Main   Analyses 7X48 by Richard Pavlicek  

The Game Is Afoot

Thank you! Whether you survived the piranha tank or not, your participation was an inspiration to Holmes, who managed to make each contract. Moriarty, being a man of his word, promptly released his captives. Watson was so grateful that he vowed to write a bridge book on play of the hand. “I’m sure it’ll be a classic,” encouraged Holmes.
Problem 123456Final Notes

These six play problems were published on the Internet in August 2003, and all bridge players were invited to submit their answers. As declarer on each problem, all you had to do was choose your line of play from the choices offered.

Zahary Zahariev Wins!

This contest had 838 entrants from 114 locations, and the average score was 37.32. Like a rock concert with “ZZ Top,” congratulations to Zahary Zahariev (Bulgaria), who topped everyone with the only perfect score. This is no big surprise, as Zahary’s worst score in the last six contests is 56. Close behind at 59 were Kamal Roy (India); Charles Blair (Urbana, Illinois); Julka Kowalska (Poland); Darek Kardas (Poland); Wojtek Urban (Poland); Marcin Zbroja (Poland); and Nick Krnjevic (Westmount, Quebec).

In the overall standings, Charles Blair increased his lead with a phenomenal 59.75 average. Poor Charles had to settle for a subpar score this month, only 59. Not far back is this month’s winner, Zahary Zahariev with 59.00. Next are Wojtek Siwiec (Poland) with 58.75, John Reardon (UK) with 57.75, and Frances Hinden (UK) with 57.50.

Several people remarked that scores this month had to be the lowest ever* because of my plus-or-fishfood scoring. That is, once you miss a problem, you should be history (aka lunch) and score zero for the rest. Funny, but being a generous kind of guy, I’ll keep the status quo. For piranha points, you can assume that a score of 6 or higher on each problem keeps you out of the tank; but all your scores count no matter if or when you took a dip.

*Actually, they were almost right, as only one past contest had a lower average score (37.17 in February 2001). I’ll take the credit for posing some attractive alternative lines. Usually the consensus homes in on at least one of the top answers, but these problems were elusive.

Bidding and defensive play by West (Moriarty) is standard, and assume expert skill. For a reference on bidding and carding agreements, see my summary of Standard American Bridge. Do not draw any inferences from East (Moran) who always passes and knows little about card play except to follow suit.

Each problem offered six plausible lines of play. The merit of each is scored on a 1-to-10 scale based on my judgment, which is also aided by many of the comments received. TopMain

Problem 1

Plus-or-Fishfood N-S Vul (very)

West
Moriarty
1 C
All Pass
North
Watson
1 D
East
Moran
Pass
South
Holmes
1 NT

1 NT South
S 10 7 5 3
H K Q 9 8
D K Q J 10
C 4
Lead: C KTableEast plays C 2
S J 4 2
H 10 3
D A 6 4 3
C A J 10 8

Your play?

PlayAwardVotesPercent
C. Win C A; D K (both follow); D Q-J10364
A. Win C A; lead H 10 to king837745
D. Win C A; D K (both follow); all diamonds7334
F. Duck the first trick513316
E. Win C A; lead the C J312915
B. Win C A; run the H 10213016

It has often been said that 1 NT is the most difficult contract — either to declare or defend — and this problem should reinforce that claim. On the surface it looks easy (many respondents thought Line A was a lock) but there are underlying cobwebs, and even Holmes might consider it a three-pipe problem.

I held the South hand in a home team game and played in 1 NT after partner doubled the 1 C opening. (I gave you the 1 D overcall because Watson would not consider North a “good hand.”) Line A looked fine to me, and I easily made seven tricks on a friendly deal. Only later did I give it more thought and realize the subtle danger. Consider this layout:

1 NT
S 10 7 5 3
H K Q 9 8
D K Q J 10
C 4
S A K 9 8
H 6 5 2
D 8
C K Q 9 7 6
TableS Q 6
H A J 7 4
D 9 7 5 2
C 5 3 2
S J 4 2
H 10 3
D A 6 4 3
C A J 10 8

East, of course, ducks the H K.* Now what? Suppose you lead the H Q to East’s ace, then a club goes to your jack and West’s queen — your discard? Ouch. Dummy is squeezed. Pitching a major suit gives the defense an easy set, so suppose you let go a diamond. West now can lead a spade to East for a club through, and you have only six tricks — down one. It wouldn’t have helped to cash any number of diamonds early, as the squeeze still looms. In fact, once you make the heart play, there is no way to succeed.

*Yes, I know East is a moron — er, I mean, Moran — but he still may duck since he might not even know which heart would win the trick. Also, note that the conditions stipulated that East “always passes” so you can’t rule out any East hand as long as West’s actions are legitimate.

What, then? Ducking the first trick (Line F) allows West to shift to hearts; then the defense can set up seven tricks before you. Running the H 10 (Line B) is worse, as whenever it loses to the jack, East can return a club and West ducks your jack to prepare the run. Worst of all is to lead the C J (Line E) as this makes the winning defense obvious, failing anytime East has an entry.

“When you eliminate the impossible, whatever remains, however improbable, must be the truth.”

The key is to lead three rounds of diamonds early (Line C) to force a few discards from West in the critical situation above. You can counter anything, but suppose West pitches clubs to reach this position:

North leads
S 10 7 5 3
H K Q 9 8
D 10
C
S A K 9 8
H 6 5 2
D
C Q 9
TableS Q 6
H A J 7 4
D 9
C 5 3
S J 4 2
H 10 3
D A
C J 10 8

Don’t touch those hearts! If you do, you’ll be swept into the same dummy-squeeze. It is tempting to lead the last diamond, but this also falls short. Instead, you must lead a spade*, which goes to the jack and king; West then shifts to heart (best) and dummy’s king is allowed to hold. Now lead the last diamond; and if West pitches the C 9, you must exit with a club (not a heart) and your discard from dummy doesn’t matter with spades blocked. Whew!

*This is almost sure to be safe based on West’s known diamond shortness — either spades will be 3-3, or West will have four. In the latter case, East is marked with a doubleton honor from West’s failure to lead spades originally. Remember, despite Moriarty’s reputation, I stated that his defense was “standard” and “expert level” so you shouldn’t assume a diabolical, double-dummy plot.

If West instead pitches two hearts on the diamonds, you would then lead the H K — the squeeze danger is gone because the defense lacks communication in hearts. (If West pitches a club and a heart, you can lead either spades or hearts, so you have considerable latitude for success.) You can always get home after winning three diamonds; but there is no lock, as West might unexpectedly turn up with S A-8 H A-x-x-x D x C K-Q-9-x-x-x; then if you lead a spade to the jack and ace, a spade return allows East to run spades and accurate defense prevails. The good news, however, is that Moran probably wouldn’t know to finesse the S 9, or what to lead next.

If diamonds are 3-2, there is a sure-trick play based on the bidding and lead. After taking three diamonds, lead the H K (ducked) then another heart. If the defense tries to squeeze dummy by leading a club, pitch the last diamond. Then if dummy is forced on lead with the last heart, you are left with S 10-7-5-3 opposite S J-4-2 C 10, so just duck a spade to ensure a seventh trick.

I’m sure you’ll agree this was an interesting problem for a lowly 1 NT. Well, maybe not if you chose Line B, E or F, as Moriarty will bid you adieu. Please try to be quiet when you take the plunge so as not to disturb the bridge players. Hint: Keep your socks on, and the piranhas may lose their appetite.

Comments for C. Win C A; D K (both follow); D Q-J

Zahary Zahariev: It looks easy, but it isn’t. Normal play (H K-Q) goes down if East wins and return a club — dummy is squeezed. So three rounds diamonds, saving the D 10 if I need a discard. I haven’t seven tricks, but I can’t lose more than six. Only this works against a typical S A-K-x-x H x-x-x D x C K-Q-9-x-x in West.

Charles Blair: …“Hideous Holmes” may wish he let Watson play a hand for once.

Nick Krnjevic: If I hadn’t been told that no inferences can be drawn from Moran’s (is that the right second vowel?) bidding, I would assume he denied responding points… Since Moriarty failed to lead a spade, I will assume he does not have S A-K-Q. … Cashing all the diamonds seems wrong, since…if I next play a heart losing to Moran’s H A-J-x-x and a club comes back, I have to pitch a heart from dummy (else risk losing four spades); then the perfidious Moriarty wins the club and reverts to hearts, setting up the third defensive heart trick… The choice between the remaining lines is a function of whether Moran would ever duck the H A; if not, the simplest line is to win the C A and lead a heart up… but this seems much too straightforward… so I’ll assume he might duck by accident. As such, it seems best to play three rounds of diamonds, preserving the ace…

Patrice Piganeau: To avoid a suicide squeeze if East has H A-J-x-x.

Manuel Paulo: Consider this likely West hand: S A-K-x-x H x-x-x D x C K-Q-9-x-x. Moriarty leads the only suit that allows Holmes to win the contract. Nevertheless, if South ducks the first trick, West leads any red card. If South wins the C A and (1) leads to the H K, East ducks; (2) runs the H 10, East wins the jack and leads any black card; or (3) leads the C J, West can duck and wait for a club lead from partner. After winning the C A, declarer should win D K-Q-J… but not the last diamond [else] dummy will be squeezed eventually.

