spades, win the K; A (diamond discard); Q and the last trump for a simultaneous double squeeze. Other lines destroy somehow the entries or menaces, or don’t lose a trick early enough.

Rob Stevens: I need the sole club guard and the K with West; both likely. West will cover the J to avoid a simple squeeze, so the hand will probably become a highly inflexible and ambiguous compound squeeze. I will need to keep spade and diamond threats in the South hand, and the need to rectify the count means I must duck the first club and ruff the second. [On the next-to-last trump] I will have to guess which of the pointed suits West abandons. If West holds six clubs, I will not even have the luxury of seeing any pointed-suit discard. …

John Reardon: I am playing for a compound squeeze and will duck to rectify the count. If West has something like: K-10-3 J-4 Q-10-6 K-Q-J-9-3, he must cover the J at trick three or he will undergo a simple squeeze in the black suits. Then I will reach… [detailed squeeze description].

Stephen Tu: I play West for 5+ clubs and all the high cards. He must cover the J (else a simple squeeze in the blacks), so I win, and run the hearts until… [detailed squeeze description].

Leonard Helfgott: For this compound squeeze to work you need to concede a trick before committing yourself and maintain a threat with entry against East’s pointed guards. Obviously, this has to be a spade quack, so Line E is best. If West doesn’t cover the J, pull trumps, [cash the diamonds], pitch a diamond on the A, and squeeze West in the blacks. If West does cover, you will force him to pitch one of his pointed guards on the next-to-last heart… [detailed squeeze description].

N. Scott Cardell: … This can always succeed if West has the K and five or more clubs (very likely on the bidding, particularly after West turns up with a doubleton heart). … If West ducks the J, he is subject to a simple spade-club squeeze…, so he must cover. Now you take four rounds of trumps sluffing a spade… [detailed squeeze description]. This deal is an example of Clyde Love’s “alternate-threat squeeze”; either the 5 or the 7 becomes the threat, depending on how West discards.

Gareth Birdsall: I need to duck the first club to rectify the count, and the second club because I don’t know what to pitch. If West ducks the J, I will have a simple positional squeeze against him. If he covers, I’m well-placed for a compound squeeze. If West’s shape is, e.g., 3=2=3=5, then on the fourth heart he must pitch one of his pointed-suit guards (or a club which is fatal) then the play will continue as a double squeeze.

Manuel Paulo: Assuming that West has the K and five or more clubs, I have 11 tricks. I can make the slam via a compound squeeze, so I need to duck a club, and it’s better to do it as soon as possible. Lines E and F both work, but I choose Line E because it leads to a simple (and easier) squeeze when West decides not to cover the J.

Bob Simkins: I’m glad they didn’t lead a diamond. …

Charles Blair: I am playing for a compound squeeze based on West having the K and at least five clubs. I think this works even if West switches to diamonds at trick two. When declarer has Q-J-x x-x x-x, West must keep three clubs. If he unguards spades, Q-K-A, A (discarding diamond), club ruff, J, heart. If he unguards diamonds (North discards diamond), Q-K-A, club ruff, heart, A, A.

Venkatesh Ramaratnam: Routine technique to execute a pure squeeze. Further continuation depends on whether West covers or not.

Grant Peacock: The A is needed for a squeeze card.

George Klemic: … If West ducks the J, then play as a simple squeeze on West (holding K-x-x and 5+ clubs). If West covers… [detailed squeeze description].

Walter Lee: I know this is an Error, but I am allergic to Failure. :(

Nigel Guthrie: A mutate! Clyde C. would “Love” it! West started with, say, K-10-x x-x Q-10-x K-Q-x-x-x, and covers the J to avoid a simple squeeze; but is in trouble on the fourth heart… [detailed squeeze description].

Gowniyan Vaideeshwar: Even if the J is covered, you are in line for a compound squeeze.

Anne Bell: As well as rectifying the count quickly, I want to preserve as many squeeze menaces as possible… (also, it’s possible that clubs split 7-1), so Lines E and F look the most promising. Line F destroys communication between the hands, whereas Line E increases it, for West is forced to cover the J in order to prevent the spade menace becoming isolated. Line E works any time West starts with five clubs or more.

Rick Kelly: A squeeze looks like best shot, so I will keep the club threat alive. Tricky discarding by the opponents could give me a guess in the end.

James Hudson: Playing West for at least five clubs. If he ducks the J, I’ll squeeze him in the black suits. If he covers, I’ll hope for an [eventual] double squeeze.

Franco Baseggio: Assume West has 5+ clubs. He must cover the J or be subjected to a black-suit squeeze. After that, run four trumps, forcing West to unguard either diamonds or spades: If diamonds, play a trump pitching a diamond then cash A-K, A; if spades, win A, A (pitch diamond), Q, heart. …

Jeff Goldsmith: If West is 2=2=4=5, I have an easy double squeeze around diamonds. If he’s 3=2=3=5, there’s a compound squeeze…

Anil Upadhyay: … To have any chance, West must have five or more clubs and the K. If he ducks the J, I have a simple squeeze against him in clubs and spades… If he covers, cash four more trumps… [detailed squeeze description].

Arvind Ranasaria: This allows me to develop one of two squeezes. If West covers the J (else he will be subjected to a simple positional squeeze in the black suits) it establishes a late Q entry to hand, and I can set up a double squeeze depending on the way West discards… [detailed squeeze description].

Final Notes

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

Comments are selected from those above average and only in support of the winning play (except Problem 1). While this might be considered biased, 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 about 80 percent of the eligible comments. If you supplied comments that were not used, I thank you for the input.

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

In this edition, the top award for Problems 1, 2, 4 and 6 turned out to be a close choice. This happens sometimes, though not usually by intention. (In two of the cases, my original choice proved to be inferior after analysis.) In the future I will try to make more winning answers clear-cut — if only to save myself some work (famous last words). I think I got all the winning choices correct, but the number of photos makes me less confident than usual.

Bone appetit! That is, if you can enjoy a meal with these dogs barking:

Bill Powell: More fun than chasing a stick!

Grant Peacock: … I hope I’m eligible for the prizes. My partner says I play the hand like a dog, I’m fully house trained, and I have 16 years of education which (as far as I can tell) focused primarily on obedience.

Anthony Golding: A good test, as always, but I hope I managed to whippet.

Phil Clayton: Does the winner of this contest get bestowed the title PAVlov’s dog?

Analyses 7V48 Main Challenge

Scores Top Dog Days of Summer

© 2001 Richard Pavlicek