Main     Analyses 7X56 by Richard Pavlicek

# The House on Phantom Lane

When the round ends, you meet with your teammates to compare scores: “Minus 100, push; minus 50, push; minus 400, lose; minus 100, push; minus 100, lose; minus 100, win.” The last result rouses Fritz, who starts to bounce in his chair, grinning and pointing at himself as if his 5  bid won the board. Argh. You wonder just how much more of this you can take, as you politely excuse yourself to go to the rest room.

 Problem 1 2 3 4 5 6 Final Notes
When you return, the room is empty! No cards; no tables; no people. What? Mystified, you walk downstairs and find the entire house also empty. Then you walk outside into the moonlit night and look for your car… it’s gone! In fact, there are no cars anywhere. Next you notice that the house is surrounded by a cemetery. What in the world?

Curiosity forces you to walk around and look at the grave markers. Finally, it all begins to sink in as you recognize the inscription “Joseph P. Ellwood.” Then you read “Judith R. Dalton.” Shivers run down your spine as you come to the next marker. What? This can’t be… it’s your name.

Now is about the time Rod Serling would interrupt the story and explain how you’ve just entered The Twilight Zone. Relax! Everything’s cool; you’re still alive — I think. Anyway, I couldn’t let you depart this world without reading the analyses.

These six play problems were published on the Internet in April 2002, and all bridge players were invited to submit their answers. While none of the contracts are makable, your goal as declarer is to salvage what you can to win or tie the board. Scoring is board-a-match.

## Leif-Erik Stabell Wins!

This contest had 690 entrants from 103 locations, and the average score was 37.29. Congratulations to Leif-Erik Stabell (Zimbabwe), who was the first of two to post perfect scores. Curiously, Leif is my only participant from Zimbabwe. Is this the dawn of a new era? Come on, Leif, get some of your friends to enter. Also scoring 60 was Tong Xu (Japan). Close behind were Gareth Birdsall (Cambridge, England) with 59, and David Grainger (Etobicoke, Ontario) with 58. Next with 57 were Wojtek Siwiec (Poland); Euzebiusz Rebajllo (Poland); Julian Pottage (Hampshire, England); and Lajos Linczmayer (Hungary).

In the overall standings, the top two positions are interchanged as Zahary Zahariev (Bulgaria) narrowly overtook Charles Blair (Urbana, Illinois), each with a cool 59.00 average. Since they both had a win, it went to a second tiebreaker (average of six scores) and Zahary had the edge by his 54 this month to Charles’s 53. Next in line are Wojtek Siwiec with 58.00; John Reardon (UK) with 57.75; then Gareth Birdsall and Frances Hinden (UK), each with 56.50.

Participation was down this month, no doubt because of my unusual theme of unmakable contracts. Fritz, you can start packing your bags — you’re fired! No big deal; with the sugarcoated players taking a vacation, we can discuss some real bridge without offending their virgin ears. Come Christmas, when the problems are covered with candy canes, they’ll be back — kind of like California’s “govenator.”

The average score was also low (not the lowest ever which February 2001 still claims at 37.19). While my decisions in the scoring control this to some extent, that was hardly the reason — if anything, the awards were generous. I’m sure it was because many of you didn’t put forth the usual effort because of that… that… jerk you were stuck with as a partner. Certainly understandable.

Bidding is standard (except as noted) and the defenders use standard leads and signals. For a reference on these agreements, see my outline of Standard American Bridge. Conditions were to assume strong but not expert opponents.
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

Board-a-Match E-W Vul

 WestJoe1 3 4 NorthFritzPass4 5 EastJudy2 PassDbl SouthYou2 PassAll Pass

 5 × South 3 J 10 9 3 Q J 10 9 2 8 4 3 Lead: K East plays 2 A 9 6 5 2 7 6 A K 5 4 3 2

D. Win K; A; ruff a spade510916
A. Win Q; duck a spade151

Fritz was not really out of line to bid 5 , although the expert route would be to bid it directly over 3 . Surely East-West have a game somewhere — indeed they do in 5  — so the phantom save against 4  is nothing to worry about. The same 5  sacrifice is likely to be taken at the other table, so it’s just a matter of who wins more tricks.

Joe’s shift to trumps was a smart move, as otherwise you would lose only three top tricks and crossruff the rest — down one. Now you are in danger of a second trump lead, leaving your crossruff a trick short.

Your next thought turns to building a heart trick with dummy’s sequence. Perhaps you could give up a heart; win the trump return; then lead the J and pitch a club — a loser-on-loser play. Alas, this won’t work if the opponents cash their club trick before returning a trump. In fact, Joe is likely to be 6=4=1=2 with A-K-Q-x, so the defense is obliged to win a club before a second trump can be led. Consider this probable layout:

 5 × 3 J 10 9 3 Q J 10 9 2 8 4 3 K Q J 10 8 7 A K Q 4 6 K 7 4 8 5 2 8 7 A Q J 10 9 6 5 A 9 6 5 2 7 6 A K 5 4 3 2

Your first decision is which diamond honor to win at trick two, and it is crucial to win in hand to keep all high diamonds in dummy. If you won the Q, you would be unable to crossruff due to Judy’s potential overruff at any time. You must keep the crossruff possibility alive.