Jean-Christophe Clement: Next step is to play the H K, and wait for the seventh trick in spades, hearts or clubs.

Mitch Edelman: I would like Moriarty to be out of diamonds when he is put on lead; besides which, he will have to weaken his holding in one suit or another, and whichever suit he shortens will tell me how to play the hand. Why guess?

Paulino Correa: By Moriarty design, everything should be as bad as possible for Holmes; i.e., East must have H A-J, together with a spade honor and three clubs. Actually, knowing it is a psychological advantage, Holmes wins the lead and gives three rounds of diamonds… and sooner or later the defense will have to concede the seventh trick.

Comments for A. Win C A; lead H 10 to king

Leif-Erik Stabell: Both Lines A and C will secure seven tricks with diamonds 3-2, and there are some distributions where only Line C will succeed on best defense… but this might require a good view later… But why get into such a situation when there is a much simpler solution? Surely, Moran will grab the H A if he has it and fire back a club at trick three. …

Venkatesh Ramaratnam: … As always the toughest problem on a bridge table is to play or defend 1 NT, and all traditional scoring methods have an unfair bias towards game and slam contracts. At least you have made a beginning by scoring it on par (staying out of piranha tank) with other contracts. :)

Marcus Chiloarnus: “A man with so large a brain must have something in it.”

David Cochener: Assumes East is too poor to duck the H A if he has it. … If East wins the H A, he probably returns a club to my 10, which West can’t duck…

Neelotpal Sahai: No line is perfect. This looks best because the H A may be onside; but even if it is offside, it will work if East wins the H A.

Richard Aronson: Lines B, E, and F can lead to easy and obvious sets… Although Lines C and D might put pressure on the defenders,… Line A has one huge advantage: Very few Easts will be willing to risk ducking the H A and letting you run away with seven tricks (and not cashing nine defensive tricks) when my hand was S J-4-2 H 10-3 D A-6-4-3-2 C A-J-9; certainly the non-bridge-playing Colonel Moran is not up to this task.

Hans Holme: I have six tricks now; then diamonds and the last heart because West is the favorite to hold the H A.

Sorry, Hans, but spelling counts. Your last name
leaves me singularly unimpressed.

Dale Rudrum: … I changed my vote to Line A because I don’t trust West, who might have six spades. Against the most devious villain in recorded history, this option is very real.

Pat Rich: East almost surely has a high spade honor, and is therefore unlikely to have the H A also; so I play West for that card. …

Albert Ohana: East cannot have a high spade and the H A but may have a spade honor and the H J.

Srikant Sridevan: Banking on the fact that Moran won’t duck holding the H A!

Ed Barnes: Don’t know how crafty this villain is, though I’d rather be fishfood than squashed by a normal lie of the cards. TopMain

Problem 2

Plus-or-Fishfood N-S Vul (very)

West
Moriarty
1 D
All Pass
North
Watson
Dbl
East
Moran
Pass
South
Holmes
2 C

2 C South
S A 4 2
H A Q 6
D A 5 4 2
C K 4 2
Lead: S QTable
S K 7 6
H 8
D 9 7 6 3
C Q 10 9 7 5

Your play?:

PlayAwardVotesPercent
D. Win S K; S A10648
E. Win S K; finesse H Q940248
A. Win S A; H A8607
B. Win S A; lead C 2 to queen5415
F. Win S K; lead C 5 to king418522
C. Win S A; lead C 2 and finesse 1038610

Watson is forbidden to bid notrump, so with a good hand his only recourse was to double. Elementary, is it not? At least it brings fish food for thought, as 2 C is an excellent contract. West’s lead of the S Q is probably top of a sequence (Q-J-10) but could be a short suit — even a singleton. (Don’t forget that Moran always passes, so you can’t rule out a long major in the East hand.)

The 1 D opening is noteworthy, especially considering your 4-4 fit. Could West have five diamonds? Hardly, as he would surely have led a diamond from K-Q-J-10-8. Therefore, he must have four (possibly three) and they should not be headed by K-Q-J.

As supported by the overwhelming consensus, the early heart finesse seems a standout with West having most of the high cards. Even if it loses, the H A will provide a discard; so it looks like a free shot. Certainly, it gives you excellent chances, but there are dangers. Consider this layout:

2 C
S A 4 2
H A Q 6
D A 5 4 2
C K 4 2
S Q J
H J 10 7 4
D K Q 10 8
C A J 8
TableS 10 9 8 5 3
H K 9 5 3 2
D J
C 6 3
S K 7 6
H 8
D 9 7 6 3
C Q 10 9 7 5

Suppose you win the S K and finesse the H Q, losing to the king (of course, with Moran sitting East the H Q might actually win); then a diamond comes back to the ace. You next pitch a spade on the H A and ruff a heart; then cross to the S A and ruff a spade to prepare for an endplay. Oops, West overruffs; down one. Alternatively, you could forget the elimination technique and just try to guess the C J; but that’s not much of a cushion against a piranha luncheon.

“Always look at the hands first, Watson, then cuffs, trouser knees, and boots.”

Rather than become involved with finesses or bad breaks, Holmes saw a superior plan in Line D. After cashing two spades, win the H A and ruff a heart; cross to the D A and ruff the last heart to reach:

South leads
S 4
H
D 5 4 2
C K 4 2
S
H J
D K Q 10
C A J 8
TableS 10 9 8
H 9 5
D
C 6 3
S 7
H
D 9 7 6
C Q 10 9

Now exit with a spade or a diamond, and you must eventually get a free club finesse to ensure two more trump tricks. This line is not foolproof, as it’s possible (with Moran East but not in real life) you could have been overruffed in hearts; though the scenario for failure is negligible.

What about Line A? Doesn’t this offer the same elimination chances? Well, not quite. The significant flaw occurs when West has a singleton spade; when you later try to cash the S K, he will ruff a winner, after which there is no recovery. Observe that with Line D, if West has a singleton spade, he can only ruff a loser.*

*Whether West ruffs or not, you have a virtual lock because he is marked for 1=4=4=4 shape. If he ruffs, you can later pick up trumps by leading low to the queen (then finesse for the jack). If he discards, you can win the S A and continue the elimination.

It was a photo for second place between Lines A and E. Line A loses outright to a singleton spade; while Line E still has chances when West has S Q-J doubleton. Rather than send it the lab for a DNA analysis, I went with the voting favorite.

Lines B, C and F are much inferior, basically relying on guessing clubs or a subsequent heart finesse. The edge goes to Line B as West is a slight favorite to hold the C J; and Line C is worst with a first-round finesse through East. Several people wondered why I didn’t include Line G: Win S K and run the C 10. Well, my format is limited to six choices, and this seemed like a weak way to start clubs. Sorry, splash.

Comments for D. Win S K; S A

Zahary Zahariev: Then H A, heart ruff, D A and ruff H Q. Now exit with a card and wait for two trump tricks. A singleton S Q is the danger [to guard against].

Charles Blair: Ruff two hearts, or hope the Professor is 1=4=4=4.

Nick Krnjevic: Given the lack of a diamond lead, I’ll assume Moran has the D Q (likely singleton). My plan is to [cash all side winners], ruff dummy’s hearts, and exit with a diamond. I’ll have six tricks in, and with C K-x-x facing Q-10-9, opponents will have to give me two trump tricks. Since there is a small possibility that the dastardly Moriarty has led a singleton S Q, I should win the first trick in hand and continue the suit. If Moriarty ruffs, I can play him to be 1=4=4=4. …

Leif-Erik Stabell: It is safe to assume East has a diamond, since West would have led one with D K-Q-J-10-8. So S K-A, two red aces and two heart ruffs brings the total to six; then I can exit passively and wait for two club tricks. If West ruffs the second spade, he must be 1=4=4=4, so I can pick up clubs for just one trump loser.

Dale Freeman: The plan is to get S A-K, H A, two ruffs, and D A, then wait for two club tricks with K-x-x opposite Q-10-9. The spade plays at tricks one and two are to check if West is 1=4=4=4.

Frances Hinden: I’m hoping to ruff a couple of hearts in hand, but I don’t want to get the S A ruffed if West is 1=4=4=4 (he can’t really have five diamonds, as no diamond lead).

Douglas Dunn: I’m assuming Moriarty would have led diamonds holding K-Q-J-10-8. If the spades and D A stand up, there are eight tricks ruffing two hearts in hand.

Bill Erwin: After winning two spades, play H A, ruff a heart, diamond to the ace (diamonds cannot be 5-0 or Moriarty would have led D K) and a heart ruff. That’s six tricks, and the remaining clubs are good for an additional two. This needs West to hold three hearts.

Venkatesh Ramaratnam: If West follows to the second spade, continue with H A, ruff a heart back, D A, ruff a heart back and exit with a diamond to wait for two club tricks. If West ruffs the second spade, win any return and play West for the C J.

John Reardon: Planning to win two spades, one heart, one diamond and two heart ruffs before I exit. I will still have C K-x-x and Q-10-9 for two more trump tricks.

Marcus Chiloarnus: Although Lambert is absolutely devoid of reason, he is as tenacious as a bulldog when he once understands what he has to do.

