Analyses 8Y24  Main Challenge

Beware the Ides of March

Scores  by Richard Pavlicek

Veni, Vidi, Vici

Hopefully the above three words apply to you! These six problems were published on the Internet in March of MMVII 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 I

II

III

IV

V

VI

Final Notes

Many people did not like the matchpoint scoring, but IMPs were unknown in ancient Rome. Roman scoring was actually called matchsticks, awarding I stick for a tie and II sticks for a win. Augustus also noted in his diary that patricians and senators were honored with III or IV sticks, and emperors with V or VI, which no doubt accounts for the decline of bridge. Plebes never stood a chance in tournaments.

Further evidence circa A.D. LVIII revealed that anyone winning even II matchsticks against Nero would be tossed into the Colosseum ring. Trust me on this. I ain’t lion!

I also received complaints about the “Roman leads and signals” with no explanation of what this entails. Sorry, but “active ethics” did not exist back then, so you were lucky to get even that much. If you asked for an explanation at the table, you might be impaled by a dagger instead. The most devious agreement was odd-even signals (odd encourages) which caught many an opponent off guard. In fact the ACBL (Augustus Caesar Bridge Legion) banned these signals in A.D. XXVII. Alas, the ban never changed anything but only ensured that all agreements would kept secret.

[Addendum MMXVI: Two millennia later another Roman pair proves that odd-even signals are obsolete! Much more information can be transmitted by pointing each played card according to a predetermined code.]

This contest revived memories of high school, where I had to choose between Latin and Spanish as a foreign language. My teachers all recommended Latin, because the root words would increase my vocabulary. This made sense, as even in elementary school I could double my vocabulary with Pig Latin, but turned out to be a mistake. The future would bring a wife whose native tongue is Spanish, let alone that people actually speak it. Oh well… Veni, vidi, erravi.

Darek Kardas Wins!

Argh! Participation in this series began with 1269 (January), 1091 (February), and now 922. At that rate I could hit zero by October, but I rate to be spared by a parabolic curve. Come on, people! Tell your friends to participate. I swear, one more downturn and I’m bringing back Fritz! The average score (41.83) was above last month (40.83) but below January (42.61) however this reflects a variety of factors including field competence, problem difficulty and my scoring decisions. A total of 470 persons scored above average (42+) to make the listing.

Only one problem (I) was aced by the consensus, though the consensus score of 50 (10+9+6+8+9+8) was well above the average score (I haven’t kept stats on this, but the gap seems unusually wide). Two problems warranted a 9 award but were not photos; each winning line proved to be clear-cut.

Overall standings count your best two scores for January, February and March. February winner Tim DeLaney is on top, followed by current winner Darek Kardas, January winner John Reardon, and Bruce Neill — each with a perfect average of 60.00. Close behind with 59.50 are Leif-Erik Stabell (Zimbabwe), Lajos Linczmayer, Dean Pokorny (Croatia), John Lusky, Rob Stevens (California), and Dmitri Shabes.

Leads and signals are Roman, but that’s all Antonius and Brutus will say, since they want to bury you.
Bidding is standard (except as noted). 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 I

Matchpoints	A K 10 8			West	North	East	South
None vul	7 3			Antonius	Plebe	Brutus	You
	A 7 5 4						1 NT
	9 4 3			Pass	2	Pass	2
				Pass	3 NT	Pass	Pass
Lead: Q		East plays 7		Pass
	7 5 3
	A K Q 9
	K Q 3
3 NT South	J 8 6

West next leads the 5 to the ace, and East shifts to the 6.

Your Play	Award	Votes	Percent
E. Win A, lead J	10	267	29
D. Win A, A, K-Q	8	238	26
C. Win A-K-Q	7	19	2
F. Finesse the 9	4	39	4
A. Win A, finesse 10	3	133	14
B. Win A, finesse 8	2	226	25

Et tu, Brute? The surprising heart shift makes you wonder what Brutus is up to. Is he out of clubs? Hardly, as with A-7 he would overtake, and you would lose the first five tricks. No doubt, he holds A-7-2, with which he could read the 5 from Antonius as a four-card suit; hence, a club return and cash-out would only book you, and Brutus might be worried about a squeeze.

But wait! Brutus led the 6, and based on the Rule of XI, you can see all five higher hearts. You could finesse the 9 for your ninth trick. Whoa! Brutus may be an honorable man, but he’s not a benevolent one. He knows you have four hearts, so you should not presume any gratuitous meaning in the 6. Finessing the 9 is at best a 26-percent chance, and surely less, as Brutus is unlikely to tip off his hand.

After rejecting the heart finesse, thoughts of a spade finesse (Line A or B) should also be rejected, as you’d be down immediately if it loses. Line A offers less than a 24-percent chance, while diamonds might be 3-3 all along, or an opponent might hold J-10-x. If neither red suit delivers, you can still succeed if West has both spade honors*; though if West follows with a low spade, it seems prudent at matchpoints to cash out for down one rather than risk down three.

*Even though you lack a reentry to hand, if West splits his Q-J-x, you can win and exit with a club to endplay him. This is not foolproof, as West might have Q-J-x J-x-x-x x-x K-Q-10-5 and pitch a spade on the third diamond; then you would fail if you played him for Q-J-x-x.

Consider a plausible layout:

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

Brutus was rightfully concerned about the danger of running clubs. Looking at a spade stopper and a potential heart stopper, he could foresee the impending squeeze. He was obliged to encourage clubs, as he wouldn’t relish a diamond shift, and Antonius might have held five clubs. What’s bad for Brutus should be good for you, so your best chance is to win the A and lose the J immediately (Line E). If Antonius cashes his last club, it rectifies the count for your squeeze. Pitch a spade from both hands; win any return (assume the J); A, K and A to reach this position:

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

The next diamond lead not only tests for a 3-3 split but squeezes Brutus in the process. Note the importance of winning the third diamond in hand to keep entries fluid. The squeeze would work just as well if Antonius protected both majors. If Brutus instead protected both red suits, a different squeeze could have been executed*, though not in combination with the play of the above layout; i.e., you would have to guess to play for it.

*Assuming the same J return, you would have to cash both top spades while your communication in diamonds is still intact.

The recommended play after Line E also produces an easy double squeeze if spades are 3-3 (honors split) and Brutus has five hearts, e.g., Q-x-x 10-x-x-x-x x-x A-7-2. Antonius must keep a diamond stopper, Brutus a heart stopper, so neither is able to protect spades.

What if Antonius is less obliging and doesn’t cash his fourth club? No problem. Whatever the return, you can safely finesse the 10 into Brutus to develop the same squeeze — or if spades were 3-3, establish the fourth spade.

Second place is a close call between testing hearts (Line C) or diamonds (Line D) first. It’s almost immaterial, as your next play should be to test the other, ending in hand; then if neither suit produces a ninth trick, you will revert to spades, either to cash out, desperately finesse the 10, or endplay West if he splits. The edge goes to Line D, which has greater potential for an overtrick if diamonds are 3-3, and was also the voting pick.

Lines A, B and F are vastly inferior and can be ranked by straight percentages, based on the presumed 4-3 club split. Finessing the 9 (Line F) is about 26 percent; finessing the 10 (Line A) is about 21 percent; and finessing the 8 (Line B) about 9 percent. Line F is arguably less in practice, but I doubt it’s 5 percent less. It’s really a cat-and-mouse game whether Brutus should lead honestly or not, so the theoretical order will stand. Alas, if any of these poor plays work, you might be in greater trouble, as Antonius and Brutus may accuse you of dishonor. If you claim you thought clubs were 5-2, they will counter with ignarus est haud indulgeo.

Comments for E. Win A, lead J

Bruce Neill: Clubs must be 4-3, else East would have overtaken at trick one. Why did East switch? He must fear a squeeze, so I’ll oblige.

Lajos Linczmayer: I suppose East holds something like Q-x-x J-x-x-x-x J-x A-7-2, or Q-J-x-x J-x-x-x J-x A-7-2, and he can see that cashing four clubs leads to an automatic double squeeze. The  J lead cuts the enemy communication and prepares the squeeze.

John Reardon: These good opponents have not blocked the club suit. There is little prospect of an overtrick, so I lose a club now, forcing West to rectify the count for my putative squeeze [or lose his fourth club].

David Lindop: Early play in clubs indicates they must be 4-3. If West doesn’t cash the fourth club, I can give myself an extra chance in spades. If he does, East may be squeezed in hearts and diamonds, or there may be a double squeeze.

Joon Pahk: Brutus wouldn’t play the seven from A-7, so clubs are splitting. It looks normal to play for nine tricks, so I might as well tighten the screws for some kind of squeeze.

Tim DeLaney: That master of treachery, Brutus, is concealing the 2. With only two clubs he would surely overtake the Q and return the suit to run the first five tricks; so I lead the J. Whether Antonius cashes the fourth club or not, I will have several squeeze chances, though there is no sure thing.

John Lusky: Clubs are 4-3, and the defenders could have cashed four tricks but chose not to. What is not in their interest must be in mine, so I will make West choose whether to cash his fourth club to rectify the count for a possible squeeze, or abandon clubs to let me duck a spade.

Dmitri Shabes: Seems West started with K-Q-10-5. If he cashes his last club, I’ll try for a double squeeze (or diamonds 3-3 or J-10-x in either hand). If not, I can duck a spade to East for the [same chances]; or additionally, spades might be 3-3.

Richard Stein: If Brutus held A-7 doubleton, why didn’t he overtake trick one so clubs could run? Antonius can have his two clubs, then a squeeze [may] produce a ninth trick like fine olive oil.

I’ll fight to the finish, ‘cuz I ate my spinach… Sorry, but Brutus and Olive Oyl got me.

Leif-Erik Stabell: Clubs are 4-3, otherwise East would have overtaken the queen. West can now take the fourth club, hopefully squeezing partner; or lead something else, which lets me duck a spade to East.

David Grainger: East has the 2, so I’d better remove it.

Terry Henry: I suppose West had K-Q-10-5. If he takes his fourth club trick, I’ll discard spades and hope for a squeeze; if he doesn’t, I’ll try to set up a spade winner while keeping West off lead.

Dean Pokorny: Clubs were obviously K-Q-10-5 opposite A-7-2. This way, I make 3 NT whenever West squeezes his partner with the fourth club; and if he refuses to do that, I will try to find a ninth trick in spades.

Manuel Paulo: Assume East has one of these two hands (H = honor): sH-9-x-x hH-x-x-x dH-x A-7-2, or sH-x hH-x-x-x dH-x-x-x A-7-2. Leading the J disrupts the defensive transportation. West may or may not cash his last club, and East will be squeezed with or without the count in hearts and spades (or diamonds).

Carsten Kofoed: If West takes his fourth club, I’ll have the tempo for a squeeze.

Adrian Barna: To break communication or set up a squeeze (West surely started with K-Q-10-5).