Next you must lead a club (not a heart) for two reasons: (1) to be able to ruff two clubs, the last of which will force Joe to make a crucial discard, and (2) to preserve your heart exit for later to endplay Joe. Judy must win the club and return a trump (else you can crossruff), which you win in dummy and ruff a club. Next comes the A and a spade ruff to reach this position:

 North leads — J 10 9 Q J 8 K Q J A Q 4 — — — 8 5 — Q J 10 6 9 6 5 7 A 5 —

When you ruff the last club, Joe is squeezed. If he parts with a heart, you can establish dummy’s fourth heart routinely; so assume he pitches a spade. Next ruff a spade and exit with a heart to put Joe on lead in this ending:

 West leads — J 10 Q — K A 4 — — — 8 — Q J 9 6 — A —

Whichever major Joe leads establishes a trick for you, so you neatly escape for down one. Joe seems a bit angry, but you notice a faint twinkle in Judy’s eye. Could she be thinking what you’re thinking?

The key to the successful ending is to retain the heart exit, as a normal ruffout squeeze will fail due to the lack of an entry in either major suit (the A must be released early to be able to ruff two clubs). It would be equally effective to cash the A at trick three (before leading the 2), but this option was deliberately not listed.

Considering that Line F is the only legitimate path to 10 tricks — not just in my example but on any plausible layout — my scoring of the also-rans was a bit generous. Nonetheless, I felt that Line C (win Q, lead 3) would usually work in practice, as Judy is unlikely to win the club and return a heart (the only successful defense), without which you have the same squeeze-endplay.

Line E (win K, lead 7) was the popular choice. While it does keep two possibilities alive (crossruff and loser-on-loser play), the likely club shift and trump return ruins both, so I couldn’t justify a higher award than 6.

Line D (win K, A, ruff spade) is worse, as it reveals the spade layout to make the defense easier no matter what you do next. Line B (win Q, lead J) is worse yet as it allows only one chance (loser-on-loser play), easily foiled by any club lead.

Last and definitely least is Line A (win Q, duck a spade), which is essentially a nullo play to ensure going down two without a fight. OK, so I needed a filler. Five votes. Hmm. Am I the testing ground for a new monkey-at-the-keyboard experiment?

Leif-Erik Stabell: Ruffing two clubs in hand should put the squeeze on West, who is probably 6=4=1=2.

Tong Xu: If West has K-Q-x-x-x-x A-K-Q-x x x-x, there is a squeeze waiting for him.

Gareth Birdsall: I hope to get to an ending where dummy has J-10-9 x-x x, and I have x-x-x x x-x. When I ruff a club, West is squeezed. A heart discard allows me to establish hearts, so he discards a spade. Now I ruff a spade and play the J. … If opponents play a heart at trick four to stop this, I need to make 10 tricks on a crossruff; hence the need for all top trump honors in dummy to prevent the overruff.

Julian Pottage: West could be 6=4=1=2, and ruffing two clubs in hand will set up a squeeze to allow me to escape for one down.

Lajos Linczmayer: The goal is to win 10 tricks. West has K-Q-J-10-x-x A-K-Q-x x x-x (East has less then eight clubs on the bidding). East’s diamond return must be won in dummy; club ruff; A; spade ruff; club ruff (West discards a spade); spade ruff; J.

Gabriel Nita-Saguna: I am playing West for 6=4=1=2 with all the remaining high cards in the majors and a club honor. If they return anything but a trump, I will crossruff for 10 tricks. If East returns her* last trump, West will be caught in a squeeze when I ruff the last club. Line C is inferior as West can win the club, cash a heart and continue with a high spade; then I can’t crossruff without East eventually scoring a trump trick.

*I have corrected everyone’s pronoun references to East (Judy) to feminine because of my story. Normally, however, I use masculine gender for all unknown third-person-singular references. No, it’s not a sexist thing; it’s the way I was taught in school. –RP

Frances Hinden: I play West for the singleton diamond, so keep all the high trumps in the dummy. This line has two ways to get me to 10 tricks: (1) Opponents don’t or can’t untangle their tricks and I’m allowed to crossruff, or (2) West has A-K-Q and a singleton diamond, in which case East must play a second trump; then West will get strip-squeezed into giving me a second major-suit trick.

Neelotpal Sahai: I expect West to have 10+ major-suit cards (something like K-J-10-x-x-x A-K-Q-x x A-x) for the bidding; but he goes down in 4  after repeated diamond leads. … I have to play for one down by ruffing four spades in dummy, or by [a squeeze]. Assuming East wins the club and returns the second trump (won in dummy), play proceeds: club ruff; A; spade ruff; club ruff. If West keeps three spades and two hearts, I exit with a heart and set up the last heart in dummy. If he keeps two spades and three hearts, I ruff a spade and exit with a heart.

Neil Morgenstern: I can probably save this for one off, as I think West will come under pressure as I ruff clubs (I assume he has 10 major-suit cards and therefore will have to discard on the second trump and third club). West might regret peaking at dummy before leading a trump.*

*Neil’s subtle point offers good advice when defending against deliberate sacrifice bids. If West had led a trump originally, the timing would never be right for the squeeze-endplay. –RP

Zahary Zahariev: We may already have won the board, as 5 is unbeatable. West normally has K-Q-10-x-x-x A-K-Q-x x K-Q. East must return the last trump to prevent a crossruff; I take with Q; ruff club; A; ruff spade. Now ruff the last club, and West is squeezed — one down.