Rob Stevens: If the S A and D A stand up, I can ensure the contract by ruffing two hearts in hand and endplaying the opponents to lead trumps.

Tim DeLaney: With all five missing diamonds, West would lead the D K; so he must have fewer. The plan is to ruff two hearts low in the South hand, cash all plain suit winners, and exit with a diamond, guaranteeing two more tricks. The heart finesse is a mirage; it cannot improve my chances of going plus. Line D is better than Line A because it allows me to deal with West’s possible 1=4=4=4 shape.

Michael Errington: West’s diamonds aren’t solid from his failure to lead them… I play up to the S A to test if West has led a singleton, in which case he must have four trumps. If he ruffs in front of the S A, I can later pick up his trumps by leading to the queen then running the 10. If he doesn’t ruff, or if he follows suit, I plan to make four more tricks with red aces and heart ruffs, then exit in diamonds and wait for two more trump tricks…

Sandy McIlwain: … The odds don’t favor a third round of spades getting through (for a ruff) if the heart finesses loses.

Carsten Kofoed: If West has three hearts, the piranhas will starve.

Ted Morris: If I can win four top tricks and two hearts ruffs, the opponents will have to play clubs for me and give two more winners there.

Leah Cohen: Then ruff two hearts. Might survive 6-1 spades.

Rainer Herrmann: Why is the play, “Win S K; H A,” not offered? Would it be a tough contender to the approach of Line D? It looks better to me should the H K drop doubleton, though Line D seems better should West have 1=4=4=4 distribution.

Rainer is exactly right. It would really be splitting hairs to judge between his alternative and Line D, so I didn’t include it. –RP

Neelotpal Sahai: This will work as long as West doesn’t have five diamonds, nor less than two spades and three hearts. If the distribution is less friendly than assumed, then I have to guess the C J.

Vlastimil Lev: West’s diamonds are not K-Q-J-10-8 (then D K lead would be led)… so S K; S A; H A; heart ruff; D A; heart ruff; then exit with a diamond to endplay opponents.

N. Scott Cardell: … Most of the time finessing the H Q will gain a trick or break even; but it endangers the contract when East has the H K and West is short in spades. The heart finesse might be necessary if West is exactly 3=3=5=2 with the H K, but then he probably would have led the D K. If West ruffs the second spade, he should be 1=4=4=4, so I will win his red-suit return and lead to the C Q.

Barry Rigal: I’d play S K, heart to ace, heart ruff, S A, heart ruff, diamond to ace, then await two more club tricks; but this line looks equivalent.

John Youdell: Eliminatory, my dear Watson. Then H A, heart ruff, D A, heart ruff, and exit… Hopefully, the D A will not be ruffed as Moriarty would likely lead from D K-Q-J-10-8 even if the S Q is singleton.

Rick Salkov: Then H A, ruff heart, D A, ruff heart, exit with a spade and wait for a trump lead.

Kjetil Hildal: Then H A, heart ruff, diamond to ace (5-0 split unlikely based on the lead), heart ruff, diamond. The endplay will ensure the survival trick.

Comments for E. Win S K; finesse H Q

Manuel Paulo: The heart finesse seems logical, and Line E is the only winning line when West has S Q H K-x-x-x D K-Q-J-10-8 C A-J-x (or A-x-x), or S Q H K-x D K-Q-J-10-8 C A-J-8-6-3.

Richard Aronson: It seems likely diamond honors are split. East almost certainly has at most 3 HCP outside his assumed D Q, and distribution is not extreme. … If the heart finesse loses, it’s [also] a discovery play. Since East has (presumably) H K-x-x-x-x D Q and didn’t bid, I can place West with the C J, avoiding the loss of two club tricks. Okay, I know that Moran was instructed just to pass, but am I supposed to play bridge or take those conditions as binding?

When in doubt, follow the directions; but you make a
good point. I might have lied about the whole thing.

Jess Cohen: … This is about finding the “Crown Emerald,” and that is a clue diamonds aren’t breaking 3-2.

Paulino Correa: … Moriarty can be truly devilish if he has S Q-J-10-x H x D K-Q-J-x C A-J-8-x, but in this case I don’t see what Holmes can do.

Samer ElSheikh: If the finesse fails, it will account for all of East’s points (H K and D K or D Q), so I can play West for C A-J. East will likely return his singleton diamond honor; I take ace, H A for a spade discard, heart ruff then run the C 10.TopMain

Problem 3

Plus-or-Fishfood N-S Vul (very)

West
Moriarty
1 S
3 D
North
Watson
Dbl
3 H
East
Moran
Pass
All Pass
South
Holmes
2 H

3 H South
S A Q 6
H K Q 10 2
D Q J 3
C A J 4
Lead: C KTableEast plays C 3
S 8 7 4
H 9 6 4 3
D 10 5
C Q 10 8 2

After winning the C A, how do you play?

PlayAwardVotesPercent
C. Lead the H 21011013
B. Lead the H 10911213
A. Lead the H K735743
D. Lead the D Q621125
E. Lead C J to queen2213
F. Lead C 4 to 101273

Watson had a better chance of going plus by passing 3 D, but he relishes being dummy. The good news is that the C K is onside; the bad news is that it’s surely singleton. With a ruff threatening it seems right to get trumps out, and the consensus was to begin by leading the H K. Predictably, the layout will be:

3 H
S A Q 6
H K Q 10 2
D Q J 3
C A J 4
S K J 10 9 2
H A 5
D A 8 7 6 2
C K
TableS 5 3
H J 8 7
D K 9 4
C 9 7 6 5 3
S 8 7 4
H 9 6 4 3
D 10 5
C Q 10 8 2

West will win the H A and switch to diamonds; then he’ll get his club ruff (well, maybe not with Moran East); down one. Does this mean our hero was destined for the seafood buffet? Maybe not.

“All the cards are at present against us.”

With a club ruff imminent, Holmes knew the cards were at present against him; but in times of danger it pays to stay calm. Moriarty’s bidding surely indicated 5-5 shape, so the singleton club dictates a holding of H A-x. He couldn’t stop Moriarty from making two trump tricks, but there was no need to waste his king in the maneuver. The unnatural lead of a low heart (Line C) neatly solves the crime. Even if Moran plays the H J (no doubt by accident), the defense can win only two trump tricks.

What about leading the H 10? This is almost the same, but there are a few rare cases where it costs. If East has H A-J-8-7 (giving West 6-5 shape) he can capture the 10 with the jack and eventually make a third trump trick; while leading the H 2 forces him to capture air (or lose a tempo) and let you succeed. In contrast, I couldn’t think of any layout where the H 10 gains over the two.

A number of people chose to lead the D Q (Line D), which is sort of a mark-time play to avoid an early commitment in trumps. Unfortunately, it leads to defeat in my example. After getting the club ruff, West will lead a third diamond; then upon winning the H A, a fourth diamond will promote the H J no matter how you play hearts. To succeed, you must lead trumps immediately.

I was generous with the scoring this time, allowing both the H K and D Q to escape the ominous fish tank (remember, a score of 6 or higher is OK for piranha points). But don’t let it go to your head; I’ll get you on the next one for sure.

The club leads (Lines E and F) are grossly inferior — kind of like saying: Take me, I’m yours — or more appropriately, taking an afternoon swim. There must be some edge in the graceful unblocking play of Line E, so those who chose Line F will make the first splash. Winning tip: Go in with a cannonball, and the little buggers may save you for dessert.

Comments for C. Lead the H 2

Zahary Zahariev: Most difficult, as the H 2 and H 10 seem equal; but I choose Line C. There are some hands that only the H 2 wins, e.g., if West has S K-J-9-x-x H x D A-K-x-x-x-x C K.

Leif-Erik Stabell: Better than the H 10, since it also succeeds in the unlikely case of East having H A-J-8-7. If I lead the 10, I cannot avoid a trump promotion later.

Douglas Dunn: … This should make when West has H A-x, whereas Line A would fail if East has a diamond entry for a club ruff.

Manuel Paulo: West’s bidding delivers at least 10 cards in the pointed suits, and the opening lead should be a singleton. Consider West distributions of 6=2=4=1, 6=1=5=1, 5=2=5=1 and 5=1=6=1 (7=1=4=1, 7=0=5=1, and 6=0=6=1 are irrelevant) with trump and diamond variances, assuming East should hold one [entry] but not two. It’s easy to see that the probabilities of the six lines follow these relationships: E<D<A, E<B<C and F<E; so it’s enough to compare Lines A and C. Within the set premises, Line C has a 5:3 advantage over Line A.

Wanna run that by me again? Maybe if you integrate
both sides it will prove that Line E = MC².

David Cochener: Surely East is not sharp enough to play the H J from J-x-x, and this guards against a singleton H A in West. This will limit my losers to two hearts and two diamonds.

Julian Pottage: If, as is likely, West is 5=2=5=1 it makes no difference whether I lead the H 2 or 10. However, if West is 5=1=5=2 with a bare H J, the two is better.