Rob Stevens: These opponents have not blocked clubs. If West wins his last club, several squeezes exist, although I may have to guess if West exists with a heart.

Toby Kenney: If East doesn’t want to play clubs, it must be correct for me to do so. This will either rectify the count, or cut communication so I can rectify the count by finessing spades.

Bill Powell: East has three clubs (he’d overtake with two). This makes when diamonds break, or if I can pick the right squeeze.

David Kenward: It looks like West led from K-Q-10-5, so any of the finessing options are fraught with danger. I hope to squeeze East in the majors or reds, whether or not the fourth club is cashed.

Herb Lavine: Clubs are 4-3, else East would have overtaken at trick one to cash five tricks. If West refuses to cash his fourth club, I will duck a spade to East. There are many squeeze and suit-split possibilities. If West is 2=5=2=4 and refuses to take the 13th club, I will probably not make it.

Roger Webb: If East doesn’t want to cash clubs, I should encourage West to do so! If he doesn’t, I will duck a spade to East.

Imre Csiszar: Clubs appear to be splitting (East would have overtaken with A-7), so this does not risk immediate defeat and prepares a squeeze that may be needed for a ninth trick.

Steve White: Breaking communication; West must rectify the count or let me play spades safely.

Travis Crump: If the fourth club is cashed, I will play along double-squeeze lines; else I’ll play a spade to the 10 [with similar prospects]. If clubs are 5-2, my opponents are idiots.

Frans Buijsen: Forcing West to rectify the count for an automatic double squeeze, [else not score his fourth club].

Barry White: I expect West holds something like x-x-x J-10-x-x x-x K-Q-10-x, so I must lead a club to sever communication between defenders’ hands.

Sebastien Louveaux: It looks like clubs are 4-3 (East would have no reason not to play ace and another with A-7). Therefore, this is safe to lose [two] tricks to prepare a squeeze.

Enno Andvere: As East didn’t overtake at trick one, I’m inclined to place clubs 4-3. Best chance to develop a ninth trick seems to be a squeeze. If West refuses to cash has last club, I will play a spade to the eight.

Barry Rigal: Assuming East would never block clubs if they’re running for five tricks, I’ll get clubs out of the way and try for pressure in the ending.

Perry Groot: If East wants to keep communication in clubs, it must be right to cut it.

Okan Ozcan: I don’t think clubs are blocked… If West cashes the fourth club, I hope East is 2=4=4=3, so I can squeeze him. If West doesn’t cash the club, I’ll duck a spade to East and still squeeze him.

Tong Xu: If West (with K-Q-10-5) takes the last club, I will try a double squeeze if diamonds are not 3-3; else I can try all my chances in three suits.

Javier Carbonero: Clubs are 4-3, else the defense makes no sense. I intend to maximize my chances by rectifying the count, pitching a spade from both hands if West cashes out. If West doesn’t cash the last club, I will finesse the 8.

Gerald Murphy: West must have only four clubs, else East would overtake the queen. If West cashes out, I will have [all but one of the remaining tricks] to put pressure on East in spades and hearts.

Daniel de Lind van Wijngaarden: Cut the communication. If clubs were 5-2, opponents could have cashed them. If West cashes the fourth club, most of the time I can succeed on a squeeze; otherwise, I will finesse the 8 to rectify the count.

Eugene Dille: If West cashes the fourth club, I have squeeze chances; else I will duck a spade to East and try for a squeeze or a simple spade finesse.

Rainer Herrmann: Clubs are 4-3. I’ll start rectifying the count, since Brutus won’t do it for me. What squeeze to play for eventually will be more of a challenge.

Thijs Veugen: If East doesn’t want to lead clubs, it must be good for me to do it. :)

Andrew de Sosa: Clubs are 4-3. I must force West either to rectify the count for a squeeze, or give up on his fourth club trick.

Dale Freeman: It looks like East has A-x-x and does not want to take four club tricks now, so as not to rectify the count; he [may] have Q-x-x and J-x-x-x… I will sever the link in clubs; and if West does not cash the fourth club, I will duck a spade to East to rectify the count. Hopefully, something good will happen.

Roland Voigt: Assuming clubs are 4-3, I will not risk an early finesse but set the stage for a squeeze. … If West refuses to cash his last club, I can take a safe finesse in spades.

Zoran Bohacek: Among other reasons, if my dangerous opponents don’t lead a third club, it should be good for me.

Stefan Jonsson: Playing for a red-suit squeeze against East, or a double squeeze. If Antonius refuses to take his fourth club, I will finesse the 8 later to rectify the count…

Leonard Helfgott: East would have overtaken with only two clubs. …I will hope West cashes his last club to rectify the count, and I guess which squeeze to try — presumably best (with no added information) is to use spades as a double threat.

Charles Blair: Based on East’s switch, I will play him for 2=4=4=3 with the Q. If West does not cash the fourth club, I can lose a spade to East and then squeeze him in the red suits.

Jian Chao Wu: West has K-Q-10-5; East A-7-2. It won’t hurt to find out more about the distribution and rectify the count for a possible squeeze.

Laurentiu Dimcica: Did West lead from K-Q-10-5-2 or K-Q-10-5? My guess is K-Q-10-5, else East should have overtaken to set 3 NT. If true, this cuts the East-West link. If West cashes his fourth club, I may have a squeeze; else I can finesse spades through West. Options A, B and F may lose the setting trick [immediately].

Steven Yang: East is marked for three clubs, else he’d have… beaten the contract. My best bet is for West to win his club tricks, …which may put a strain on stoppers or reveal the layout.

Jim Munday: Clubs are certainly 4-3. This forces West to cash his fourth club to rectify the count (else lose it); then I’ll have chances in each of the other suits, as well as squeeze chances. Either of the major-suit double finesses is too low percentage to gamble on overtricks.

Jordi Sabate: I can’t imagine that I can win 10 tricks against good defense, after East [refuses] to cash their club tricks. … So I want to rectify the count and play for a squeeze later.

Fred Upton: Why hath Brutus not continued clubs? Held he a doubleton? No, Brutus is an honorable man, and clubs are 4-3. When I lead a third club to sever the defenders’ communications, this is the unkindest cut of all.

Junyi Zhu: Forcing West either to give up his fourth club winner, or adjust the count for a squeeze.

Julian Wightwick: If East had A-7 doubleton, he would have overtaken at trick one. I will pitch spades from both hands on the 13th club, then hope to make on some sort of squeeze.

Brad Theurer: Clubs must be 4-3, so best is to cut communication and force West to cash his remaining club (else lose it), potentially squeezing East in two of the three remaining suits.

Alon Amsel: If West cashes the fourth club, East will be squeezed; if he doesn’t, I can try a spade finesse.

Sandy Barnes: …East has three clubs. I need a squeeze, or to break the bridge between the defending hands.

David Woulds: Presumably, West has K-Q-10-5;…and East [probably] has at least Q-x-x not to return a club. Leading the J cuts defenders’ communication, and also rectifies the count for a squeeze if West cashes the fourth club.

Thibault Wolf: To rectify the count if West cashes out…then I have to choose a squeeze, unless diamonds are 3-3 or J-10 falls. When West has four diamonds, a double squeeze may be best odds. …

Neelotpal Sahai: If East had A-7, he would have won the first trick and returned the 7; so he is clearly [worried about a squeeze]. My best option is to do what an expert defender doesn’t want. If West decides not to cash the fourth club, I can safely finesse spades, in which case I succeed if spades or diamonds break, or if [a squeeze] materializes.

David Caprera: I initially went for Line D, but I can’t believe East has screwed up the club suit. … Squeeze possibilities look great if West cashes his fourth club; or if he abandons clubs, I can hook spades…

Adrian Petculescu: East cannot have A-7 (he would overtake and return the suit), so he is laying a trap.

Rob Wijman: Clubs are 4-3. I will rectify the count while I have sufficient communication.

Jim Tully: Sure looks like balanced hands all around. I need to prepare for a squeeze in case diamonds don’t break. Finessing the 9 is just too risky.

Jonathan Ferguson: “Aggressive and resourceful,” fine; but are Antonius and Brutus any good? If clubs were 5-2, they had the first five tricks; so assuming clubs are 4-3, only this line makes sense.

Nigel Guthrie: Cutting communication and trying to rectify the count.

Marvin Levine: What is going on? East surely has a third club, or he would have overtaken the queen; so he [may] foresee a heart-diamond squeeze if clubs are continued.

Len Vishnevsky: If West cashes the long club, I will play for a double squeeze; else I can finesse spades into the safe hand…

Peter Hall: Brvtvs has another club, of course. If I take a losing finesse, I will be one down quickly and have to fall on my sword — as kibitzers mourn, “O judgment, thou art fled to Brvtvs East.” Playing the J breaks communication and rectifies the count for a squeeze if Antony cashes his fourth club, or allows me to duck a spade to Brvtvs if he doesn’t. And if Pavlicvs has misled us, and Brvtvs stupidly blocked the club suit? I still get some matchpoints for being one down with the field.

Problem II

Matchpoints	A Q 8 6 4 3			West	North	East	South
N-S vul	Q 7 3			Antonius	Plebe	Brutus	You
	6 3			Pass	1	Pass	2
	A 6			Pass	3	Pass	4 NT1
				Pass	5	Pass	6
Lead: J		East plays 7		Pass	Pass	Pass
				1. Roman Blackwood
	2
	A K J 10 9
	A 2
6 South	K 9 7 4 3

After winning the A:

Your Next Play	Award	Votes	Percent
D. Win A, K, ruff club with Q	10	154	17
F. Win A, K, lead club and pitch 6	9	590	64
E. Win A, K, ruff club with 7	7	78	8
C. Finesse the Q	5	23	2
B. Win A, lead spade and pitch 2	2	60	7
A. Win A, ruff spade	1	17	2

Note: West follows to third club.

Several respondents questioned the bidding, not only for its aggressiveness (I’ll take the Fifth) but for the response to 4 NT. Some thought it should be 5 to show the trump queen, but that’s Roman key-card Blackwood. In Roman Blackwood, 5 shows two aces of the same color or rank (5 shows two unlike aces), so with two black aces the response is correct. Julius Caesar was adamant about this convention until Cleopatra changed his persuasion about queens.

The nice-fitting dummy makes 6 a fair contract, offering two basic options: Establish spades (possibly with a finesse) or establish clubs. Either path requires some fortune, but establishing spades probably needs two friendly breaks (spades and hearts), while establishing clubs may need only one (clubs or hearts). Working on clubs also fits the sound general strategy, when in doubt, to establish the side suit in the long trump hand. Consider this challenging layout:

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

Suppose you win the A and start clubs: ace, king and another. On a good day, Antonius would show out, making the play a cinch; but here he follows, and you face the danger of an overruff. Should you ruff high (Line D)? Or with the 7 (Line E)? Or discard the diamond (Line F)? If clubs are 3-3, of course, you’re home with any play. Line E should be rejected, as it fails whenever Brutus has the 8. The best play is to ruff with the Q (Line D), as Brutus pitches a diamond.