Charles Blair: If West is 6=4=1=2 with A-K-Q, there is a crossruff or a ruffing squeeze…

Weidong Yang: The best result I can obtain is down one. … I choose to play West for 6=4=1=2, and he will be squeezed in the majors if I play in the correct sequence. In fact, opponents do have a game in 5  (instead of 4 ).

Rainer Herrmann: If West has A-K-Q, East will have to win and return a trump to avoid the crossruff. Winning the trump return in dummy and ruffing eventually the last club will trump-squeeze West with the help of a heart endplay.

Frans Buijsen: Playing for one down (two down is easy). This leads to a heart-spade [squeeze-endplay] against West. …

Carsten Kofoed: West will be squeezed at trick eight when I ruff the last club — one off.

Tibor Roberts: If I lose a club now, I can strip-squeeze West unless they switch back to hearts, [then crossruff]. …

To each his own… but I think I’d rather
strip and squeeze East.

Toby Kenney: East must return her trump to prevent a complete crossruff. I win this in dummy; ruff a club; A; ruff spade; and ruff club for a trump squeeze against West.

Tim DeLaney: If West has six spades, our teammates can make 5 . If not, I hope West is 5=4=1=3 with A-K-Q-x, in which case he’ll be squeezed in the majors. If West is 5=4=2=2, he can break the squeeze by cashing one more heart before leading the diamond. …

Chuck Lamprey: If opponents play a second trump, I hope to develop a major-suit squeeze against West by ruffing clubs in hand.

Bill Powell: East will have to win and play a diamond. At the end, I’ll force West on play to lead from K A-x.

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## Problem 2

Board-a-Match None Vul

 WestJoePassDbl NorthFritzPass2 *4 EastJudyPassPassAll Pass SouthYou1 NT2
*Jacoby

 4 South 2 K 9 8 7 5 J 4 3 Q J 4 3 Lead: A East plays 6 A K Q 5 A 10 4 9 8 5 2 K 2

West wins A-K-Q (East follows) then leads the J to your ace. Your play?

E. Win K; lead 5 and finesse 10527139
D. Win K; A2659

Fritz could be forgiven for the first board, but here he removes any shadow of doubt that he’s a lunatic. The 4  raise is absurd, not only an overbid but you might have held a doubleton heart. Even with your maximum and fit, the contract is hopeless — though it would be sweet if you could switch your spade and diamond holdings.

Oh well, back to reality. What can you do to salvage this mess? It looks pretty grim, since the opponents can’t make anything, but your contract is undoubled. If you could escape for down one, there’s always a chance of a push, e.g., if 3  were played at the other table. Alas, you seem to be destined for down two barring a miracle in trumps.

Your first thought might be to steal a club trick, then the remaining clubs can be pitched on the K-Q and 13th diamond as East (probably) ruffs with her natural trump trick. Joe should have the A for his double, so the deal rates to be something like this:

 4 2 K 9 8 7 5 J 4 3 Q J 4 3 J 10 9 7 J 2 A K Q A 10 9 7 8 6 4 3 Q 6 3 10 7 6 8 6 5 A K Q 5 A 10 4 9 8 5 2 K 2

Suppose you try Line F and lead the 2. Would Joe be caught napping? Unlikely, as the club lead is suspicious. A good player would be aware that you must have the K and K, so there is no way for the defense to win a second club trick. Ducking the club would be a bad play, especially because it’s the setting trick.

Forget the larceny; resign yourself to a club loser and focus on the trump suit. It might be possible to avoid a trump loser, and this does not require Q-J doubleton or a blank honor East. By trump reduction, you might be able to nullify the enemy trump trick in an ending called a devil’s coup — rather appropriate for the occasion, too. Reaching the critical ending, however, is not so easy as three spades must be ruffed in dummy.

Only Line B allows you to succeed. Ruff a spade and lead the Q, which Joe must win (else you will switch horses and avoid a club loser). Suppose Joe returns a club to your king. Next ruff a spade, ruff a club and ruff a spade to reach this ending:

 North leads — K 9 — J — J 2 — 9 — Q 6 3 — — — A 10 9 —

When the last club is led, Judy has no answer. If she ruffs low, you will overruff with the 10. If she ruffs with the queen, you will overruff with the ace and finesse Joe for the jack.

If Joe returns a spade instead of a club (when he wins the A), the ending is slightly different. Ruff the spade, win the K and ruff your last spade to reach:

 North leads — K 9 — J 4 — J 2 — 10 9 — Q 6 3 — 8 — A 10 4 9 —

Now you cash the J to pitch your diamond; then the last club effects the coup. Having the extra trump in hand doesn’t matter as long as dummy’s trumps have been shortened.

Line C (ruff spade, 3 to king) gets second place because it works when Judy has the A (albeit unlikely) or if Joe has the A and doesn’t return a club. Line F (lead the 2) is slightly worse as it offers no legitimate chance, though it does put Joe to the test (he must win the A and return a club).