Javier Carbonero: If East has H A-J-x, I am already fishfood; so forget it. West desperately wants a ruff because of the lead… so he may have (1) S K-J-10-x-x H A-x D A-x-x-x-x C K, or (2) S K-J-10-x-x H J-x D A-x-x-x-x C K. The danger is the loss of three trump tricks (H A-J plus a club ruff) so trumps must be led (Lines D, E and F are inferior) — a small one (two or 10) in Case 1, or a big one (king or queen) in Case 2. According to the bidding and lead, Case 1 is by far more probable…

Richard Aronson: It’s easy to assume West has one club. If West has nine pointed cards, Lines E and F risk losing two club ruffs. Line D lets them get all the tricks they deserve (probably one club ruff as East should have only one entry)…which works fine if West is 5=3=4=1, but goes down if West is 5=2=5=1 and East has H J-x-x. So a trump lead is the [best] course of action. … The H K works when East has no entry (possible on the bidding) or when hearts are favorable; the H 2 works even if hearts are unfavorable…

Sapan Desai: I need West to hold H A doubleton and a hand pattern of 5=2=5=1 for his 3 D bid. If East wins the H J, then West can only get a club ruff with the H A.

Jean-Christophe Clement: Line A is the winner if West has H A-x-x; but West is more likely to hold H A-x, in which case Lines B and C are OK. …

Brian Patmore: Paradox, here: I cannot win if East has H A-J-x, as I must lose two diamonds, two hearts and the obvious club ruff; yet I can win against a 4-1 split. West’s shape must be 5=2=5=1 or 6=1=5=1. In either case a small heart to the nine is the best play. If East wins the jack from J-x-x, West is welcome to ruff a club with the H A.

Albert Ohana: By playing a small trump, if East wins the jack, West will have to ruff with the ace. More probably, West will take the ace and obtain a ruff; but then I won’t lose any more trump tricks.

Sheila Dickie: Looks like the only chance to keep my heart losers to [two] is to find A-x on my left… If so, even with diamond honors split, I can stand the ruff.

Elianor Kennie: I’m playing West for H A-x for his three-level bid… If East has H A-J-x, nothing can be done to stop the ruff and defeat of the contract.

Murat Azizoglu: The hope is to limit my losses to two trumps and two diamonds. Maybe East will duck with his H J, or maybe West will have H A-x.

Comments for B. Lead the H 10

Charles Blair: I’m playing Professor Moriarty for 5=2=5=1, but Line C looks equivalent. Am I supposed to worry about 4=2=6=1?

Nick Krnjevic: The auction and the lead suggest that Moriarty is 5=2=5=1…and is missing the D A or D K. Lines A, D, E and F all fail to a combination of ruffs and uppercuts that enable the defense to score three trumps and two diamonds. …

Dale Freeman: It looks like West is 5=2=5=1 with H A-x (otherwise strange lead). Any method other than Lines B and C has a good chance of losing H A, H J, one ruff and two diamonds. …

Bill Erwin: West is 5-5 in the pointed suits with H A-x. Playing the H 10 gives a trump trick to East, but a club ruff will be with a natural trump trick. East [probably] has a high diamond, so the H K will permit a club ruff in addition to two diamonds and two hearts. …

Venkatesh Ramaratnam: On the bidding…West rates to hold at least 10 cards in the pointed suits. Playing the H K from dummy loses if West holds H A-x and East has a diamond entry to give West a club ruff. …

John Reardon: West is likely to be 5=2=5=1. If East wins with the H J, West’s only remaining trump will be the ace. I will therefore be able to dispose of North’s third spade on the long club in time.

Rob Stevens: West appears to be 5=2=5=1. The H 10 allows South to draw trumps quickly enough to run clubs and discard the spade loser. West’s club ruff will be with the H A.

Tim DeLaney: The 3 D bid must surely show a five-card suit, so West is 5=2=5=1 or 6=1=5=1. In the latter case, I will be forced to guess who has the D K unless I can coax Moran to cover the heart. …

Toby Kenney: West must be 5-5 in the pointed suits, and the club lead is clearly a singleton. If West has two low hearts, or if the spade finesse fails, there is nothing I can do. Leading the H 10 caters for either doubleton honor with West, unless East has both H A and D K.

Gareth Birdsall: Assuming West is 5-5, then the H K loses when West has H A-x. I don’t see much difference between playing the H 10 or H 2.

Michael Errington: On the bidding and lead West is probably 5=2=5=1 with H A-x. His rather speculative choice of leads suggests he doesn’t have D A-K, hence East will have an entry for a club ruff. Leading the H 10 permits me to pick up trumps with just two losers.

Carsten Kofoed: The bidding and lead suggest that West is equipped with S K-J-10-9-x H A-x D A-x-x-x-x C K.

Catalin Lazar: West has H A-x and a singleton club; otherwise, he would not risk leading the unsupported C K. Therefore, I should play the H 10; opponents can take only two hearts and and two diamonds, assuming the S K is onside.

Julian Wightwick: Moriarty would expect the C A to be in dummy, but that’s still an odd lead. Perhaps he has H A-x, and the diamond honors are split. In that case, he is presumably 5=2=5=1, and I am in danger of losing two diamonds, two hearts and a club ruff. The low heart now means they won’t be able to unravel all the tricks. …

Andrew de Sosa: Looks like Moriarty started with 5=2=5=1 distribution with H A-x and, from his failure to lead diamonds, only one top diamond honor. I can afford to lose two hearts but not three, so I’ll concede the H J to either opponent and negate Moriarty’s ability to ruff a club with advantage.

Sandy Barnes: This should restrict heart losers since West has only two hearts, one of them expected to be the ace.

Jess Cohen: Ruffs are looming over the moors, not only the apparent one in clubs but the hidden one in diamonds. … Give West S K-J-10-x-x H A-5 D A-x-x-x-x C K. If I lead a diamond, East wins and gives West a club ruff; then ace and another diamond; now when West wins the H A, he plays a fourth diamond to let East win his H J en passant. Lines E and F also lead to the same way to Reichenbach Falls. The H 10 wins against the envisioned West hand. … I note that if East has S x-x H A-x-x D K-x-x C x-x-x-x-x, the H 10 is won by West’s jack; diamond to king, and a club ruff sets me. Well, the dog holding that hand didn’t bark out a notrump; and even though he is a non-bidder, I still take the dog who didn’t bark as a clue.

David Davies: If I play the H K and West has H A-x the defense can go: diamond to king, club ruff, and I still have a diamond and a heart to lose. Playing the H 10 means I cannot lose more than two hearts in this position.

Karel de Raeymaeker: Got to play opener for H A [blank] or H A-x.

Mike Kerr: If West is 5=2=5=1, he must have a heart honor, or I lose. If West has H J-x, leading the H K wins; but the H 10 loses only if diamond honors are split… If West has H A-x, leading the H 10 wins; but the H K loses if diamond honors are split.

Carlos Dabezies: West figures to have one or two hearts, and I want to stop a ruff with a low trump. Playing the H K will lose if West has H A-x, and I may want the H 9 for an entry later on.

Adam Folke: I can afford to lose two hearts and two more tricks. … Since West has either 6=1=5=1 or 5=2=5=1, even if he gets his ruff it will be with a natural trump trick. If hearts divide 4-1, I’ll just play diamonds to set up my trick before I run clubs and throw the losing spade.

Stu Goodgold: The doctor, er, I mean, professor, must have led a stiff C K. I can lose two diamonds and two trumps, so do I play Moriarty for 5=2=5=1 or 5=3=4=1? I don’t see how to cover [both], but if he has H A-x, the H 10 looks good. TopMain

Problem 4

Plus-or-Fishfood N-S Vul (very)

West
Moriarty
2 S*
All Pass
North
Watson
3 C
East
Moran
Pass
South
Holmes
3 NT
*weak; undisciplined

3 NT South
S J 8 3
H K
D A 6 5 2
C K Q 10 8 7
Lead: S 10TableEast plays S Q if you play jack; else S 4.
S A 2
H A Q J 5
D K Q 10 4
C 5 3 2

Your play?

PlayAwardVotesPercent
B. Play S J; win second round1010312
E. Play S 3; win second round; win H K823428
A. Play S J; win first round6223
C. Play S 3; win first round; win H K523328
D. Play S 3; win first round; lead C 2214718
F. Play S 3; win second round; lead C 219912

Considering Professor Moriarty’s infamy, it was hardly necessary to note that his weak two-bids are undisciplined; but there’s something to be said for full disclosure even at plus-or-fishfood scoring — kind of like honor among thieves. With any other partner, you would have passed 3 C; but the pressure might have been too much for the good Doctor, even in a laydown contract.

Three notrump is excellent, probably with nine top tricks, so it is easy to rank Lines D and F in the basement. Giving up a club before testing diamonds is like dangling your feet over the edge of the piranha tank. I suspect that some who chose these lines miscounted their tricks. No problem; splash.