Careful now. Don’t lead a trump! Cash the A, ruff a spade, lead another club and pitch the diamond. Regardless of the return, you can ruff your diamond in dummy (with the 7 in case it matters*), draw trumps, and enjoy the good club. With West holding four clubs, you needed 3-2 trumps** — certainly a better chance than finding the 8 in West.

*If East held three diamonds and two clubs, he could sluff all his diamonds in time to overruff dummy. This is far-fetched, however, as West would surely open 2 or 3 with 6-4 in the minors at favorable vulnerability.

**Additionally, you can succeed against four trumps in East, if he has K-x or a blank K. Leading the established Q from dummy forces East to ruff, allowing you to retain control.

A close second goes to pitching a diamond on the third club (Line F). This is slightly inferior, as East might be 2=3=6=2 and pitch both spades before you can cash the A, while Line D flows smoothly. You could counter this, of course, by reverting to a spade finesse, but then you would fail against more common shapes. Further, Line F gives up any chance for an overtrick if clubs are 3-3. Granted, this may require a risky spade finesse, and you could go down; but the decision can be postponed until trick 12. Indeed, an overtrick could be risk-free if the K were singleton, or if the sly Brutus blanks the K trying to set you. Ineptio, Brute!

Third place goes to ruffing with the 7 (Line E). While failing in the diagram, it preserves the overtrick chance when clubs are 3-3; and if clubs are 4-2, it works whenever Antonius has the 8, even against a 4-1 trump break.

The immediate spade finesse (Line C) gets fourth place. This dynamic venture will likely score a top if it works, either by netting all 13 tricks, or by allowing you to cope with a bad trump break as you establish clubs or crossruff. Clear sailing on the Mediterranean — unless it loses, of course, then… to the lions!

Worst of all is to try to establish spades with Line A or B, as this requires 3-3 spades (or a doubleton king) and a 3-2 trump break. Further, even the friendliest breaks can never produce an overtrick (if you ruff a club in Line A, you cannot enjoy the good spades). Differences between Lines A and B are negligible, so they’re ranked by the voting.

Comments for D. Win A, K, ruff club with Q

Bruce Neill: Options D and F are virtually equivalent if clubs are 4-2. Both play for 3-2 hearts — better odds than finding the 8 in the hand with long clubs. If clubs are 3-3, there is a small unnecessary risk of a spade ruff if I pitch on the third club.

Lajos Linczmayer: If clubs are 4-2, I play A; spade ruff, and pitch a diamond on the fourth club. This play is better than Line F if clubs are 3-3.

John Reardon: … This is better than Line F because it caters for East having doubletons in both spades and clubs.

David Lindop: Easy if clubs are 3-3. If clubs are 4-2,…I can play for hearts 3-2, pitching a diamond on the fourth club.

Joon Pahk: Equivalent to Line F, except it preserves my chances of an overtrick. If clubs go 3-3, an “aggressive, resourceful” Brutus might well bare the K in an attempt to set the contract.

Tim DeLaney: If trumps are 4-1, I must find clubs 3-3. If clubs are 4-2, I will return to hand with a spade ruff, and discard dummy’s diamond on the fourth club. Ruffing with the Q gains whenever clubs are 3-3, and the Q scores a trick. Even Antonius and Brutus will have difficult discards if clubs are 3-3 and the K is onside. Others will be in this slam, so I might take a slight risk to make an overtrick.

Gonzalo Goded: [If clubs are 4-2], I will ruff a spade and throw dummy’s diamond on the fourth club. This is similar to Line F but might make an overtrick.

John Lusky: Playing on clubs offers the best percentage chance. … When West follows to the third club, choice is between this and Line F (both require 3-2 hearts or 3-3 clubs). [If clubs are 4-2], I will continue by cashing the A, ruffing a spade, and playing the fourth club to pitch a diamond from dummy. Line F is slightly inferior because it fails when East holds x-x x-x-x K-x-x-x-x-x x-x (unless I play double-dummy). Also, this retains the chance of making seven when clubs are 3-3, although I may be reluctant to risk the contract for the overtrick, so it may require the K singleton.

Dmitri Shabes: If West has four clubs, this is as good as Line F (both require 3-2 trumps); but if clubs are 3-3, this retains the chance for an overtrick.

Leif-Erik Stabell: If clubs are 4-2, I will cash the A next, [ruff a spade], and follow up with a loser-on-loser play. Line F might give a problem if West continues clubs and East discards two spades, since cashing the A then will fail if East is 2=3=6=2.

Manuel Paulo: Consider East hands containing 8-x-(x), K-x-x-x-(x) and x-x. Next I will cash the A, ruff a spade, and pitch a diamond on the fourth club; then I win any return, ruff a diamond, and claim.

Adrian Barna: This works if clubs are 3-3 (any trump split); if West has two clubs (trumps at worst 4-1); or if West has four clubs and trumps are 3-2…

Rob Stevens: There is a subtle difference between this and Line F. Both need hearts 3-2 when clubs fail to divide. In Line F, if East discards a spade on the third club, and West continues clubs for a second spade discard, I will have to guess whether East originally held two spades (take finesse) or still has a spade remaining.

David Kenward: If clubs break 4-2, I continue with the A, spade ruff, and throw a diamond on the next club. Eventually, I will be able to ruff a diamond low. The advantage over Line F is that if clubs break 3-3, I potentially can win 13 tricks if I read the two-card ending.

Imre Csiszar: Unless desperate for a top, my first priority is to make 6 , for which this or Line F give best (equal) chances. If clubs split 3-3, this retains a small chance for an overtrick.

Steve White: If clubs are 4-2, I’ll cash the A, ruff a spade, then pitch the diamond on the fourth club. If clubs are 3-3, this beats Line F about 3 percent of the time.

Barry White: I think this is about 70 percent or so, slightly better than Line F.

Claude Valiquette: If clubs break 4-2, I’ll return to hand with a spade ruff, and pitch the losing diamond on the last club.

Eugene Dille: If clubs break 4-2, on my next club lead I will discard a diamond, then eventually ruff a diamond.

Dale Freeman: If clubs are 3-3, I will make an overtrick if the K is singleton; so this is better than Line F. If clubs are 4-2, I will play the A, ruff a spade, and pitch a diamond on the fourth club — better to hope for [a 3-2 trump break] than for West to have the 8.

Charles Blair: If East has two clubs, I will ruff a spade, discard a diamond on the fourth club, and hope nothing bad happens. …

Amiram Millet: This produces all 13 tricks when West has J-10-9-7-5 — Q-J-10-x-x J-x-x.

Brad Theurer: Lines D and F are similar (cold with clubs 3-3, needing 3-2 trumps with clubs 4-2), but this maintains a chance for an overtrick. If clubs are 3-3, I can draw trumps, run clubs, and make seven if an opponent has a singleton K — or if I’m daring or crazy enough to try the spade hook, which I’m not.

Sandy Barnes: If clubs are 3-3, I’m home. If not: A; spade ruff; club to pitch dummy’s diamond, which depends on 3-2 hearts.

Johnny Utah: If clubs are 3-3, I am home. If clubs are 4-2, I will ruff a spade, and play a fourth club to discard a diamond from dummy.

Thibault Wolf: There are two main possibilities: Hoping for the 8 in West (Line E), or hoping for 3-2 hearts (Line D or F). Latter odds are better, and Line D seems better than Line F because I might make seven if clubs are 3-3 and, e.g., the K is singleton. …

David Caprera: This reduces the risk of a spade ruff [versus Line F].

N. Scott Cardell: We found a great 27 HCP slam, …so I won’t risk it for an overtrick. … If West showed out on the third club, the contract would be almost 100 percent on a crossruff. When West follows, [technique explained], I get home if trumps are 3-2 or if East has four trumps and a short K. Discarding a diamond on the third club (Line F) looks like a textbook safety play, but it is less safe than ruffing high; East [may] discard a spade, and a resourceful West…will lead another club (ruffed high) as East discards another spade. Now I must guess whether to finesse in spades (East 2-2 in blacks) or cash the A.

Problem III

Matchpoints	7 6 5			West	North	East	South
N-S vul	A K J 7 4			Antonius	Plebe	Brutus	You
	A Q 10			1 NT	Dbl	Pass	Pass
	Q 3			2	Pass	Pass	3
				Pass	4	Pass	Pass
Lead: K		East plays 4		Pass
	A Q J 8 3
	10 5
	J 8 4
4 South	8 5 2

West continues A-J, ruffed in dummy (East plays 7 then 9).

Your Next Play	Award	Votes	Percent
B. Win A, A-K	10	203	22
C. Win A, run J	8	196	21
D. Win A, finesse Q	7	42	5
A. Win A, lead J	6	280	30
E. Finesse the Q	3	132	14
F. Win A-K, finesse Q	2	69	7

Veni, vidi, fugi would hardly appeal to Caesar, but Antonius is a practical soul. The double of 1 NT was evidence enough. “I came, I saw, I ran” was sensible, not cowardly. No doubt, Antonius has A-K-J-10-6 and is just minimizing casualties, though he would have done better to sit if you make 4 .

With only 16 HCP outstanding and no jacks, it seems Antonius must have them all. While this dooms the spade finesse, it is good news in the red suits. You can afford a loser to the K, so your contract looks cozy if you simply draw trumps quickly to avoid a potential uppercut. Consider the following layout:

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

One trap is to take the spade finesse, as Antonius will win and lead a fourth club, allowing Brutus to ruff with the 9.* Ouch! The obvious solution is to win the A and lead an honor (Line A); when West wins the K, there is nothing he can do. Either red-suit return can be ducked to hand, then you can draw the last trump and claim. Nothing to it.

*A more subtle danger is that you might lose to a singleton king. While rare, I think most experts would agree that the best description of K Q-x-x K-x-x-x A-K-J-10-x is to open 1 NT. I certainly would.

Are you satisfied? You shouldn’t be, as the aqueduct could spring a leak. Does Antonius really have to hold the Q? After all, disciplined bidding was hardly a priority in the days of gladiators. Even today, many experts will open 1 NT with K-10-x 9-x K-9-x A-K-J-10-x. Fudging a point is commonplace with a good five-card suit, especially at the vulnerability. Thus, Line A will fail miserably when Antonius exits with a heart. If you duck, you are down immediately; if you win A-K and ruff a heart, West will overruff.

The proper solution is to cash A-K before leading a second spade (Line B). This only needs the K onside*, a virtual certainty. Also note that if Antonius drops the Q on the first round, you would not cash a second (in case he opened with a blank queen), since the second heart can be won in hand if he produces another. Even the ancient Romans wouldn’t open 1 NT with a low singleton (I hope).