Line E ( K, then finesse 10) was the popular choice, but it really only guards against going down three if East has Q-J-x-x — as do all other lines with routine follow-up (except Line D). Note that if West has a blank heart honor, you cannot prevent East from winning a trump trick. In fact, if an honor appears, you should abandon the finesse and play for Q-J doubleton as the only hope. (The only 4-1 break that can be picked up is a blank honor in East, but this is contraindicated by West’s takeout double.)

Line A ( K-Q, ruff spade) does nothing toward solving the trump problem because two clubs must be pitched on top spades, leaving only Q-J opposite K-2. In the end, of course, you could revert to the safety play of Line E to avoid down three; but playing four rounds of spades early only increases the risk with no advantage.

Line D ( K, A) is clearly worst as it’s probably the only way to go down three. Also note that if hearts break normally, it leaves you poorly placed. Now you can’t even gain by sneaking a club through, as you have no entry to your hand if Joe ducks.

Did you notice Joe’s slip on defense? After cashing three diamonds, if he next leads A and a club, the coup is foiled for lack of communication. This was my main reason for the contest conditions that Joe and Judy were “strong players but not experts,” as it seems an expert would find this defense — maybe not for the subtle reason here but because East could have a singleton club (without a natural trump trick).

Leif-Erik Stabell: I have to hope that East is 4=3=3=3 with one heart honor — then her heart trick will eventually disappear.

Tong Xu: West cannot duck, then I will try to ruff all my spades. On a good day, my trump loser will disappear.

Sorry, but I’m afraid you have that wrong…
On a good day, Fritz will disappear.

Gareth Birdsall: Keeps the communication to play for the devil’s coup.

Lajos Linczmayer: My goal is to win nine tricks. If West has J-10-x-x J-x A-K-Q A-x-x-x, or J-10-x-x Q-x A-K-Q 10-x-x-x, nine tricks can be won by a devil’s coup. (It does not matter which heart honor West has.) If West has the A, the low club lead does not work.

Neelotpal Sahai: A normal contract would be 3 , which will go one down if heart honors are divided; so I have to [try for] only one down in 4 . … I have to reach an ending with North on lead holding K-9 x; East J-x-x; South A-10 and any other card; and West Q-x x. … Assuming West has a hand like J-10-x-x Q-x A-K-Q A-x-x-x, I must ruff a spade and lead the Q. If West ducks, I draw two rounds of trumps ending in hand and throw three clubs away on the K-Q and 9. … If West wins the A, I can reach the ending after a spade or club return. If he returns a heart [honor], I hope to guess right.

Neil Morgenstern: … I will attempt a devil’s coup and hope to find West with H-x, East with H-x-x, and for West to be 4-4 in the black suits (likely given his double). … If West does not take his A, I will be able to play K, A, two top spades and a diamond throwing all the clubs. So West wins and may lead a club back (why I kept the king); then spade ruff; club ruff; spade ruff; and a club from dummy…

Zahary Zahariev: Against a typical West hand ( J-10-9-x J-x A-K-Q A-x-x-x) this is the way for nine tricks. West must take the A, else I draw K-A and pitch all the clubs on K-Q and last diamond. On any return (spade or club) after A, I ruff all my spades and play a club from dummy. [Ending described].

Bill Erwin: My objective is to achieve down one to tie the opponents’ 3 down one. This is possible by playing for a devil’s coup, nullifying their [apparent] trump trick. If heart honors are split and East has…4=3=3=3 distribution, I can succeed. The  Q loses to the ace (else I cash two hearts ending in hand and pitch dummy’s clubs on the spades and diamond); club to king; ruff spade; ruff club; ruff last spade; then dummy’s last club…

Len Vishnevsky: Then win the club return (best); ruff spade; ruff club; ruff spade. If it’s overruffed, East must be 3=4=3=3 on the auction, so win the trump return and claim [down two]. Otherwise, lead the club for a devil’s coup [to go down one].

Weidong Yang: I cannot lose a trick in trumps, so only a trump coup is suitable. After calculating the entries, Line B is the answer. Remember: Don’t be misled by those big cards in the side suits.

Rainer Herrmann: If West holds 4=2=3=4 shape with heart honors divided, all remaining black cards can be crossruffed until the last club is played from dummy to avoid a trump loser. Should West duck the Q, he will lose his club trick.

John Reardon: … Best chance seems to be a devil’s coup. West may well have something like J-10-x-x J-x A-K-Q A-x-x-x, in which case I will make nine tricks. If he ducks the Q, I take K-A and throw clubs on K-Q and the long diamond; otherwise, I have the entries to neutralize their heart trick.

David Cochener: If West ducks the Q, the remaining clubs go on high spades and the good diamond (after two rounds of trumps). Otherwise, crossruff spades and clubs, playing for split trump honors with East having three trumps. West might have J-10-x-x J-x A-K-Q A-x-x-x. [Ending described]. This may tie the board if 3  goes down at the other table.

Marcus Chiloarnus: Illusion is the dust the devil throws in the eyes of the foolish.