The key play appears to come at trick one. Instinctively, it feels right to play low from dummy and win the first trick (Line C) as spades will be blocked if Moriarty has a six-card suit. But then you remember the “undisciplined” clue. If spades are 5-3, it doesn’t seem to matter what you do, as the suit will always be runnable; but maybe it does. Consider this deal:

3 NT
S J 8 3
H K
D A 6 5 2
C K Q 10 8 7
S K 10 9 7 6
H 3 2
D J 9 8 3
C A 9
TableS Q 5 4
H 10 9 8 7 6 4
D 7
C J 6 4
S A 2
H A Q J 5
D K Q 10 4
C 5 3 2

Suppose you start with Line C. After winning the H K, you come to hand with the D K and cash hearts to put pressure on West. This is the position before you lead the last heart:

South leads
S J 8
H
D A 6 5
C K Q 10
S K 9 7 6
H
D J 9 8
C A
TableS Q 5
H 10 9 8
D
C J 6 4
S 2
H J
D Q 10 4
C 5 3 2

The H J squeezes West out of a good spade. Alas, this doesn’t help because it also unleashes two heart winners for East, so there’s no way to succeed. If only East didn’t have an entry, you’d be in great shape, and therein lies the solution.

“Circumstantial evidence is occasionally very convincing, as when you find a trout in the milk.”

At trick one, you must cover with the S J to force East to play the queen. (Actually, “force” might be too strong with Moran sitting East, as the S J may even win.) Then West would have no escape in the above ending; when he perforce pitches a spade, cross to the D A, discovering the layout, then exit with the C K to ensure the contract.

Either Line A or B succeeds in my example, but Line B is much better as it also caters to the common 6-2 spade breaks when East has the C A, i.e., when Moriarty has S K-10-9-x-x-x H x-x D J-9-8-x C x. Luckily, Line A keeps you out of the fish tank.

Between Lines C and E, it may seem that winning the first spade (Line C) is better, but this is an illusion. The only danger exists when West has a diamond stopper, in which case the holdup cannot lose toward making the contract (it might cost an overtrick or two). In contrast, winning the first spade loses when West has, say, S K-10-9-7-6 H x-x-x D J-9-x-x C A. You cannot succeed after leaving the opponents a double spade entry, but Line E works fine. In fact, Line E is even better than Line A.

I was generous on the last problem, but this time you’ll have to go swimming with Line C. Sorry. It may not seem right to put Line C in the same class as Lines D and F, but it’s getting late and the piranha are in a frenzy.

Comments for B. Play S J; win second round

Zahary Zahariev: If West has D J-x-x-x, I must be sure that only he can take the S 8 when I throw him in.

Charles Blair: Then H K, D K, run hearts, D A, and exit with the C K if necessary. This will work if the Professor has S K-10-9-x-x-x H x-x D J-9-x-x C x.

Nick Krnjevic: I must cater to Moriarty holding D J-x-x-x and the C A. Additionally, since the evil Moriarty is undisciplined, he may hold a five-card spade suit; consequently I cannot simply win the first spade and play a club. Instead, I must win the second spade; play a heart; then a diamond to the king and cash out hearts. In the six-card ending Moriarty comes down to two spades since he must hold three diamonds and the C A; then D A (to confirm the suit break) and a club honor. If Moriarty has the ace, he is endplayed; if Moran has it, I need him to hold a doubleton spade. I had to play the S J at trick one to prevent Moriarty from being able to exit with a low spade to Moran’s queen to cash heart tricks…

Patrice Piganeau: In case West holds S K-10-9-x-x H x-x D J-9-x-x C A-x.

Leif-Erik Stabell: “Undisciplined” certainly indicates that spades may be 5-3. If West has S K-10-9-x-x H x-x D J-x-x-x C A-x, an endplay is looming; but it will fail if I don’t cover at trick one since East will have the S Q entry to his heart winners. The endplay will also work if West has one more spade and not the C A; he will then discard two spades on the hearts, and I must exit with the C K. If West wins, I have an extra diamond trick in the end; if East wins, an extra club trick. … I cannot win if West has S K-10-9-x-x H x-x D J-x-x-x C x-x (he will discard one club and one spade on the hearts), but surely he is not that undisciplined.

Dale Freeman: Then H K, D K, three more hearts and D A, going for an endplay if West has four diamonds. The only hand that will give me a problem is West with S K-10-9-x-x, D J-x-x-x and no C A (that is undisciplined) but then East might have made a noise in spades with S Q-x-x, C A and a singleton diamond.

Sorry, but the only noises you’ll hear from the Colonel
will be a grunt or two when he breaks your arms.

Frances Hinden: My basic plan for nine tricks is to make four diamonds. This play in spades ensures I can strip-squeeze West if he started with D J-x-x-x and either the C A or a club void.

Douglas Dunn: This play knocks out East’s entry in case West started with S K-10-9-x-x H x-x D J-x-x-x C A-x. Now West can be thrown in with the C A after cashing heart winners and two top diamonds.

Bill Erwin: Nine tricks are there if West has fewer than four diamonds (to the jack), so club plays cannot be right. Next win H K, D K and H A-Q-J; then a diamond to the ace reveals the 4-1 break. Now the C K or S 8 will endplay West, but the C K is better since East may have the C A [and no more spades].

Venkatesh Ramaratnam: This removes a late spade entry to the East hand, as well as cutting communication if spades are 6-2. Continue with H K, D K, cash hearts and play a diamond to the ace. If West shows up with four diamonds, I [may] need to read the ending correctly to exit with either S 8 or C K.

John Reardon: The only danger is that West has D J-x-x-x, in which case I will know what to do in the endgame. West may well be 5-4 in spades and diamonds, then I will succeed if he has the C A.

Marcus Chiloarnus: “I have no desire to make mysteries, but it is impossible at the moment of action to enter into long and complex explanations.”

Rob Stevens: Playing low and winning the S A will work whenever spades are 6-2. But this isn’t necessary since the contract is cold anyway unless East has 7+ hearts — if West has four diamonds, he will be strip-squeezed. But if West has only five spades and the C A, the S J will remove West’s later exit to East. The S J also works if West got tricky and led from S K-Q-10-9-x.

Nigel Guthrie: Then H K, D K, H A-Q-J and D A to cater for West’s S K-10-9-x-x H x-x-x D J-x-x-x C A.

Tim DeLaney: Then H K, D K, run hearts, and cross to the D A. If West has a diamond stopper, play the C K to endplay whoever wins it. If West has fewer than two hearts, or fewer than six spades, I must hope he has the C A; or I am fishfood.

Toby Kenney: If diamonds don’t work (West has D J-x-x-x), the run of hearts will effect a squeeze-endplay against West; but if East still holds a top spade (West having only five), West can exit with a spade to East, who can then cash his hearts.

Michael Errington: If the bidding were true, spades would be blocked and the hand laydown, even if West has a diamond stopper. But your “undisciplined” hint (did East alert?) suggests I have to cater for S K-10-9-x-x, too. No problem; I ought to be able to gauge the distribution by cashing hearts then testing the diamonds. If West should turn up with D J-x-x-x, he will be endplayable — but only if have made the precautionary play in spades to exhaust East’s entry to his long hearts.

Carsten Kofoed: The S J removes the connection between East and West and leads to an endplay.

Manuel Paulo: The problem of cashing nine tricks arises only if West can stop diamonds. Consider these West hands: (1) S K-10-9-x-x-x H x-x D J-x-x-x C A (normal bid), (2) S K-10-9-x-x D x-x C J-x-x-x A-x (undisciplined bid); (3) S K-10-9-x-x-x H x-x D J-x-x-x C x (?!? bid). … Only Line B works against all three…

Rich Pavlicek: I can’t see how to make this if West has S K-10-9-x-x H x-x-x D J-9-8-x C x; but this would make his hand extremely weak. … If West has the C A, I can make the contract by forcing East to give up his spade entry; then I can throw in West (assuming he has diamonds stopped).

Connie Delisle: In case West has only five spades and the C A, a squeeze-endplay will work.

Leah Cohen: Then unblock H K, D K, [run hearts and D A]. If West has four diamonds, exit with the C K. This wins if spades are 6-2, or if 5-3 and West has the C A.

Julian Pottage: If West is 5=2=4=2 with the C A, it is vital to play the S J; and if West is 6=2=4=1 without the C A, having played the S J, it is essential to win the second round.

Julian Wightwick: I only have a problem when Moriarty has D J-x-x-x. I’ll unblock the H K, cash the D K and all hearts, then cross back to the D A. When Moran shows out, I can endplay Moriarty…

Pratap Nair: Next a heart to the king, return to the D K and cash…hearts. A diamond to the ace reveals the position; finesse diamonds or throw in West.

Frans Buijsen: Preparing the three-suit strip squeeze if West has S K-10-9-x-x H x D J-9-8-x C A-x-x. TopMain

Problem 5

Plus-or-Fishfood N-S Vul (very)

West
Moriarty
1 H
3 H
North
Watson
2 H*
3 S
East
Moran
Pass
All Pass
South
Holmes
2 S
*Watson make-me-dummy transfer

3 S South
S A K Q J 10 9
H 10 5 3 2
D 5
C K Q
Lead: H KTableEast plays H 6
S 8 6
H J 4
D Q J 4
C A 8 6 5 4 2

West next leads the C J (won by king) as East plays C 3. Your play?