*Unless Antonius, the rat, opened 1 NT with K-10-x Q-x-x-x K A-K-J-10-6. When he exits with the K, you could still succeed by ruffing a heart back to hand, but this loses to the previous hand.

Second place is a close call between Lines C and D. Winning the A and leading a diamond allows you to succeed against any plausible layout, however, you may have to guess West’s shape. For example, suppose you lead a diamond to the queen (Line D), cash A-K, and exit with a spade; West wins and locks you in dummy with the K, forcing you to guess whether he has a third heart or a third diamond. If you lead the J first (Line C), you must guess sooner; e.g., if West has two hearts and three diamonds, you must cash all your red-suit winners before leading a spade, else be locked in dummy without recourse. Postponing the decision seems to have no advantage — Antonius and Brutus aren’t going to help you — so Line C gets the edge per the voting.*

*From comments received, it was apparent that many who chose Line C or D did not intend to follow up correctly; however, comments do not affect your score. Generally, each line is judged by its merit if followed up to best advantage with logical play (not double-dummy), unless the choice of line clearly implies wrong intentions.

Clearing spades immediately (Line A) gets a close fourth. While always failing when West has K-x-x x-x, at least it prevents the uppercut. Presumably, you will duck the heart return from West (hoping he has the Q), as winning in dummy fails against K-x-x Q-x; but it is also reasonable to win A-K, succeeding against x-x-x regardless of whether West has two or three spades.

A distant fifth goes to the immediate spade finesse (Line E). Not only does this pay off to the uppercut when East has 10-x or 9-x (with three clubs), but it might lose to a blank king as mentioned earlier.

Worst of all is to cash A-K before a spade finesse (Line F), which only creates another scenario to fail. (Communication is not an issue with a spade still in dummy.) While unlikely, West might have only four clubs, e.g., K-9-x Q-x-x-x K-x A-K-J-10, so you have just nailed shut your own coffin with an uppercut in hearts.

This deal is from “The Most Puzzling Situations in Bridge Play” by Terence Reese, slightly modified to make the bidding realistic. Thanks to Henry Sun (California) for posting it on rec.games.bridge and for sending me a photocopy of the book page. (I used to have this book, but it was one of many I had to throw out when it became mildewed.)

Comments for B. Win A, A-K

Bruce Neill: Since West has five good clubs, he might have only 14 HCP. This avoids a heart overruff if he has K-10-x x-x K-x-x A-K-J-x-x.

Lajos Linczmayer: This play is necessary when West has K-10-x x-x K-x-x A-K-J-10-6… If I don’t cash two hearts, West will return a heart, and I don’t have a sure way to draw the last trump.

John Reardon: I must avoid a trump promotion when West has five clubs and K-9-x.

David Lindop: I want to guard against an uppercut and getting locked in dummy, if West has something like K-10-x x-x K-x-x A-K-J-10-x.

Joon Pahk: Did they have dentists in Caesar’s time?

Tim DeLaney: The trump finesse has zero chance and runs the risk of an uppercut. I must prepare an Appian Way back to Rome (my hand). Brutus could have a dagger hidden under his toga — the Q! Might not the thief, Antonius, open 1 NT with K-x-x x-x K-x-x A-K-J-10-x?

Gonzalo Goded: My jaw is too fragile for an uppercut, so I’d better call a dentist before it’s too late.

John Lusky: Lines E and F risk a trump promotion. Only this line relieves me from having to guess West’s red-suit doubleton, if he is 3=2=3=5 or 3=3=2=5. East could have the Q in light of West’s quality club suit.

Dmitri Shabes: I will not finesse in trumps, due to a possible trump promotion. Line A is good enough in most cases, but this is safer if West stretched to open a 14-count (missing the Q) — after all, he showed up with five [good] clubs. Lines C and D are worse, as they [might] lose to any [red] doubleton in West.

Richard Stein: There is no point to finesse when Antonius is marked with the K. Verily, he could be getting artful with a singleton K; then I can trump-coup Brutus’s 10-9-x-x for 11 tricks. Antonius also could be bidding on the merit of his strong clubs, without the Q. With 3=2=3=5 shape, he could trap me in dummy if I didn’t remove his hearts. If Antonius should be unkind enough to hold four spades, I’m just down.

Leif-Erik Stabell: West might be 3=2=3=5 with two small hearts, in which case I might be locked in dummy if I don’t cash the hearts first.

David Grainger: Next a spade. [This prevents] being locked in dummy, and takes away the risk of an uppercut on the fourth club.

Terry Henry: Lines E and F are silly, as a fourth club could promote a second defensive trump trick. Line A is dangerous if West has bid 1 NT on K-10-x x-x K-x-x A-K-J-10-x; I’ll be off on a heart switch. Lines C and D are dangerous if West has a red-suit doubleton, as I’ll have to guess his distribution to get back to hand safely.

Dean Pokorny: Since I don’t know which red-suit doubleton West has (3=2=3=5 or 3=3=2=5), a dentist’s coup is needed to avoid the overruff and make sure West must put me in hand to draw the last trump.

Adrian Barna: After cashing the A to avoid the uppercut, cashing A-K ensures a safe entry to hand… West might have bid 1 NT with a 14-count.

Rob Stevens: Needed if West has an offbeat notrump with a singleton K; or three spades and five clubs, to prevent a trump promotion; or a mere 14-count with x-x, else he can lock me in dummy if I play two rounds of spades immediately.

Toby Kenney: The diamond finesse must work, and the spade finesse must fail; so the only danger is losing two trump tricks. This can happen through an uppercut if I take the losing spade finesse, or by an overruff if West returns a heart to trap me in dummy. Line B avoids both possibilities.

Bill Powell: Then a spade. In case West exaggerated slightly with K-10-4 x-x K-x-x A-K-J-10-x. …

Wei Victor Zhang: To prevent a trump promotion if West holds K-10-x or K-9-x, and to prevent a possible overruff on the third round of hearts.

David Kenward: Finessing the spade could cost a trump promotion if East has a doubleton IX or X. Line B also avoids getting locked in dummy if West holds K-9-x x-x K-x-x A-K-J-10-x. A better defense is a small diamond at trick three; then I have to guess whether West has two diamonds or two hearts.

Herb Lavine: Two dangers: East might uppercut with 9-x or 10-x, or West might lock me in dummy to get an overruff. West may have K-10-x x-x K-x-x A-K-Q-x-x.

Roger Webb: This fails if West has K-x Q-x-x-x-x K-x A-K-J-x, but gains (over Line A) against the more likely K-x-x x-x K-x-x A-K-J-10-x…

Raghavendra Rajkumar: This prevents both the uppercut in clubs, and being locked in dummy.

Imre Csiszar: Antonius is famous for a historical success with a bid on subminimum values, against his present partner. Perhaps he tried again and opened 1 NT on K-10-x x-x K-x-x A-K-J-x-x; then the obvious Line A fails. Cashing A-K should be safe before leading the second trump to defend against this remote contingency, losing only if East had a single heart (inconceivable on the bidding and play).

Steve White: I cash the A to prevent an uppercut; and A-K to remove West’s heart exit. This is marginally better than Line A, since West might have opened a 14-point 1 NT, upgrading his club suit.

Travis Crump: West should have every missing HCP for his 1 NT bid; but I unblock A-K, so I don’t have to risk the heart finesse, in case he upgraded a 14-count. [Main] danger is an uppercut on the fourth round of clubs after losing a spade finesse…

Barry White: Next I play a trump. This should work when West holds K-10-x x-x K-x-x A-K-J-x-x. Cashing A-K avoids an unnecessary finesse, after thwarting a possible uppercut.

Sebastien Louveaux: A trump finesse might run into a trump promotion; and Line A runs the risk of a heart switch, stranding me in dummy.

Enno Andvere: I must avoid the traps of East promoting West’s K-10-x (K-9-x), and being thrown in dummy with a heart. This is superior to Line A, as there is just room for East to hold the Q.

Barry Rigal: Might that sneaky Antonius have opened 1 NT with K-10-x x-x K-x-x A-K-J-10-x? I knew him, Horatio; a fellow of infinite variety? …

Perry Groot: This counters a possible uppercut in trumps when East has 9-x or 10-x. Furthermore, if West opened a 14-count without the Q, this prevents being locked in dummy. Taking one round of diamonds may force me to guess West’s [distribution].

Okan Ozcan: In case West opened with K-10-x x-x K-x-x A-K-J-10-x (or x-x-x K-x). If I play the A and J directly, West can play a heart, and I would be stuck in dummy (else risk an unnecessary heart finesse).

Tong Xu: Then a spade to my jack. This prevents any trump promotion, in case West upgraded a hand like K-10-x x-x K-x-x A-K-J-10-x.

Claude Valiquette: Refusing the losing trump finesse avoids a trump promotion if East has 10-x or 9-x. Playing A-K before the second trump avoids being locked in dummy…if West has x-x.

Nigel Weeden: Danger is West holding K-10-x or K-9-x, and an uppercut [or an overruff]. Playing off A-K [guards against] East holding the Q, which is possible if West opened a [14-pointer], and costs nothing if West has the Q.

Gerald Murphy: I must be careful not to get locked in dummy. After cashing A-K, nothing can embarrass me…

Nothing? What if Brutus takes off his toga and starts dancing on the table?

Rainer Herrmann: Brutus could possibly have the Q.

Andrew de Sosa: Followed by a spade to the jack; then any return can be won in hand to draw the last trump…

Dale Freeman: If Romans upgrade without the Q (14 HCP and five good clubs), I’d better cash A-K before leading a second trump, or I may get stranded in dummy. Of course, if the Q falls on the A, I will not cash the K; Romans have also been known to open 1 NT with a singleton queen.

Roland Voigt: West must have the K for his bid, but there is a chance that East holds the Q. If I play two rounds of trumps immediately, West will return a heart… The [main] danger is a trump promotion, so the spade finesse is out of question.

John Haslegrave: Lines E and F could lose to an uppercut. Lines A-D all seem to work if 1 NT is genuine, but this gives extra chances…

Jerry Fink: Antonius is honorable enough to have at least 14 HCP ( K, K and A-K-J), but I cannot count on him to have the Q as well.

Stefan Jonsson: This secures communication after I play a spade to West’s king, as he is forced to put me in hand to draw trumps and take the winning diamond finesse. If I don’t take A-K, West can exit in hearts, then I am in danger of an [overruff].

Leonard Helfgott: To avoid dummy-lock (as with Line A) when West wins the K and leads a heart… An early diamond finesse is insufficient, because…I will have to guess whether West is 3=2=3=5 or 3=3=2=5. Lines E and F are poor, allowing an uppercut when East ruffs with 10-x or 9-x.

Ognjen Stanicic: West probably has something like K-9-x Q-x K-x-x A-K-J-10-x; but if he doesn’t have the Q, I need to cash both top hearts so I don’t get locked in dummy. I can’t afford to finesse in trumps, because a club return could promote a second trump trick for the defense.