Manuel Paulo: Consider this West hand: J-10-x-x J-x A-K-Q A-10-x-x. … To win or tie the board, I assume our opponents at the other table have overbid; so I need nine tricks. … If West ducks the Q, I cash the trump king and ace, and pitch clubs on the spade marriage and last diamond. If West wins the A and returns a black card, I ruff spades and end with a trump coup; if he returns a trump, I play for split honors and take the balance.

Toby Kenney: Whoever has the A must win this, otherwise I cash K-A, K-Q and 9 to discard my clubs. Suppose a club is returned: Win  K; ruff spade; ruff club; ruff spade; then lead the last club for a devil’s coup.

Venkatesh Ramaratnam: The best chance to go one down is to telescope an obvious trump loser if West is 4=2=3=4. If West wins the A, I have enough entries to reach the right ending. If he ducks, I draw two rounds of trumps and pitch all of dummy’s clubs on the K-Q and the 13th diamond.

Dale Rudrum: Setting up a crossruff. All these high cards are useless!

TopMain

## Problem 3

Board-a-Match N-S Vul

 WestJoe1 Pass NorthFritzPassPass² EastJudyPass1 NTPass SouthYouPass2 ¹
1. Michaels
2. Fritz no like Michaels

 2 South A 9 7 9 8 7 5 J 2 K 10 9 7 Lead: K East plays 3 K 10 8 6 4 A Q 10 8 6 5 4 3

Joe grins as he leads the K to your ace. Despite the horror, you might win the board! Your play?

F. Lead 4 and finesse 10107811
B. Win A; K; lead 54558
A. Win K; A; lead 93355

I almost didn’t use this problem because it would scare people away — sigh, I think it did. How can there be any logic in playing a stupid contract of 2 ? The only sensible thing to do is to beat up Fritz; but then, the guy looks like somebody already did that. Seriously, I really liked this problem because it separates the real bridge players from the crowd. If you can play a contract like this with any conviction, your opponents are in serious trouble.

The only realistic hope not to lose the board is that your teammates bid and make a game, and 4 seems to have chances. Joe should have six hearts (no raise from Judy) which gives him eight top tricks, and a successful club finesse makes nine. Close! Just one more trick from spades or clubs (or a squeeze) would bring 4  home. Therefore, this is like a defensive problem presented in a different light. You must find the defense to take four tricks so your score of minus 400 will win the board if your teammates are plus 420. Wouldn’t that be sweet?

The first assumption you must make is that Judy has the A, else 4 would have no chance. It is also apparent that Judy cannot have four spades (no 1  response) so spades must be 3-2 barring the remote chance that Joe is 4-6 in the majors. The deal might be something like this:

 2 A 9 7 9 8 7 5 J 2 K 10 9 7 5 2 K Q J 10 4 2 A 7 4 Q J Q J 3 6 3 K 9 3 A 8 6 5 2 K 10 8 6 4 A Q 10 8 6 5 4 3

After winning the A, you must lead a diamond (Line D) to establish a diamond trick before Joe can establish a 10th trick in spades. While plausible, this layout is unlikely because of its restricted composition — both spade honors in East, diamonds 3-3, and Q-J tight in West. Note that Judy can’t hold any more HCP because she is already tiptop for the 1 NT response.

Now consider a more realistic layout:

 2 A 9 7 9 8 7 5 J 2 K 10 9 7 Q 5 2 K Q J 10 4 2 A 4 Q 2 J 3 6 3 K 9 7 3 A J 8 6 5 K 10 8 6 4 A Q 10 8 6 5 4 3

Suppose you lead a diamond as before. Joe will let it ride to the jack and king, then Judy (inspired by her spectral presence) will lead the J forcing you to win the king, else Joe can establish a spade trick. If you exit with a diamond, Joe will lead all but one trump to reach this position:

 West leads A 9 — — K 10 9 Q 5 2 — Q 2 — — 9 A J 8 6 10 8 — 10 8 4

When Joe leads his last trump, dummy is squeezed. You must discard the 9 (else you lose all the rest), then Joe exits with a spade to endplay dummy. This doesn’t even require good card reading (as it would declaring 4 ) because the key hand is exposed.

If you return a club after winning the K, the play goes queen, king, ace. Judy will then lead a second spade, ducked by Joe to reach this position:

 North leads A 9 8 7 2 10 9 7 Q Q J 10 4 2 A 2 — 6 9 7 3 J 8 6 5 10 8 6 — Q 10 8 6 3

You now face the task of stopping a dual threat: You must (1) lead a trump to prevent a spade ruff in Judy’s hand, and (2) lead a club to break up the impending black-suit squeeze. Alas, you can’t do both.

It should be apparent by now that your diamond lead at trick two cost a tempo. Instead, you must lead a club, intending to finesse the 10 (Line F) if Joe plays low. This removes one of Judy’s crucial entries; then if Judy leads the J as before, you will win and lead a second club to erase the other. This keeps you a step ahead, and you can counter any move. Note that the diamond entries are useless to Joe, since your hand can’t be squeezed.

The second example represents a lot of actual deals. Note that the Q-J could be swapped, or the Q-J, or the A-K. In all cases, the bidding would be true, and only the club switch gains a fourth trick for your side.