PlayAwardVotesPercent
B. Draw trumps; lead D 5108610
D. Draw trumps; win C Q; lead D 5914718
A. Draw trumps; lead H 36354
E. Lead the H 3539247
F. Lead the D 54597
C. Draw trumps; win C Q; lead H 3211914

For most players, North’s 2 H cue-bid is Michaels (spades and a minor); but for Watson it shows only spades, a suit he is not permitted to bid. How con-veen-ient, allowing Holmes to declare another one. When Moriarty competes to 3 H, the good Doctor is happy to raise with his adequate trump support.

Charles Blair brought up the interesting point that with dummy producing 150 honors, Holmes could just claim eight tricks for down one and go plus. OK, wise guy, I neglected to say that honors don’t count. As the shameless inventor of P-or-F scoring, I’ll make up the rules as I go. No freebies.

With eight tricks guaranteed, chances are excellent, and the first thought is to try for a heart ruff in hand. Normally, this would do fine, but Moriarty’s club shift reeks of a singleton. Danger lurks:

3 S
S A K Q J 10 9
H 10 5 3 2
D 5
C K Q
S 4 3
H A K Q 9 8 7
D A 10 7 6
C J
TableS 7 5 2
H 6
D K 9 8 3 2
C 10 9 7 3
S 8 6
H J 4
D Q J 4
C A 8 6 5 4 2

After winning the C K, suppose you lead a heart (Line E). This may seem OK because an immediate club ruff is not fatal; you will gain a heart ruff in exchange and may gain another trick by ruffing a second heart, or winning the C A if they shift to trumps. Not really. Upon winning the heart trick, Moriarty can shift to a trump; then if you take your heart ruff, you will be stuck in hand and forced to surrender a club ruff. There’s just no legitimate way to succeed.

Ah! So maybe you should lead a diamond immediately (Line F). This has some merit with Moran at the table, but it still falls short. East wins the D K and gives the club ruff; then Moriarty can beat you in two ways: (1) Return a trump, then East can ruff the next heart and clear trumps, or (2) cash a heart on which East pitches a club, then shift to a trump. In the latter event, when you next ruff a heart, East sheds his last club rendering the C A useless — or you could try to cash it and suffer the ignominy of both opponents getting a club ruff.

“In solving a problem of this sort, the grand thing is to be able to reason backwards.”

Holmes considered the preceding events, and one piece of evidence was overwhelming: Moriarty’s club shift. This had to be a singleton, else he would have led a trump to eliminate any chance of a heart ruff.* Therefore, if there were any path to success, it must begin by drawing trumps. Even the greatest masters must get the children off the street sometimes.

*In view of dummy, the trump shift would be routine by an expert as it would beat the contract outright in many situations. Yes, Moriarty is a crook and might do anything based on illegal knowledge of your hand; but the conditions said to assume “expert defense.” A few respondents noted that Moriarty might not have led a trump because he didn’t have any. While this may be true, it is far-fetched to assume that to justify an immediate heart lead. Lacking specific information, you should assume the more common situation.

Holmes drew trumps, including a few extras (five rounds can be safely led) to reach this ending:

North leads
S 9
H 10 5 3
D 5
C Q
S
H A Q 9
D A 10 7
C
TableS
H
D K 9 8
C 10 9 7
S
H J
D Q J 4
C A 8

Holmes now exited with the D 5 (Line B) and the defense was stifled. If Moriarty captures the D Q with the ace, he can cash only one heart; then on the diamond return, a heart is pitched from dummy to establish the D J. What if Moran hops with the D K and returns a club? Win the C A (crashing the queen) and ruff out the D A; then exit with a heart to endplay West for a ninth trick.

In the above ending it is equally good to cash the C Q before leading the D 5 (Line D), however, this would fail if Moriarty held both diamond honors — he would cash one heart then exit with a high diamond, leaving you without recourse.

I should also mention that Line B fails (and Line D succeeds) if Moriarty had another club — he would win the diamond, cash a heart and exit with a club. Nonetheless, this possibility is remote in light of the defense, while the case for both diamond honors is realistic; so those who chose Line D must settle for second place.

Note that exiting with a heart after drawing trumps (Line A) is inferior as it works only when Moriarty has both diamond honors. If diamond honors are split, Moriarty will win the heart and lead a low diamond to Moran; then a club return seals your fate. If you chose Line A, consider yourself lucky to survive the fish tank.

Lines E and F are worse as, besides needing D A-K in West, they also require West to have fewer than three trumps — assuming the C J is singleton, which is my primary basis in evaluating all lines. Worst of all is Line C, as I don’t think it works against any plausible layout.

Comments for B. Draw trumps; lead D 5

Zahary Zahariev: This looks 100 percent if the C J is really a singleton (most likely).

Charles Blair: I am reluctantly concluding that the Professor really has a singleton club; otherwise, a trump switch would seem natural. Line D fails if the Professor has D A-K. If the Professor has outsmarted me, I will argue that down one with 150 honors is a plus score.

Nick Krnjevic: Moriarty must have a singleton club, else he would simply have led a spade at trick two. If Moriarty has D A-K, he’ll be endplayed; if Moran wins the first diamond and plays a club, I will win in dummy, ruff out Moriarty’s presumed diamond honor and exit with a heart. I can’t cash the second club since I’ll go down if…Moriarty has both diamond honors; nor can I exit with a heart since, if Moran has a diamond honor, the vile Moriarty would lead a diamond to Moran, who would exit with a club.

Leif-Erik Stabell: This guarantees the contract provided East has no more hearts, and West no more clubs and at least one diamond honor. Line D does not work if West has everything.

Dale Freeman: Why did West switch to the C J? That is the question, and I think he has a singleton; if not, he fooled me. I’m trying to endplay West.

Frances Hinden: If West had two clubs, he [would switch] to the obvious trump at trick two; so to start with, I’m playing him for at least one diamond honor and a singleton club. If he’s very short in spades, I may change my mind and play five rounds of the suit, triple-squeezing him when he has three or four clubs.

Bill Erwin: This keeps East from ruffing a heart and giving West a club ruff. When West has all red-suit honors, he is endplayed into giving me the ninth trick… A diamond [exit] is better than a heart since, if Moran wins and plays a club, I can win in hand and ruff out the remaining diamond honor; then endplay the Professor with a heart.

Nigel Guthrie: This is OK when West has S x-x-x H A-K-Q-9-8-7 D A-K-x C J, or S x-x-x H A-K-Q-9-8-7 D A-x-x C J; and if he has S x H A-K-Q-x-x-x D A-K-x C J-10-x, run trumps for the triple squeeze.

Toby Kenney: The C J is surely a singleton, so I will [eventually] endplay West. …

Gareth Birdsall: If West has a singleton club and East a singleton heart, this should wrap up the contract.

Daniel Bertrand: It seems that Moriarty has a singleton club since he is not playing his partner for a singleton heart and S 8-7 (by continuing with a high heart, heart ruff, diamond back and another heart ruff). …

Carsten Kofoed: The C A is my entrance to a diamond trick.

Manuel Paulo: Trying to ruff a heart is a mirage; so it must be right to draw trumps. Afterwards, against West hands like S x-x-x H A-K-Q-9-8-7 D A-K-x C J, I should lead a low heart or the D 5; against S x-x-x H A-K-Q-9-8-7 D A-x-x C J, I should lead the D 5 or C Q. To deal with both cases, I lead the D 5.

Rainer Herrmann: Line B wins whenever West’s C J is a singleton. Hard to tell whether an expert would switch to the C J from anything else (e.g., J-10-x); too tough if clubs are 3-2 all the time.

Andrew de Sosa: Moriarty must hold H A-K-Q-9-8-7, at least one top diamond and a singleton C J. … If Colonel Moran wins the diamond and…returns a club, I win the C A and take the ruffing finesse in diamonds; the Professor covers perforce, but when I ruff and exit with a small heart, he will be endplayed… So the Colonel must duck the diamond, and I split my honors; but now, with no more clubs, the best Moriarty can do is cash a heart and exit with a low diamond; I’ll pitch a heart from dummy, conceding the remaining top diamond to Colonel Moran, and claim nine tricks…

Vlastimil Lev: I will play for West to have singleton club.

Sandy Barnes: With hearts 6-1, opponents can win only three hearts and one diamond, or two hearts and two diamonds, since I have a club entry left…

Gerald Murphy: … If East wins the diamond, he has no more hearts so must either lead a diamond (ruffing out West’s honor) or a club; then win the C A and lead the D Q, again ruffing out West’s honor, and endplay West with a heart to the jack. If West wins the first diamond, he can cash only one heart and lead a diamond, in which case I [pitch a heart from dummy].

Comments for D. Draw trumps; win C Q; lead D 5

Venkatesh Ramaratnam: Irrespective of the trump split, this line scores whenever diamond honors are split and West has six hearts, which is very likely on the bidding and the defense up to this point. Opponents can choose to give either a heart to dummy, or a club or diamond to hand with East a stepping-stone…

John Reardon: This is certain so long as diamond honors are split. Line B is tempting but fails when the C J is not singleton.

Marcus Chiloarnus: “I have a peculiar taste in these matters.”

Rob Stevens: [Assuming split diamond honors], either West will be endplayed to set up North’s H 10, or East will be endplayed to allow South to reach his diamond and club winners. South should cash the C Q lest West have two clubs rather than the expected singleton.