Gerald Cohen: This way, West…can’t lock me in dummy or beat me with an uppercut, if he is 3=2=3=5 or similar.

Jim Munday: The [main] danger is a trump promotion; an early spade finesse could allow an uppercut if East has three clubs and 10-x or 9-x. I also need to avoid being locked in dummy, on the off chance West holds K-10-x 9-x K-x-x A-K-J-10-x; so I cash A-K before leading a second spade, [rather than] rely on West to hold the Q…

Mark Chen: To guard against K-10-x and x-x with West. After West wins the K, he will be forced to put me back in hand.

Jordi Sabate: Taking the spade finesse is dangerous, because West may promote a trump trick with another club. Cashing A-K is necessary if West has three trumps and two [low] hearts; then I can win any return in hand to draw the last trump…

Anthony Golding: Guarding against West having opened 1 NT with K-10-x x-x K-9-x A-K-J-10-x (I would). An immediate trump finesse runs into an uppercut; and not cashing A-K, an [overruff] when West exits with a heart.

Fred Upton: Cowards die many times before their deaths. The valiant cash the A and A-K before continuing trumps, and never taste of death but upon a 4-1 trump break. Other lines will succeed if Antonius can be trusted to hold the Q; but Brutus, not Antonius, is the honorable one. I must cater to Antonius opening 1 NT with K-x-x x-x K-x-x A-K-J-10-x.

Ted Morris: This guards against an upgraded 14-count; i.e., the only picture card East could hold is the Q. Why is it that, whenever I am West and declarer finesses the Q, I hold specifically K-10-9?

I wouldn’t know for sure, but those old cat-food commercials come to mind.

Junyi Zhu: To ensure an entry to hand after playing a second trump.

Julian Wightwick: Dental work is necessary before a second round of trumps. With a good club suit, West might well be missing the Q…

Brad Theurer: [One] danger is that West upgraded K-10-x x-x K-x-x A-K-J-10-x (reasonably enough), so I must avoid being dummy-locked… I won’t take the spade hook because of the uppercut potential.

Julian Pottage: When West wins the K, he will be forced to give me an entry to hand, even if East has the Q.

Thibault Wolf: West certainly has the missing kings for his 1 NT opening, but the K can be stiff; so the A must be cashed. Cashing A-K is important; otherwise, West can return a heart; then if East has Q-x-x-x, I will be overruffed when I try to come to hand.

David Caprera: Only thing worse than being uppercut by an opponent is to uppercut yourself.

N. Scott Cardell: … To avoid the looming uppercut, I must play the A before losing a spade to West. … If I were certain West had the Q, I could just play A, J; but few aggressive players would consider K-10-x 9-x K-9-x A-K-J-10-6 too weak for a 15-17 notrump. So I cash A-K before leading a second spade. (Of course, if West plays the Q on the first round, I just lead a spade catering to an off-shape 1 NT.)

Nigel Guthrie: Extracting Antonius’s teeth!

Problem IV

Matchpoints	A K 6 4			West	North	East	South
E-W vul	A 6 4			Antonius	Plebe	Brutus	You
	A 6 4						1 NT
	J 6 4			Pass	4 NT	Pass	6 NT
				Pass	Pass	Pass
Lead: J		East plays 2
	7 5 3
	K 5 3
	K 3
6 NT South	A K Q 10 9

Your Play	Award	Votes	Percent
C. Win A, A-K-Q-10, duck spade	10	141	15
E. Duck, win A-K, A-K-Q	8	259	28
F. Duck, win A, A-K-Q	7	248	27
A. Win A, A-K, duck spade	5	37	4
B. Win A, A-K-Q, duck spade	3	40	4
D. Win A, all clubs, duck spade	2	197	21

This deal was played by Julius Caesar and his wife Pompeia in 64 B.C. and was influential in his being declared Pontifex Maximus. Historians believe that dummy’s spot cards, as recorded by Pompeia in her diary, were altered to commemorate the year (she was the sentimental type) but the deal has been verified through alternate sources. Caesar was not much for holdup plays (Pompeia’s diary confirms this via premarital sex) so he won the A and cashed his club honors before ducking a spade. Hail Caesar!

With 11 top tricks, the obvious source of a 12th is a 3-3 spade break; plus there are various squeeze chances if spades do not break. The Roman lead (showing Q) and even signal (discouraging) suggest that Antonius, if anyone, has spade length. This puts dummy’s spade threat behind the stopper, which is ideal for a successful squeeze. Evidently, the only issue is when to concede a spade.

Modern players are taught to “rectify the count” as early as convenient if a squeeze might occur, so it seems right to duck the first trick. Certainly, it’s convenient. Consider a routine layout:

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

Suppose you win the second spade, then cash the other top spade and A-K-Q (Line E) to reach this position:

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

The next club forces Antonius to unguard a red suit, as you pitch a heart from dummy. If he pitches a heart, the ensuing double squeeze is easy, and any sensible play succeeds. If he pitches a diamond, however, you must win the A and K before leading the last club.

All well and good… maybe. But what if Antonius didn’t continue spades? Even though Options E and F presume this, you are still liable for any variation that might occur. If you duck the first trick, Antonius, being made of “sterner stuff” will shift to a diamond. You must win the K to keep a winner with the threat, but losing the extra entry to your hand will doom the squeeze. I won’t go into specifics here but refer interested readers to my study on Pure Squeezes (Type 2-B).

The proper start is to win the first trick. The question of how many clubs to cash is determined by the comfortable discards you have in dummy — just one (a heart) so you cash four clubs (Line C) then duck a spade to reach:

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

Note that Antonius chose to give up his diamond stopper, which is the strongest defense. It doesn’t matter which defender is on lead or which suit is returned, though a heart is best, as it will force you to guess whether a squeeze has occurred or spades were 3-3 all along. Win the A; A; K; then lead the last club (West pitches a heart), and you’ve reached the moment of truth. In the above layout, you must pitch a spade from dummy then cross to the K to squeeze Brutus in the red suits. If spades were 3-3, however, you must keep the spade which is good, which brings to mind the old Roman proverb: Only Caesar could fail on a 3-3 break.

If a spade or diamond is returned, the play is easier, as you don’t need to guess the spade break. From the diagram, win the K and A, then cross to the K to lead the last club. The dual heart entry now provides communication for a simultaneous double squeeze. The only decision necessary with this case was which red suit West abandoned, as a different sequence is required if he gave up hearts. This kind of decision is inherent to many squeeze positions, though an expert will get it right a high percentage of the time, either from the order and reluctance of discards, or simply judging the most likely distribution.

Second place is a virtual tie between Lines E and F (ducking the first trick). Unless spades are 3-3, either fails only on a diamond shift*, which would be difficult if West has an unattractive holding to lead from, e.g., Q-x-x. Between them, I see no strategic difference (with Line F you would cash the K later), so they’re ranked by the voting.

*Barring a preconfigured double squeeze (e.g., East having five hearts) or a remote simple squeeze (e.g., West having five hearts); and even then, you’d have to guess what to play for.

Fourth place goes to cashing A-K before ducking a spade (Line A). While equivalent to Lines E and F in theory, it is inferior in two ways: (1) Opponents will know you have a solid club suit when you duck a spade, and (2) East might be able to win the spade trick and shift to diamonds comfortably.

Cashing only three clubs (Line B) gets a lowly fifth place. This destroys communication for the diagrammed squeeze no matter what the return, though you can succeed in the unlikely case of a preconfigured double squeeze (East with 5+ hearts or 6+ diamonds) provided you guess which to play for. In practice, you’d better hope spades are 3-3.

Worst of all is to cash all five clubs (Line D) as it squeezes dummy, killing any squeeze chance, except a remote simple squeeze against West. According to Pompeia’s diary, Caesar was about to do this when his LHO muttered, “satis stipes iam,” so he pulled back the 9 and ducked a spade to oblige.

Comments for C. Win A, A-K-Q-10, duck spade

Bruce Neill: A routine (LOL) compound squeeze. I won’t let West break my communication by a diamond switch, say, with Q-J-10-9 J-x-x J-10-9-8 x-x.

Lajos Linczmayer: West might have, say, Q-J-10-9-8 Q-x-x Q-x-x-x x. If I duck the first spade, a diamond switch destroys the double squeeze; so I must postpone rectifying the count. On the fourth club, West must give up control in one of the red suits.

John Reardon: I must exert just enough pressure on West, assuming he guards spades, to force him to give up a red suit. Then I can duck a spade and manage any return safely to complete my squeeze.

David Lindop: I don’t want to duck and have West switch…at trick two; so I run four clubs to make West unguard a red suit, then duck a spade to rectify the count.

Joon Pahk: Looks like a compound squeeze. I will cash all but one club to squeeze Antonius out of a red-suit guard before rectifying the count…

Tim DeLaney: This is the only way to keep entries intact for the pure squeeze. (When in Rome, do as the Romans do. Only a barbarian would call it a compound squeeze.)

Gonzalo Goded: I have no clue, but this looks so odd that it must be the right answer. …

I can fool some of the people all of the time… but never God — or His editor.

John Lusky: If West has spade length, I can make 12 tricks on a compound squeeze if I read the position. (In one variation there will be ambiguity whether to play West for spade length or for spades 3-3). The problem with other lines is that West can damage my entry position by shifting to diamonds, then abandon his diamond guard if I win in hand, or his heart guard if I win in dummy. This forces West to [commit] before I commit to the order I will [cash winners]. I can also make the hand if East has spade length, if East has the only heart guard or West has the only diamond guard — if I can read the position in time.

Dmitri Shabes: If West has four spades, there is a compound squeeze (assuming I can guess red-suit lengths); but it is so delicate that I cannot afford to duck a spade immediately, as a diamond switch destroys it. So I must first squeeze West, then duck a spade. Too bad I can’t combine this with spades breaking 3-3, as a heart return forces me to choose which to play for. …

Richard Stein: Presumably, if spades are not breaking, Antonius started with four (or five). Ducking the first spade permits a surprise…shift, which could make things hairy. Antonius will have to unguard a red suit on the fourth club, whether the count is rectified or not…

Leif-Erik Stabell: West will probably switch to a heart, and I will go down with spades 3-3 in search of glory.

David Grainger: If West has 3+ spades, this only fails when East is 2=3=3=5* and [wins second spade], as long as I guess which red suit West keeps [and maybe the spade break].

*David makes an interesting but subtle point. If East has five clubs and wins the spade duck, a club return kills the squeeze by forcing you to win your club prematurely. -RP

Terry Henry: I have I chance in VI to get this right.

Dean Pokorny: Four rounds of clubs (throwing a heart) is the right way to preserve tempo and communication for a compound squeeze. I will succeed if I guess the [distribution].