Besides the subtle squeeze defense, there are many cases where the East-West clubs are 4-3, and a club shift simply establishes a club trick before they can establish a spade trick. For example, if Joe has x-x K-Q-J-10-x-x A-K J-x-x, only a club lead works. Note that the same defense against 4  (heart lead, club shift) is unlikely, so chances are good to win the board. In contrast, when a diamond return is right, prospects are bleak because North is likely to lead the J against 4 .

Line D (diamond lead) clearly merits second place; but other options are considerably worse. Line E (club to king) is fruitless if it wins, because you’ll lose the board anyway with no game for East-West — but it still might suffice in some blocked positions when it loses, or if West is obliged to play an honor leaving no option to finesse.

Lines A, B and C (leading spades) are about equally bad, as they help the opponents establish the one trick you’re trying to prevent — indeed, this might be how 4  is made at the other table, when North decides to lead the A after South showed spades. Any difference among them is negligible, so they’re ranked by the voting.

Considering the hellish nature of this problem, I was generous in the scoring. Hopefully, your partners aren’t like Fritz, and you won’t face many debacles like this in real life. Even so, the exercise may toughen your game. Nice pass, Fritz… you moron.

Leif-Erik Stabell: … If East has x-x x-x x-x-x-x A-Q-x-x-x, she might not find the spade switch (and 4  will be laydown). Or if East has Q-J-x x-x x-x-x-x A-J-8-x, only a heart lead and club switch will beat 4  — hardly an obvious defense.

Tong Xu: West can make 4 with x-x K-Q-J-10-x-x A-K Q-x-x barring an unlikely heart opening lead and [club switch].

Gareth Birdsall: I need to lead clubs twice in case West has Q-x-x K-Q-J-10-x-x A-x J-x or similar; otherwise he will either give his partner a spade ruff, or squeeze dummy in clubs and spades.

Gabriel Nita-Saguna: From the bidding I think I can assume hearts split 6-2. My best chance, and probably the only one, is to hope my teammates make 4  and I will not go down more than four tricks. The implication is that I will have to play East for the A; otherwise, 4  can’t be made. I think this is better than Line D as it might be a timing problem, trying to get my fourth trick in clubs before they can setup their 10th in spades.

Rainer Herrmann: I need to find four tricks, which would require a difficult defense to get against 4 . Give East both spade honors and the A, and West 2=6=2=3 distribution.

Andrew de Sosa: If I can make four tricks and [our teammates] make 4 , we will win this board. [For this to happen] spades must be 3-2, and Judy must hold the A for 4  to make. [I will also assume] diamonds split 4-2, and Judy holds Q-J-x to engineer a club pitch. Thus, I must finesse clubs twice to have a shot at a third-round club winner, while preserving the A as an entry.

Frans Buijsen: To win the board, East-West probably need to make 4 at the other table. They can do this if East has A-Q-J; but in this case I will go five down. I’m playing East for [ A-Q or A-J], in which case Line F [may be] the only way to go only four down, and the presumed 4  contract [might be allowed to make].

Carsten Kofoed: I’ll try for the third “phantom.” My aim is to lose only 400 to East-West, so I attack their connection lines. With the grin West showed, he might have Q-J-x-x K-Q-J-10-x-x-x A J. Afterwards, with a hideous grin, maybe I’ll hum “Rikiti-titiki-tin.”

Tibor Roberts: Assuming East-West can make 4 , the A must be offside. Then I can win the board by scoring just four tricks and need but one in clubs. I need only wish that West has one or both of the Q-J, and that spades are 3-2.

Quentin Stephens: I want the opponents to break the spade suit.

Michael Errington: If West holds x-x K-Q-J-10-x-x A-K J-x-x or similar, I can establish a club trick before he can establish a spade trick. Minus 400 against plus 420 at the other table?

Frances Hinden: My best chance is to endplay West, so I can’t touch spades. I need the A to be wrong, so Line E is unlikely to gain. … If West has Q-J-x-x K-Q-J-10-x-x A-x x, I need to play a diamond now to stop my hand getting strip-squeezed. Opponents may not find a heart to the ace and a diamond switch against 4  in the other room.

Neelotpal Sahai: Playing for four tricks in a voluntarily bid eight-trick partscore was never so tough. For me to succeed and to make, West should hold something like Q-x-x K-Q-J-x-x-x A-x J-x (4  goes down only after a diamond lead)… When I lead a diamond toward dummy, Joe has to step up with the ace and attack clubs immediately. Did you mention that Joe and Judy are not experts? …

Zahary Zahariev: I give West J K-Q-J-x-x-x A-x A-x-x-x. Now East-West can make 4  with any lead, except the blocking K. If I play a diamond, a fourth trick is sure because trumps are blocked and West is short an entry. So minus 400 against plus 420.*

*All true, and Zahary’s example shows that 4 can be made with the A in the West hand. Alas, this is possible only if East would bypass a four-card spade suit to bid 1 NT. I suspect Zahary is unfamiliar with Standard American bidding — which many would applaud as good news. –RP

Weidong Yang: How can I win the board with such a stupid contract? Only if East-West can make 4 ! Then down four is OK. I need to win two spades (West cannot have a stiff spade since East didn’t respond 1 ), one heart and one diamond. (I cannot count on the K, as otherwise 4  will fail.) …

Marcus Chiloarnus: My opinions may have changed, but not the fact that I am right.