Catalin Lazar: I’ll win every time East has a diamond honor, as he will be endplayed into giving me a ninth trick.

Bill Powell: I think this’ll endplay the bounders.

Aivar Tihane: I play this kind of transfer with my wife (mainly 3 S transfer to 3 NT). You say that a system should be homogeneous? Well, it is, only I never use the transfer.

And when she reads this, you may prefer
your chances in the piranha tank.

David Davies: I don’t think East has more than one heart. If East wins the diamond, he has to play another diamond; this is ruffed, then a heart to the jack uses West as a stepping-stone. If West wins the diamond, [he can cash only one heart] before playing another diamond; this is ducked to East, who must return a minor-suit card to South.

Barry Rigal: This avoids the embarrassment of West getting a club ruff or having a second club to exit with if you play diamonds before clubs. And if West has only five hearts, smack him ‘round the head.

Thijs Veugen: If West has S x-x H A-K-Q-9-8-7 D A-x-x-x C J, he can cash only one heart [after winning the first diamond] then must play a diamond. If East instead wins the first diamond and plays a diamond to West, I’ll ruff and play a heart. … TopMain

Problem 6

Plus-or-Fishfood -S Vul (very)

West
Moriarty
1 H
2 H
3 H
North
Watson
Pass
Pass
4 D
East
Moran
Pass
Pass
All Pass
South
Holmes
2 D
3 D

4 D South
S 7 5 2
H J 10 4
D K Q
C K 10 5 4 3
Lead: H KTableEast plays H 2
S J 4 3
H A
D A J 10 8 7 6
C A 9 2

You win D K-Q on which West pitches two hearts. What next?

PlayAwardVotesPercent
B. Lead S 2 and duck it1018822
A. Lead S 2 to jack9496
D. Ruff heart; draw trumps8455
C. Lead H J (East plays H 5) and pitch a spade539147
E. Lead C 3 to ace; draw trumps39011
F. Lead C 3 and finesse nine2759

Well, this is it. Your last chance to go swimming! Despite the lack of an easy 10th trick, Watson appears to have done the right thing over 3 H — had he passed you would surely go minus in 3 H with Moriarty void in diamonds.

Aside from a miracle in clubs, the best chance appears to be the loser-on-loser play in hearts (Line C) as overwhelmingly selected by the voting consensus. Unfortunately, this presumes Moriarty to have only six hearts when his bidding suggests seven. Consider this typical layout:

4 D
S 7 5 2
H J 10 4
D K Q
C K 10 5 4 3
S A Q 6
H K Q 9 8 7 6 3
D
C Q 8 7
TableS K 10 9 8
H 5 2
D 9 5 4 3 2
C J 6
S J 4 3
H A
D A J 10 8 7 6
C A 9 2

If you follow Line C, you are headed for a quick splashdown. Moriarty will win the H Q and lead a third heart for Moran to ruff, ruining your discard.* If you then lead all your trumps, Moriarty will escape any endplay by coming down to S A-Q C Q-8-7 — and on your spade exit, he plays ace-queen, allowing Moran to overtake and win a third spade. Yes, I know, Moran would probably be asleep at the switch; but you won’t stay out of the tank on that account.

*Several respondents noted that Moran played up-the-line in hearts, suggesting a 6-3 heart division; but as I carefully stated in the conditions, Moran’s plays are meaningless. Only Moriarty can be assumed to play with expert credibility.

It is also easy to dismiss Line F as an exercise in futility. Moriarty would diagnose the club situation exactly and realize he needs Moran to have the S K or a singleton heart. The latter is illogical because Holmes would have an easy make with S J-x H A-x D A-J-10-x-x-x C A-9-x (cross to the C A, draw trumps and concede a heart). Therefore, the switch to spades stands out.

Line D (ruff heart, draw trumps) offers a good try. This will be the position after trumps are drawn:

South leads
S 7 5
H J
D
C K 10 5
S A Q
H Q
D
C Q 8 7
TableS K 10 9 8
H
D
C J 6
S J 4 3
H
D
C A 9 2

With spades blocked, opponents can win only three tricks, so you exit with a spade. Moriarty must win with the ace and cash the H Q, which squeezes you. If you pitch a spade, Moran can overtake the S Q (yeah, right). If you pitch a club, Moriarty wins the S Q and returns a low club, which Moran carefully or accidentally ducks. How frustrating!

Line E (crossing to the C A) also leads to a dead end, and the defense is hardly challenged due to the relaxed pressure in clubs. If you make any attempt to rectify the count, a second club lead will send you packing, er, I mean, swimming.

“When once your point of view is changed, the very thing which was so damning becomes a clue to the truth.”

Holmes studied the clues and weighed his options. The most damning thing about this hand was the three losing spades. Such a burden normally focuses your attention elsewhere, but there’s a fine line between a liability and an asset. It might only be a matter of perspective, like classical physics versus relativity. Holmes knew the only realistic chance was to harness the spade suit to his advantage.

After winning the D K-Q, Holmes led a spade and ducked (Line B) when Moran produced the eight. If East-West take their spade tricks, it only corrects the count for a club-heart squeeze; so assume Moran returns a heart, ruffed by Holmes. Next come trumps to reach this ending before the last trump is led:

South leads
S 7 5
H J
D
C K 10 5
S A Q
H Q
D
C Q 8 7
TableS K 10 9
H
D 9
C J 6
S J 4
H
D 10
C A 9 2

On the D 10, Moriarty was obliged to pitch a spade and chose the ace to retain flexibility; but the timing now favored declarer. Holmes pitched a spade from dummy, then led a low spade to the blank queen. East could not overtake because it would establish the jack, so West was isolated. Moriarty won the H Q (Holmes pitching the S J) then made a valiant effort by leading the C Q; but this was child’s play for the master sleuth, who played Moran for the C J.*

*Playing for split club honors is not only right percentagewise but for a subtle reason: If Moriarty held C Q-J-x, the contract could have been beaten by a club shift when Moran won the S 8. This may be far-fetched with Moran East, but it does provide food for thought — or at least, food for fish.

What about Line A? Does it really matter which spade you play on the first round? Yes, it does. If you play the S J, Moriarty can defeat you by winning and leading a low spade to Moran, who returns his last heart. You must ruff this to have any chance, and you lead trumps to reach this ending:

South leads
S 7
H J
D
C K 10 5
S A
H Q
D
C Q 8 7
TableS K 10
H
D 9
C J 6
S 4
H
D 10
C A 9 2

When you lead the last trump, Moriarty can pitch his last spade, leaving you no solution. The count is wrong for a squeeze; and you can’t throw Moriarty in with a heart without breaching the club suit, which removes the endplay.

Comments for B. Lead S 2 and duck it

Zahary Zahariev: I hope to squeeze West if he has something like S A-Q-x H K-Q-9-8-7-6-3 D C Q-x-x.

Charles Blair: If the Professor has S A-Q-x H K-Q-9-8-7-6-3 D C Q-x-x, he can support his local aquarium against some of the other choices by playing the S A on the first round.

Nick Krnjevic: Moriarty is likely to be 3=7=0=3 on the auction, and is missing the S K given his lead. I will therefore try for a club-heart squeeze; but for this to operate I have to clear some spades and [preserve] my heart threat. I cannot lead a spade to the jack since the perfidious Moriarty…will win and return a spade to Moran…who will push a heart through; then in the five-card ending Moriarty will be able to pitch his last spade and hang on to the H Q and honor-third in clubs. …

Leif-Erik Stabell: West must have two spade honors and probably 3=7=0=3. The only problem will then be whether to play West for one or both club honors in the end when he has to lead a club. The odds favor one, and also because East in an inspired moment (slip of the hand?) might have defeated the contract by winning the first spade and switching to a club with C x-x. Not that this is a likely defense at any level, but a very nice point — wonder if I will live long enough to ever see this coming up at the table?

Dale Freeman: I do not think West has four spades; therefore 3=7=0=3 or 2=7=0=4 (unlikely 3=6=0=4). With the club guard in West, if opponents cash three spades, an easy squeeze. If East wins and plays a heart, I must ruff to save the heart threat and run diamonds. West will have five cards left (one spade, H Q and three clubs); if he started with two big spades, I can get him to break clubs. The S J is important [to keep] so East cannot overtake.

Venkatesh Ramaratnam: West rates to have seven hearts on the auction, hence the straightforward line C won’t work. If West holds at least three clubs and two spade honors, a strip squeeze on West should fetch the 10th trick. The S J should be retained and could come in handy in the endgame. I presume that by this time Moran must be tired of all this and must be contemplating the details of a sniper attack with an air rifle. …

John Reardon: West did not lead a spade so let East have the S K; West only bid hearts so conclude he may have S A-Q-x H K-Q-x-x-x-x-x D C Q-x-x. If I ruff a heart and draw trumps, West will come down to S A-Q H Q C Q-x-x; then when I exit a low spade, West wins with the ace and squeezes me by cashing the H Q. If I duck a spade first, the timing is right for the strip squeeze.

Marcus Chiloarnus: “These are much deeper waters than I had thought.”