Manuel Paulo: Assuming West has four or five spades and at least three cards in each red suit, I can set up a compound squeeze. On the fourth club, West must pitch a busy card; only then can I duck a spade to rectify the count.

Carsten Kofoed: I’m betting on a composite squeeze.

Adrian Barna: On the fourth club, West is squeezed. Assuming he keeps three spades, a double squeeze will work after the spade duck. I can’t duck the first trick (Line E or F), since a diamond return would kill the compound squeeze (no return to hand other than the K).

Rob Stevens: An almost unique compound squeeze… I must run all free-suit winners but one then duck a trick. Ducking trick one allows West to shift to a diamond, and then discard diamonds to ruin the squeeze. I will still have to guess the ending, of course — and will probably go wrong if spades were 3-3 all along!

Toby Kenney: A compound squeeze. I need to see what West pitches on the fourth club in order to know where to win the return after I duck the spade.

Bill Powell: It would be easier to read the position with Line E, but a diamond switch would destroy the compound squeeze.

David Kenward: If I duck the first trick, the killing defense is a diamond shift, which I have to take with the king; then West can discard a diamond on the fourth club; and he is under no pressure on the fifth, because the A cannot be cashed. Winning the first spade forces West to commit on the fourth club (dummy discards a heart), then I duck a spade. If West has thrown a diamond, I win the return and cash A, K and the last club for a double squeeze around hearts. If West has thrown a heart, cashing K, A, K and K before the last club completes a double squeeze around diamonds.

Roger Webb: Lines E and F are easy if West continues spades — hoping I duck again? — but a diamond shift causes entry problems. By forcing West to decide which suit to unguard before I duck the spade, I can choose where to win the diamond [accordingly]. I still have to guess the distribution, so I hope they signal clearly. It would be embarrassing to go down attempting a squeeze when spades were 3-3.

Steve White: Forcing West to unguard a red suit before I [lose] the lead, so I know where to win a diamond return.

Frans Buijsen: Retaining the last club to perform the [second part] of the squeeze, without squeezing dummy first.

Sebastien Louveaux: Playing four clubs reduces West to five red cards, so he has to unguard one, which paves the way for a…double squeeze.

Ruben Buijs: Let opponents trouble themselves with as many discards as possible [before ducking a spade]. Cashing the fifth club is not good, because dummy has [no viable discard].

Javier Carbonero: All plans look mainly for an [eventual] double squeeze, …but this way…I will not compromise my communication.

Claude Valiquette: A compound squeeze. I must not fall into the trap of ducking the first trick, because a diamond…return would ruin my communication. This preserves the needed flexibility, until I have an indication of the suit abandoned by West (assuming he protects spades) when triple-squeezed.

Daniel de Lind van Wijngaarden: Discarding a heart on the fourth club. This allows the timing [and communication] for a double squeeze.

Rainer Herrmann: A nice exercise in compound squeeze technique. Anyone can make this contract if spades are 3-3 — except an expert against expert defense (Antonius or Brutus will shift to hearts after the delayed duck). The entry position is less comfortable than it looks. If I duck the first trick, Antonius should switch to diamonds; then keep diamonds if won on the table, or hearts if won in hand.

Roland Voigt: A compound squeeze. Assuming West has at least four spades, he must unguard one of the red suits on the fourth club. Later I will have a double squeeze, if I read the discards right. A fifth club would squeeze dummy.

Jerry Fink: Odds are 4-to-1 that Antonius has led from Q-J fourth or fifth, rather than Q-J third. If I duck immediately to correct the count, a diamond shift could dagger our slam; but four quick rounds of clubs force Antonius to [unguard] one of the red suits. Assuming I can read the discards correctly, the threat of the early diamond shift will be buried.

Ognjen Stanicic: West has to give up a red suit on the fourth club; I pitch a heart, then give up a spade to rectify the count. I now know which double squeeze to play for, so I can win the return in the correct hand…

Jim Munday: I can’t afford to duck the first trick, as a diamond switch will mangle my entries. I need to force West to unguard a red suit but can’t cash all my clubs, lest I squeeze dummy; so I play only four rounds. I’ll have to watch closely and read West’s discards, then I can duck a spade and succeed with a double squeeze.

Bas Oosthoek: I’ll give West stoppers in both red suits and the spade length. All seems plain sailing: Duck a spade; win the spade return; check for 3-3 spades, and start a compound squeeze on the fourth club. West, however, may shift to a diamond. To avoid this, win the first spade, cash four clubs (throwing a heart) and duck a spade. Now the compound squeeze will work. For example, give West 4=3=3=3. If he discards a diamond and returns a diamond, win A, A, K and last club; or a heart, win A, A, K and last club (I can’t afford the luxury to check if 3-3 spades). If he discards a heart and returns a diamond, win K, K, A, K and last club; or a heart, win A, K, K, K and last club. I may have to read the position well, but it’s better than giving West a chance to shine.

Fred Upton: Assuming Antonius has at least four spades, this is a compound squeeze, which the defense threatens to break up by leading a diamond. But I am made of sterner stuff. :) This forces Antonius to unguard one of the red suits, and the die is cast for a double squeeze. I can duck a spade and choose where to win the diamond (or any) return accordingly.

Grant Peacock: I can afford to have West make his choices as early as possible.

Neelotpal Sahai: Danger of ducking is that West can fatally shift to diamonds, so I must cash precisely four clubs to see West’s discard before ducking a spade. …

Nigel Guthrie: Then claim on a mutate compound squeeze. With any luck, neither opponent will dispute the claim for fear of losing face in front of his archenemy.

Problem V

Matchpoints	2			West	North	East	South
Both vul	A J 7 2			Antonius	Plebe	Brutus	You
	5 3				1	Pass	1
	A Q J 8 5 4			Pass	2	Pass	2
				Pass	2	Pass	3 NT
Lead: Q		East plays 4		Pass	Pass	Pass
	K Q 10 9 8
	8 3
	A K 9 2
3 NT South	10 2

You duck. West continues with 10, won by the jack (East plays 5).

Your Next Play	Award	Votes	Percent
A. Lead spade to the king	10	133	14
F. Lead 4 to the 10	9	310	34
B. Finesse the 10	6	136	15
E. Lead the Q	4	43	5
C. Win K, run 10 (win ace if covered)	3	141	15
D. Win K, run 10 (duck if covered)	2	159	17

Oh, matchpoints. Many players consider it a bridge tragedy (travesty?), but it’s an important part of the game — like match play versus stroke play in golf, or gladiator bouts at the Colosseum. Indeed, it’s the most common form of scoring in duplicate bridge, so we’re stuck with it and need to apply winning strategies. If that doesn’t sell you, try “When in Rome…”

My perception over the years is that there are fewer differences between IMPs and matchpoints than most people realize, especially in the bidding. Differences are more common in the play, but even there it’s uncanny how seldom it matters. One indication was the difficulty in preparing good lesson deals; e.g., if I created a deal to illustrate matchpoint strategy, the same play was often valid at IMPs.

This problem seems to fit the mold, as I would lead a spade to the king (Line A) at any scoring — even Roman matchsticks. I think this offers the best chance for the most tricks, as well as the safest route for nine. Later, I may face a critical decision in clubs when the first finesse wins (you know it will), but I’ll worry about that when it happens. Consider this layout:

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

After routinely ducking the Q and winning the continuation with the jack, it is discomforting to have no outside entry to dummy’s clubs. Leading a club to the 10 seems reasonable, ensuring the contract if it loses; but what will you do if it wins? Probably you’ll lead the K. Suppose Antonius wins the A and returns a club. You can succeed, of course, by winning the A, cashing the A, and establishing spades; but you’re at the mercy of the distribution. Antonius would defend the same with A-J-x K-Q-10-9 x-x-x K-x-x (note the clever club duck) and you’d be down, while Line A operates smoothly. Thus, Line F ensures nothing.*

*Only advantages of Line F (over Line A) are when West has K-Q-10-9-6 with (1) A and K, or (2) a club void. Case 1 is far-fetched, as almost everyone would overall 2 . Case 2 is plausible but remote. Note that if West has A-J-x-(x) K-Q-10-9-6, and East K-x-x-(x), all lines fail.

In 35+ years of bridge teaching I have stressed the importance to knock out aces early, and this deal is no exception. Leading a spade to the king leaves you in a strong position whether it wins or loses. If Antonius takes the A and continues hearts, you can guarantee nine tricks by leading a club to the 10* (correct at IMPs) then switching to spades; or you can cross to the K and run the 10** (correct at matchpoints). Whether to repeat the club finesse is a concern, and I’d want to be at the table to decide. Insidior, Brute? Just be happy it wasn’t part of the problem.

*If West held five hearts, there’s no guarantee; but it’s still the best play, as West’s failure to overcall almost surely places the K with East.

**Dangers are (1) West may show out, then East would win the first club to leave you with only eight tricks, or (2) West may cover, then if you win the ace hoping for the most tricks, a 4-1 break spells doom.

Think positive! Julius Caesar did, and he won 12 tricks with Line A. When the deal arose in 44 B.C. on the eve of the March Ides, Brutus actually held A-x-x-x x-x Q-10-x-x x-x-x; and when he ducked the spade lead, it was all over. Caesar next led the 10 (covered) and ran clubs, winning the rest on a fateful double squeeze. This humiliated Brutus, who stomped out of the playing room in a rage, only to return the next day for revenge. And the rest, as they say, is history.

A close second goes to leading a club to the 10 (Line F). While not a true safety play, it feels like one; and it takes quite a parlay (plus a misguess) to go down. If the 10 wins, continuing with the K will usually produce the same number of tricks as Line A. The main downside is that it may give Antonius a free trick with K-x, costing you some matchsticks.

Finessing the 10 (Line B) gets a distant third. This fails miserably in the diagram, as Antonius will return a heart to ensure four tricks in the majors; then you have only eight tricks without the club suit, so the K sets you. On a lucky day ( J and K-x-x with Brutus), this could produce a good score.

Leading the Q from dummy (Line E) gets fourth place. This technical debacle allows either defender with K-9-x-x or a blank K to win and obliterate you with a diamond shift. If clubs split, however, the clumsiness is forgiven and you can revert to spades as in Line A or B.

Worst by far is to cross in diamonds to lead the 10 (Line C or D) which could be ugly. What will you do if it wins? It’s too late to set up spades (only one diamond entry) so suppose you repeat the club finesse. Even if clubs run, it will be hard to score 11 tricks with the A isolated. But if there’s any justice in Rome, the second finesse loses, and a diamond is returned. Great Caesar’s ghost! (Perry White comes into play.) Between Lines C and D, if the 10 is covered, it seems better to win the ace at matchpoints (duck at IMPs).

Comments for A. Lead spade to the king

Bruce Neill: Sadistic of you to make this matchpoints. IMPs would be hard enough. I can’t bring myself to give up the club finesse completely; but I still haven’t decided what I would do after a spade to the king holds, and the 10 wins next.