Amit Raturi: Four tricks are needed to win the board, so assume West is 2=6=3=2 with the A offside; don’t touch spades as that is their 10th trick in a 4  contract.

Manuel Paulo: Consider this West hand: Q-x K-Q-J-x-x A-K 8-6-5-2; East-West can make 4 . Trusting our teammates to be plus 420, I need four tricks for minus 400. [Because West has led the K], East-West can win only nine tricks (four trumps, two diamonds and three clubs) if I lead a diamond.

Richard Higgins: Hoping they bid and make 4 , so I need four tricks ( A, A-K and a diamond).

Jack Rhatigan: Why did I drive through a storm for this?

Pat Rich: Words fail.

Mary Jo Branscomb: I need to set up a diamond trick before I lose my only entry in spades.

Roger Morton: Start to build a diamond trick and hope something good will happen after they have drawn dummy’s trumps. I need a fourth trick to beat a possible 420 in the other room. …

Sorry, but there is no “other room.”
Pay attention to my damn story.

Dick Winant: Down four will win the board when 4 is bid and made at the other table. So I’ll assume the clubs are sitting nicely for East-West, and I need to build a diamond trick. The key is that the K lead may have blocked hearts (doubleton honor in East); so opponents cannot cross to West to draw trumps and [finesse clubs twice] without setting up a diamond trick for me.

Bill Powell: Obviously, I need the A offside and a fourth trick somewhere. Perhaps diamonds are 3-3.

TopMain

## Problem 4

Board-a-Match Both Vul

 WestJoe2 Pass NorthFritz1 2 3 EastJudyDbl3 All Pass SouthYou1 Pass

 3 South 9 7 6 5 A 7 3 2 A K 5 4 7 Lead: J East plays K K Q J 8 8 6 4 9 6 3 Q 6 4

B. Duck a heart816724
C. Win A-K7588
E. Ruff a club; lead 2510215
F. Ruff a club; win A-K321131
D. Duck a diamond27311

Here you are again in a hopeless contract, and in grave danger of going down two, when the opponents would have failed in 3  (barring a singleton spade or diamond). Even going down one might not do any good, but that’s the best you can hope for. I guess the only good news is that Joe and Judy didn’t bid 5 , as then you’d be in five spades. Right, Fritz? [Fritz can’t speak, but his foaming at the mouth seems to confirm it.]

Judy’s trump shift makes it impossible to ruff both clubs in dummy, so it looks like you need to establish the fourth card in hearts or diamonds as your eighth trick. Which red suit rates to split 3-3? Probably neither, as Judy’s most likely shape for the double and club raise is 3=4=2=4. (I’m assuming she has only three spades, as a 4-1 break is worse news.) Consider this typical layout:

 3 9 7 6 5 A 7 3 2 A K 5 4 7 4 3 Q 10 Q J 8 7 J 10 9 5 2 A 10 2 K J 9 5 10 2 A K 8 3 K Q J 8 8 6 4 9 6 3 Q 6 4

As soon as you give up the lead, the defense will lead ace and another trump, putting you down two — unless you can develop an endplay against East. The idea is to put East on lead in hearts after extracting her diamonds to force an eventual club lead to set up your queen. Therefore, you must not ruff a club early.

The proper play is simply to lead back a high trump (Line A) to East, who returns her last trump. Next duck a heart. Win the heart or diamond return and cash all your red-suit winners to reach this ending:

 North leads 9 7 3 5 4 — — — Q J 10 9 5 — K J — A 8 3 8 8 9 Q 6

Now exit with a heart. Judy will then lead her fourth heart — but don’t ruff. Just pitch your diamond loser, then the forced club return gives you the rest. Is that a teardrop you see in Judy’s eye? The recommended play also works when either red suit is 3-3. Note that if Judy had another diamond, leading that suit would establish dummy’s fourth diamond.

If Joe wins the first heart and leads a club (trying to break the endplay) you would simply pitch a diamond from dummy. Judy can win the A, but now you lose no diamond trick as the Q provides another pitch. Eight tricks either way.

Line B (duck a heart) would work just as well if the defense cleared trumps, but there’s a hitch: A heart continuation ruins your endplay. You must win the A; then if you cash A-K and lead a spade (or heart) to Judy, she will always have an exit card — though it might be worth it to see her smile.

Line C (win A-K) is third best, offering fair chances if you next lead a low heart (leading a third diamond is poor). Curiously, this lets you succeed against the diagrammed distribution if spades are 10-x opposite A-x-x. Line E (ruff club, lead 2) loses that edge and basically requires a 3-3 heart break.

Lines D (duck a diamond) and F (ruff club, win A-K) are worst and about equivalent (ranked by the voting). Accurate defense now prevents you from succeeding when hearts are 3-3.

Leif-Erik Stabell: East is most likely 3=4=2=4, in which case she eventually will have to give me a second club trick.

Tong Xu: I hope East is 3=4=2=4, and I can throw her in with dummy’s fourth heart. Then my Q may be a winner.