Rob Stevens: If West has S A-K-x he can always be endplayed, or else South can get a trick with S J. But if South ruffs a heart and runs trumps, West can escape with S A-Q-x. He comes down to S A-Q H Q C Q-J-x, and when South leads a spade, he plays the winning heart to squeeze South’s hand (he can exit a low club if South discards a club). Therefore, South must tighten up the position by playing a round of spades, keeping the S J.

Tim DeLaney: Assuming West has three clubs and at least two spade honors, he will have a serious problem if he is forced to win this trick (best is to lead a club right away, but that may not be clear). If East wins trick four cheaply and leads a heart, I [ruff] and transpose to the strip squeeze…

Toby Kenney: Hoping West has three clubs and three spades (which must include two spade honors to justify his bidding). East must win the [first] spade trick and switch to a heart to save West from an immediate endplay, but I ruff this and run trumps; then I can endplay West…

Gareth Birdsall: Should make if West has S A-Q-x and C Q-x-x or J-x-x, and [might make] if S A-Q-10 and C Q-J-x.

Sandy McIlwain: Too much to ask East to have three hearts on this one. I need some spade blockage to appear and force West to lead hearts or clubs. West may yet prevail if…he switches to the C Q [early], as I will be forced to guess clubs before a squeeze [develops]. If I stayed dry this long, it’s a miracle anyhow; so here goes.

Rich Pavlicek: Best hope is to play West for at least three clubs. (Playing hearts early won’t help because East will trump my winner). I will try to correct the count by leading spades, and I have to hope West has at least two spade honors. Their best defense is for East to win and come back a heart, which I ruff and lead all my trumps. West is squeezed in three suits and forced to discard one of his spade honors; then I throw him in with a low spade (preserve the jack!) so he must lead a club eventually.

Leah Cohen: This requires making an inference. If West has six hearts, Line C works; but, unless he’s exactly 3=6=0=4, he’d probably make a different second or third bid. So I try for a strip squeeze, which works if West is 3=7=0=3 and club honors are split (or if West has C Q-J-x and I guess it), and it still picks up 3=6=0=4. The conditions of contest are a bit odd in that West bids normally even though East passes all the time…

Rainer Herrmann: Apart from some unlikely, lucky club distributions, best chance is to play West for something like 3=7=0=3. If West holds two top honors in spades (quite likely on the bidding), he will have to break clubs. The squeeze endplay works with three but not four losers, so rectify the count.

Julian Pottage: The only way home if West has something like S A-Q-x H K-Q-x-x-x-x-x D C Q-x-x.

Julian Wightwick: Judging from the lead, Moran has at least one spade honor. I shall play for split club honors with Moriarty having three or more clubs, and strip-squeeze him in three suits. If Moran wins the first spade and leads another low one, I cover; eventually I will ruff the fourth spade (or a heart from East) and draw trumps. … If the defense has played three rounds of spades, Moriarty is squeezed between hearts and clubs. If they played only two spades, I must hope that Moriarty began with two spade honors (then the S J is now good). If Moran switched to hearts after the first spade and it looks as though Moriarty has come down to a singleton spade honor, I exit in spades and endplay him. Finally, if Moriarty pitches both spade honors, I cross to the C K and lead up to the S J.

Hans Holme: Line C will fail because East holds only two hearts. My best chance is to squeeze West in clubs and hearts, so I play spades every time… I reckon West has two honor cards in spades…

Vlastimil Lev: Before playing for a heart-club squeeze, I need to reduce the number of losers.

Bill Powell: Looks the best chance to get some pressure on.

Yi Zhong: [Best] hope is that West has three or more clubs. If West has S A-Q or K-Q tight, I am home. If West has three spades, and East doesn’t [hold the trick], I am home. If East wins the spade and returns heart, I ruff and play diamonds. … If West pitches a spade honor on the last diamond (keeping S Q H Q C Q-x-x), throw him in with a spade.

Barry Rigal: I think West has seven hearts, so leading hearts won’t help me; but West may get squeezed if I time it right.

Daniel Korbel: Looks like West might be 3=7=0=3. If so, I can squeeze him in the round suits if I’m careful.

Tim McKay: East’s count can’t be relied on, so the H J is out. …

Dale Rudrum: Either East has three hearts or West has three clubs, or the contract is doomed. West knows the deal and leads the H K? Because it doesn’t matter? Or because it is the only lead that gives me a sporting chance? I know that you know that I know that you know that I don’t have a clue. I’ll go for the clubs in West, I think. …

Paulino Correa: This one looks pretty desperate; Holmes should expect Moriarty to be 3=7=0=3 — if East had three hearts, it would be too easy. :) …

Audrey Kueh: I need to rectify the count.

Len Vishnevsky: It has to be right to play for a round-suit squeeze. I duck in case West has S A-Q H K-Q-9-8-7-6-3 D C Q-J-x-x.

George Klemic: The goal is to force an endplay in clubs, then take a finesse (or squeeze West in hearts and clubs). … Best way to do this is just to exit in spades; start small, hoping the suit will block. Even if East wins the first spade…all is not lost as long as West holds 3+ clubs.

Brian Zietman: Since West did not lead spades, I take East’s only points as the S K. There are squeeze possibilities against both opponents with the major-suit jacks as menace cards… therefore, I must duck a spade to rectify the count.

Richard Morse: This appears to give the best chance of an endplay and/or squeeze against West in hearts and clubs.

Phil Grand: I am not sure that this poor Colonel gives the heart count; otherwise, Line C is elementary, my dear Watson. I’ll play my three losing spades each time and see whether West will offer me a free club finesse or a good heart to pitch a losing club. Moriarty, I’ve been told that fried piranha are delicious with garlic! I’m starving.

Comments for A. Lead S 2 to jack

Michael Errington: Playing West to be 2=7=0=4. If West has two stiff spade honors, he is endplayed immediately. Otherwise, continued spade leads rectify the count for a heart-club squeeze. If East has, say, S A-Q-x-x-x, he may go in with an honor to lead a club. Now I can’t continue spades, as East will get a club ruff; but I can draw trumps and establish clubs for a spade discard whilst spades are blocked. An interesting variation is when East has, e.g., S A-Q-10-9-x and plays the nine or 10 first; I must play the S J, else East will win cheaply and lead a club. …

David Cochener: If West breaks clubs, it guesses the suit; and a heart return gets rid of a spade loser. If East-West cash three spades, they have rectified the count for a heart-club squeeze against West. I think the S J is better than the two, since West may credit me with S K-J and break clubs.

Richard Aronson: I’d prefer Line A if it said “Lead S 2 covering if necessary to force West to win.” Line C is awfully tempting; as long as Moran has three hearts, I am cold. But would Moriarty bid all the way to 3 H with only six hearts missing three honors? I think not, so hearts are 7-2, and reds are 7-7. …

Mitch Edelman: I hope to catch West in a round-suit squeeze, coming down to H J C K-10 opposite C A-9-x. … If West is 1=7=0=5, then I guess East will negotiate a club ruff and beat me, but the defense could have done that at trick one. …

Carlos Dabezies: Assuming West has seven hearts, I want opponents to break clubs. Putting up the S J may look like a finesse and tempt West into a club shift, whereas East can always shift to a diamond. TopMain

Final Notes

Comments are selected from those above average (top 365), and on each problem only those supporting the winning play or close seconds. While this might be considered biased, I feel it’s the best way to ensure solid content and to avoid potential embarrassment by publishing comments that are off base. On this basis, I included over 70 percent of the eligible comments. If you supplied comments that were not used, I thank you for the input.

Use of a comment does not necessarily mean I agree with it, but generally they are all worthy. Comments are quoted exactly except for corrections in spelling and grammar. Where I have included only part of a comment, an ellipsis (…) indicates where text was cut. Text [in brackets] was supplied by me to summarize a cut portion or fix an omission. Comments are listed in order of respondents’ rank, which is my only basis for sequencing. I am confident that my lengthy study of these problems (combined with the input of comments) has determined the best solutions in theory. Nonetheless, it is possible that I overlooked something. Anyone who wishes to debate the analyses, or thinks there is a reason for a scoring adjustment, is welcome to e-mail me (richard@rpbridge.net).

“Come, friend Watson, the curtain rings up for the last act.”

I hope you enjoyed this Holmesian episode; and based on the many story-based comments, it seems that you did. Thanks to all who entered and especially those who offered kind remarks about my web site. What’s that I hear? It seems to be Inspector Lestrade knocking at my door, so I’ll leave you in the hands of his flatfoots:

Raul Martino: I offer 100 kilograms of the best Argentine beef to toss into the piranha tank just before you evaluate my answers.

Anthony Golding: Perhaps I can lull the piranhas with sweet violin music, or dope them.

Gabriel Ip: If Holmes can’t get out of this one, I’ll eat my words — Alimentary, my dear Watson.

Carsten Kofoed: Now I know why the dog didn’t bark — it was silenced by piranhas.

Eugene Hung: Pity you couldn’t find a winning play with a 7-percent chance — a “Seven-Percent Solution.”

Kay Jones: Hey, even piranhas gotta eat! TopMain

Credits to Sir Arthur Conan Doyle (1859-1930) creator of Sherlock Holmes.
Photo is Basil Rathbone and Nigel Bruce as Holmes and Watson.
© 2003 Richard Pavlicek