Lajos Linczmayer: I think the problem would be more difficult at IMPs. At matchpoints, I take the club finesse. If East has, say, A-x-x-x x-x-x J-x-x-x x-x, I can win the rest of the tricks. …

John Reardon: This looks like the safest way to try for 10 tricks, which should be a good result.

David Lindop: Trouble with the 4 to the 10 (ducked) is that I might have a nasty guess if West wins a spade and leads a club. … This should be OK if East has the A; I continue with the Q to East’s ace, win the diamond return, 10, and back to spades. If West wins the A and continues hearts from four, I lead a club to the 10 and continue spades. If West wins the A and continues hearts from five, I win the K, 10, and clear spades, hoping East has the J.

Joon Pahk: I’ll set up a spade trick before broaching clubs. …If clubs behave, I can take 11, [maybe 12] tricks; and even if they don’t, I will often still scramble nine.

Tim DeLaney: Finessing the 10 is tempting,…but it risks the contract if West has something like A-J-x K-Q-10-9 J-x-x-x x-x. After scoring a spade trick, I run the 10, which will surely hold; then I revert to spades. (Crossing the Rubicon with a second club finesse is a poor idea.)

John Lusky: It is unclear whether to play for the contract or [overtricks]. This play defers that decision (unlike Line F)… and also puts more pressure on the defense to do the right thing. If West wins the A and hearts are 4-3, I am in control, since the defense must duck the first club to shut out dummy; and in contrast to Line F, cannot sever my link to dummy by leading a second club after winning the A. Also, East might rise with the A to continue hearts, since it would the winning defense if West held K-x-x K-Q-10-9 Q-x-x-x x-x. …

Richard Stein: At matchpoints, I choose to play for things to work within [reasonable] limits. If Brutus has the A, he will be obliged to duck; then I will switch to the club horse. …

Terry Henry: Does this give the best chance of the most tricks? I’m more of an IMP guy myself.

Dean Pokorny: At first sight, Line F looks the safest for nine tricks. Looking deeper, Line A seems better, as it is also safe and offers additional possibilities for overtricks… If the K wins and the 10 is ducked all around, I’ll lead the K to East’s ace, win the diamond return, play another spade, and hope poor West is caught in a heart-club show-up squeeze. If the K is taken by West’s ace [and a heart is returned with East following], I’ll play a club to the 10, then again spades.

Carsten Kofoed: While there are matchpoint aspects, West having K-x-(x) is only 34 percent; and with North declarer, a diamond lead would create problems, e.g., when East has the K. This is flexible, and allows me to control the tempo.

Toby Kenney: I’ll probably need some spade tricks to make this contract, so I start them immediately. If the K holds, I’ll run the 10.

Bill Powell: Going for 11 tricks. Line F will not guarantee nine tricks, because of a club switch when West wins a spade.

David Kenward: At matchpoints, the trickier decision seems to be how to continue after the 10 holds; but this seems to be the best start, whether I am aiming for nine tricks or 11.

Daniel Korbel: I wish this wasn’t matchpoints. Still, Line A is a nice hedge, as the contract is pretty close to cold (three spades, two clubs, two hearts, two diamonds), or I can go for the gusto and finesse clubs twice — and you didn’t ask which!

Imre Csiszar: On a good day, East has the A and ducks, and West has K-x-(x). Then a double squeeze nets 12 tricks.

Et tu, Imre? An ominous comment from a guy whose name may be a derivative of Caesar.

Travis Crump: If the K loses and a heart comes back, I’ll assume the K is wrong (no 2 bid) and play a low club to the 10, then work on spades hoping East has the J. If it wins, I’ll run the 10 and play for 12 tricks.

Frans Buijsen: Removing the possible A entry from West will get the most tricks against most common distributions.

Okan Ozcan: I think I should try for overtricks when obvious, but the contract is not safe if East has the K and ducks the first club. … If West wins the A and returns a heart, I will take it and play a club to 10. If the K wins, I play the 10; and if it wins, I revert to spades.

Tong Xu: Then give away a spade, finesse the 10, and lose another spade. Contract is at risk only if West has A-J-x-(x) and five hearts. In some cases, this will have chances for an overtrick…

Gerald Murphy: If the K wins, I lead the 10; if that wins, I lead the 10, eventually winning three spades, two hearts, two diamonds and two clubs.

Dale Freeman: At matchpoints, I am going to need at least one spade trick sooner or later; so why not now? Lines C and D weaken the diamond position [prematurely].

Leonard Helfgott: At matchpoints in a normal spot, I must try for maximum club tricks; so I’d reject Lines D, E and F. If the club suit runs, I will probably come to 11 tricks — but never more and possibly less (abandoned A) if I [postpone] leading spades. If I lead a spade immediately, East may err and duck the ace, allowing a double squeeze for 12 tricks, or perhaps more flexibility if clubs break badly.

Jian Chao Wu: Guarding against A-J doubleton and five hearts with West.

Gerald Cohen: I intend to play for all the marbles, getting a good score if the club finesses works and clubs break. This is better than Line C, since it gives some chances if the club finesse loses, and prevents me from being squeezed on the club run.

Linda Lubeck: I’ve got to get spades going but don’t want to lose two spades, two hearts and the K. If the K wins, I’ll play the 10, which should win; then the Q.

Jordi Sabate: … If West did not have the K, a heart continuation may be dangerous, because I could have the K (e.g., K-Q-10-9-8 8-3 A-10-9-2 K-2) and his best move is a diamond switch; so I think West is a favorite to have K-x-x (hoping I have a singleton) or K-x-x-x, and I’ll play to make the maximum number of tricks. …

Grant Peacock: Most lines involve building a spade trick at some point, so why wait? If this holds, I can lead the 10, then decide how greedy I want to be.

Robert Eachus: At matchpoints, rather than worry about [bad news], I will assume clubs run and let the opponents worry about what to throw.

Walt Williams: It might win! Then running the 10 [could win the rest].

Problem VI

Matchpoints	A 7 5 4			West	North	East	South
N-S vul	K			Antonius	Plebe	Brutus	You
	A K Q J 10				2	Pass	2
	A Q 10			2	3	Pass	4
				Pass	4	Dbl	5
Lead: 10		East plays Q		Pass	6	All Pass
	6 3 2
	A 8 7 5
	9 8 6 4 3
6 South	2

Note: West has one trump.

Your Play	Award	Votes	Percent
D. Win A, A-K, K, A, ruff club	10	293	32
B. Win A, A-K, A (overtake), finesse Q	8	417	45
F. Duck the first trick	7	85	9
C. Win A, A-K, A (overtake), finesse 10	6	58	6
E. Win A, A-K, A, ruff club	2	53	6
A. Win A, A-K, A (overtake), ruff heart	1	16	2

Despite the circus atmosphere, you conducted a sound auction. At worst, 6 depends on a finesse for a king through the enemy bidder — normally a favorite, but you probably can’t trust Antonius any more than you’d turn your back on Brutus. Indeed, no one could be trusted to have outside strength at this vulnerability; opening 2 is a standing invitation: Step right in, the water’s fine!

Antonius surely has K-J-10-9-8, in itself enough to bid, since Brutus will usually be on lead against the 2 bidder. (By similar logic, there is less reason for Brutus to bid.) Some respondents even feared that Antonius might have only four spades, but I find this surreal. Not only does it require a bizarre bid, but it means Brutus played the queen from Q-x, else Antonius made the wrong Roman lead from K-10-9-8. Anything is possible, of course, but even Shakespeare would have trouble topping those theatrics.

Since the location of the K has no real effect on the bidding, the available-space principle dictates the odds. West is known to have five spades and one diamond, so he has seven spaces; East is known to have one spade and two diamonds, so he has 10 spaces. Therefore, the odds are 10:7 against the club finesse (Line B) so our reasonable contract seems to be fading fast.

Alternately, you could play West for the J (Line C) since Brutus will be out of spades if he wins the K. Alas, this has the same chance — any missing card is 10:7 to be with Brutus — though slightly diminished by the possibility of being duped by a four-card overcall.

Is there any other chance? Yes! If Brutus has five or more hearts, he can be stripped and endplayed — clearly a frightening thought, so it may help to picture Pompeia in the play. Consider this layout:

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

After winning the A, draw trumps (Antonius pitches a spade), cash the K, A, and ruff a club (Line D). Next cash the A, ruff a heart and ruff a club to leave:

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

Finally, lead your last heart and pitch a spade. Brutus must win and yield a ruff-sluff, which you ruff in hand to pitch dummy’s last spade.

Based on the known diamond break and presumed spade lie, Brutus will have 5+ hearts about 58 percent of the time — a lot better than the 41-percent chance of the club finesse — and it’s even better if you consider that Brutus might have Q-J-10-9 (or fail to unblock with Q-x-x-x) or the K falls doubleton in West. Thus, Line D is a clear winner.

Second place goes to finessing the Q (Line B) after overtaking the K to reach your hand. Even if it loses, there is a slim extra chance that West holds J-x; but don’t hold your breath.

Third place is a close call between finessing the 10 (Line C) and ducking at trick one (Line F). Both are inferior to Line B: Line C due to the possible con job (four-card overcall), and Line F because it gives up the chance of J-x (you are committed to finesse the Q later) as well as the scary possibility that Antonius led fourth-best from K-Q-J-10-x.* I won’t pursue these inferior options in detail, so Line F gets the edge per the voting.

*Note that information about Brutus playing the Q is unauthorized if you duck the first trick.

Lines A and E are almost hopeless. Rather than discuss them here, I have organized a luncheon at the Colosseum. The first person to make 6 with either play does not have to stay for lunch. If you think I’m lion, join the group.

Comments for D. Win A, A-K, K, A, ruff club

Bruce Neill: More likely that East has 5+ hearts than the hand with long spades has the K (or J).

Lajos Linczmayer: I hope East wins the fourth heart trick (I pitch a spade) — a better chance than the club finesse.

John Reardon: My plan is to eliminate and then throw in East with the fourth heart.

Great idea. Caesar should have, too! Just one problem: How do you throw Brutus in after you eliminate him?

David Lindop: East might have doubled 2 with six clubs, so I’ll play East for five hearts and avoid having to guess the club position (which might be unguessable). I continue with the A pitching a spade; heart ruff; club ruff, and a heart discarding a spade.

Joon Pahk: Then A; heart ruff; club ruff; and a heart (pitching a spade) to East forcing a ruff-sluff. Assuming spades are 5-1, all this line needs is for Brutus to have longer hearts (or fail to unblock with Q-x-x-x), which seems more likely than guessing which club honor Antonius might have.

Tim DeLaney: Brutus is a favorite to have five or more hearts, so I plan to throw him in with the fourth heart to give me a ruff-sluff.

Gonzalo Goded: I don’t like this one. Brutus seems the kind of guy who would double 2 on K-x-x-x-x, so the club finesse is very tempting. I also think it is normal to [double] with long clubs, but [maybe] not with a two-suiter.

John Lusky: This works if East has at least five hearts among his 10 cards in clubs and hearts, as I can endplay him with the fourth heart at trick 10. This seems a better chance than playing West for either the K or the J, since East is more likely to have club length; and West’s 2 bid is not a reliable indication of strength.

Dmitri Shabes: Hoping for East to have 5+ hearts and a singleton spade.

Richard Stein: I thumb my nose at the club finesses, for they are but for practice. This will be followed by a heart ruff, club ruff, then the A and a fourth heart discarding spades from dummy. Brutus will be stuffed like a prize pheasant, and I shall graciously accept the ensuing ruff-sluff. I snicker at Brutus’s feeble attempts at stern defense!

Leif-Erik Stabell: With West having six known cards and East three, the best chance seems to be to play East for the heart length.

David Grainger: I plan to discard a spade on the fourth heart and hope East has to win it. If a club finesse is necessary, it goes into East’s long suit — [surely] a lower chance than this.

Terry Henry: Hoping to throw East in on the fourth heart (pitching a spade) for a ruff and discard, which seems to work if East has 5+ hearts or Q-J-10-9. I might change horses and overtake the K if East produces the queen, as this looks like the start of an unblock with something like Q-J-10-2.

Dean Pokorny: I plan to eliminate clubs and throw in East with the fourth heart, hoping he holds 5+ hearts and a singleton spade, and also catering to the possibility of K-x with West.

Manuel Paulo: Consider this East hand: Q J-x-x-x-x x-x K-J-x-x-x. After discarding a spade on the A, I ruff a heart, ruff a club, and pitch another spade on the last heart; East is thrown in, and must give a ruff and sluff.

Carsten Kofoed: I’ll endplay East on the fourth heart because he has 10 free places against seven by West; plus some small extra chance of K doubleton.

Adrian Barna: Starting to crossruff for an elimination play, attempting to endplay East on the last heart, working when East has at least five hearts or Q-J-10-9, or Q-x-x-x and fails to unblock.

Bill Powell: With five hearts and five clubs, East can be thrown in on the fourth round of hearts to concede a ruff and sluff. (With six clubs, East might have doubled 2 to suggest a sacrifice.)

Herb Lavine: Then A (sluff a spade), heart ruff, club ruff, and a fourth heart sluffing another spade, hopefully for East to win and give a sluff-ruff. …

Roger Webb: I’ll throw a spade on the fourth heart, making if East has five or more hearts, or if West has K-x. With West having five spades, this is better odds than the club finesse.

Raghavendra Rajkumar: Then A, heart ruff, club ruff, and a heart discarding a spade, hopefully to throw in East.

Imre Csiszar: [Percentages] greatly favor this over Line B, …however, many cases in which East holds the K are eliminated by East’s failure to act, shifting the odds toward Line B. Exact calculation is impossible without knowing which 6-4 and 5-5 holdings East would act with at the vulnerability; but I guess Line D retains its edge. …

Travis Crump: Then A, heart ruff. West probably has a two-suiter for his bid. If it looks like the blacks, ruff a club and throw East in with a heart. If it looks like the majors, pitch a spade on the Q regardless [of East’s play].*

*Travis brings out a subtle point that East might not cover the Q with the king if he were out of hearts and could be endplayed; hence, the spade pitch, as strange as it seems. In any case, I’d have to be strongly convinced that West were 5-5 in the majors to do this, and no enemy carding would convince me, especially because a silent East would have seven clubs to the king. -RP

Barry White: If West holds something like K-J-10-9-8 Q-x-x x x-x-x-x (a lean and hungry bid), [later I can] lead my last heart and pitch a spade from dummy. Tui indico, Brute!

Barry Rigal: Hope I can endplay East with the fourth heart (pitching a spade) for a ruff and discard.

Perry Groot: With six known cards in West versus three in East, it seems better to go for a heart throw-in against East. This needs 5+ hearts in East, with some small additional chances.

Okan Ozcan: Hoping East has five or more hearts, I’ll continue with the A (discard spade), heart ruff, club ruff, and a heart discarding a spade; East will give me a ruff and discard for a 12th trick.

Tong Xu: If spades are 5-1, this offers [about] a 60-percent chance (West having less than four hearts or K-x). Actual odds compared to Line B or F depend on what people need to overcall 2 [and other factors]. …

Javier Carbonero: Eventually, putting East in with a heart… [Best] chance to find a 12th trick.

Nigel Weeden: Then the A (spade discard), heart ruff, club ruff, and a heart — hopefully, to put East in to give a ruff and discard. (This plays for West to have at most three hearts.)

Gerald Murphy: Playing East for a singleton spade and long hearts. …

Daniel de Lind van Wijngaarden: [Play described]. When East started with five hearts (or Q-J-10-9), he must give me a ruff and discard…

Eugene Dille: I will strip hearts and clubs, then play my last heart to pitch a spade, hoping to endplay East for a ruff-sluff.

Rainer Herrmann: Best chance seems to play Brutus for five hearts or more.

Thijs Veugen: My plan is to eliminate clubs and throw in East with the fourth heart, succeeding when East has at least five hearts.

Roland Voigt: At this vulnerability, West could overcall with nothing in clubs, so it seems better to play East for long hearts (five at least) than to rely on a finesse. I plan to ruff two clubs and one heart, then throw a spade on the fourth heart, endplaying East.

John Haslegrave: The plan is to eliminate clubs, ruff one heart, and pitch a spade on the last heart to throw East in.

Jerry Fink: Assuming Antonius would use a Roman jump overcall with 5-5 or 5-6 in the majors, I make it about 2-to-1 odds that Brutus holds five or more hearts. If so, he will be endplayed in hearts at trick 10. …

Laurentiu Dimcica: … I have two [realistic] options: the club finesse, or to throw East in with the last heart (after eliminating clubs). The latter requires East to hold 5+ hearts (or precisely Q-J-10-9), which seems better because East might have doubled the 2 opening with 6+ clubs. …

Steven Yang: I’m alarmed because three options suggest overtaking the K with the ace, and I don’t see a strong benefit in doing so. … I will play to endplay East, if he has five hearts. If East didn’t start with five hearts, perhaps I’m toast…

Yes, but in view of the occasion we’ll make it hot garlic bread.

Jim Munday: I see two chances: a club finesse, or a strip and throw-in. Either club finesse is 50 percent a priori;…but West has only seven available spaces (five spades, one diamond known), while East has 10 (one spade, two diamonds known), [so either finesse is 10:7 against]. Chances of East having to win the fourth heart are about 60 percent (5+ hearts or Q-J-10-9) plus a chance that East is caught napping [with Q-x-x-x]. …

Birol Guvenc: … Distribution of hearts-clubs East may be 5-5, 6-4, 7-3, 4-6 or 3-7, and the probability of the first three (longer hearts) is 59.5 percent. Therefore, I will play to endplay East, which is much better than the club finesse. …

Roger Morton: I’ll play to eliminate clubs and throw East in with the last heart for a ruff and discard.

Fred Upton: Options, like all Gaul, are divided into three parts: Finesse the Q, finesse the 10, or hope to endplay East in hearts. I trust not Antonius to hold any club honors at this vulnerability, but he is a reasonable favorite to have fewer than four hearts.

Grant Peacock: I know it’s matchpoints and favorable vulnerability; but do you normally bid on K-J-10-9-8 with a 2 bidder on your left? I don’t. If I assume that West’s excuse for bidding is 5-5 shape, Line D is 100 percent.

Junyi Zhu: Planning for an endplay on the fourth heart.

Meelis Tiitson: If this doesn’t work, I go to Plan B.

Brad Theurer: With East having only three pointed-suit cards, odds are good that he has 5+ hearts,…which is better than trying to guess which club honor (if any) West has. …

Alon Amsel: Playing East for five hearts, and throwing him in with my last heart.

Johnny Utah: I will ruff two clubs, one heart, and discard a spade from dummy on the A; then I will try to endplay East with the fourth heart, pitching another spade.

Julian Pottage: This makes anytime East has more hearts than West.

Thibault Wolf: The problem seems to be: What are the odds that West has the K after his 2 bid? In my opinion it’s [no better than vacant-space odds], as he just wanted to indicate a lead or defense — with five spades, I hope! Odds are better that West has less than four hearts, so I will play to endplay East on the fourth heart — and that’s much more elegant than a simple finesse!

Roger Miller: Then A, heart ruff, club ruff, and pitch a spade on the last heart to endplay East. I’ll be disappointed if West has more than three hearts.

Jonathan Brill: [Endplay described]. This makes whenever West is 5=3=1=4, and also with 5=4=1=3 if East wins the fourth heart.

Rob Wijman: This elimination play wins whenever East has to win the fourth heart, or if the K is doubleton — quite a bit better than a straight club finesse.

Jim Tully: Choice is between a club hook and a strip and endplay of East in the heart suit. West having a stiff spade and a doubleton diamond makes the latter a favorite.

N. Scott Cardell: … Odds are way against West having 4+ hearts for his 2 bid; and if he does, they are [probably weak], and even a good East player might fail to unblock with Q-J-10-x. [Endplay described].

Jonathan Ferguson: If East has 5+ hearts, or four and can’t or doesn’t unblock, this will succeed on a strip and loser-on-loser endplay.

Nigel Guthrie: I hope that East has five or more hearts, or the suit is blocked.

Final Notes

I hope you enjoyed the contest, as well as the ancient Rome theme. I knew if I waited long enough, I could find a reason for taking Latin. Thanks to all who entered, and especially those who offered kind remarks about my web site.

Attention! Everyone who scored below average please form a line at the south entrance of the Colosseum, then proceed single-file when the clarions play March of the Gladiators. Good luck, warriors!

Comments are selected from those scoring 49 or higher (top 210) or in the overall Top 100 prior to this contest, and on each problem only those supporting the winning play. This may be considered 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 about 80 percent of the eligible comments. If you supplied comments 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. If I use only part of a comment, an ellipsis (…) shows where text was cut. In some cases I have inserted text [in brackets] to supply an omitted word or phrase, or to summarize a cut portion. Comments appear in the 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.

Gotta go… Olive Garden tonight. The plebes can have the final words:

Paulino Correa: Tough, these Romans. Now I know how the Barbarians felt!

John R. Mayne: Man, nothing like a Roman National, where kibitzers are fed to the lions!

Richard Stein: The sword of Antonius and dagger of Brutus shall be cruel to him who is proud. Caveat declaror!

Bill Cubley: Expressing my confidence this month: “Quid? Me anxius sum?” -Alfredus E. Neumanus

Joon Pahk: If you have tears, prepare to shed them now. This was the unkindest cut of all.

Nigel Guthrie: Veni, vidi, revoki!

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