Gareth Birdsall: I can succeed in managing eight tricks if East is 3=4=2=4 or 3=4=1=5. I plan to draw trumps and duck a heart; then on a red-suit return, I will cash A-K then endplay East with a heart. If instead West returns a club, I will discard a diamond and eventually discard a second diamond on the Q and ruff a diamond in dummy.

Julian Pottage: East presumably has the A, and there is a good chance I can get out for one down by endplaying East with the third round of hearts.

Gabriel Nita-Saguna: This might be nonintuitive, but it’s the only sure line to eight tricks when East is 3=4=2=4, having…the A and A-K. I plan to duck a heart and then endplay East in hearts after eliminating her last trump and diamonds. When she leads the fourth heart, I will discard my diamond loser. Now she must present me with a trick in clubs. Line B could be an alternative, but they might surprise me by continuing hearts instead of spades, ruining my plan.

Frances Hinden: As the A-K are on my right, I need spades 4-1 or diamonds 5-1 [for 3  to make]. If spades are 4-1, I think I’m stuffed; so I will aim to endplay East in hearts to give me the Q.

Neelotpal Sahai: Draw trumps. For East-West to go down in 3 , spades have to break 3-2, and diamonds 4-2 or 3-3. East’s likely holding is A-10-x K-J-10-x x-x A-K-x-x. After trumps are drawn, [a heart] should be ducked; then cash A-K, A and endplay East in hearts [pitching a diamond on the fourth heart]. … If West shifts to a club, then sluff a diamond from dummy (instead of ruffing).

Neil Morgenstern: OK, I am playing for East to be 3=4=2=4. Draw trumps and duck a heart. If a heart is returned, win the A, A-K, and lead a third heart; East must win and will probably lead a fourth round, but I throw my diamond — now East has to lead a club to establish my Q for just one off.

Len Vishnevsky: The basic idea is to play East for something like A-10-2 K-J-10-9 7-2 A-K-8-2; so draw trumps and duck a heart… Cash the red honors and throw East in with a heart to endplay her in clubs. …

Bill Erwin: My objective is to endplay East to [establish] the Q. To do this, I need to remove her trump and diamond exits. So East wins the A and returns a trump; then I duck a heart; win the red-suit return; cash the remaining red-suit winners, and play a heart. When East plays a fourth heart, I pitch a diamond to endplay her. Down only 100 may [salvage something].

Charles Blair: Later I will duck a heart, cash A-K, and throw East (presumably 3=4=2=4) in with a heart. Ducking a heart immediately (Line B) loses if they return the suit.

Rainer Herrmann: Play East for 3=4=2=4 or 3=4=1=5 and endplay her in hearts for a club return. This is also reasonable should East be 4=4=1=4, but then for two down, which is unlikely to win the board. Anyway, East may have doubled with four trumps.

Toby Kenney: … Suppose East wins the A and returns a diamond. Win this; draw the last trump; duck a heart; win the diamond return; A, and exit with a heart to East. Then pitch a diamond on the last heart, leaving East endplayed to give me the Q.

Julian Wightwick: … I must hope 3 is making, and find a way to go only one off in 3 . The  Q would be a trick against 3 , so either spades must be 1-4 or diamonds 5-1. Plausible shapes for Judy are 4=3=2=4 or 3=4=1=5. Fortunately, neither defender can lead clubs without giving me my eighth trick. I plan to draw trumps, duck a heart, then cash the red-suit tops and exit with a heart to endplay Judy. If Judy is 3=3=2=5, then 3  was going off; but I might even make if she forgets to unblock in hearts. If Judy has four trumps, she will probably continue with a third round; then I duck a heart and press on with my plan, hoping for hearts 3-3 and the endplay.

Tim DeLaney: I must hold the loss to down one, because East-West cannot make game; so spades must be 3-2. Therefore, they cannot even make 3 ; so I hope our teammates either lead a heart originally, or switch to a heart after leading a club. This defense would allow East to play the fourth heart before her exit card (third trump) is removed. Otherwise, East will have to lead clubs in the endgame.

John Lusky: Playing West for x-x K-Q Q-J-10-2 J-10-x-x-x, and planning to duck two rounds of hearts if East wins and plays a third spade.

Robert Eachus: I’m going to play East for A-x-x, four hearts and the A. [Endplay described]. Note that if West wins the first heart trick and leads a club, I am fine; I sluff [a diamond] from dummy…

TopMain

## Problem 5

Board-a-Match None Vul

 WestJoeDbl4 NorthFritz1 4 * EastJudyPass1 All Pass SouthYou1 2
*Fritz like Yarborough

 4 South 9 6 5 2 5 4 8 7 5 4 3 9 4 Lead: K East plays 9 A K 8 4 3 Q 6 2 A K Q 6 2

West continues with the A (East plays 7). Your play?

F. Pitch a diamond811316
A. Ruff; win A-K; A-K-Q617525
B. Ruff; win A; A-K-Q5467
C. Ruff; win A; A-K; lead 2419729
E. Ruff; win A-K; lead 238012

What? You mean Fritz only found two bids with those cards? I guess you’re lucky Joe didn’t double, as Fritz might redouble — then you’d probably lose control and be faced with a murder charge. No biggie, as any competent defense lawyer could get you off for justifiable homicide, let alone that Fritzicide is legal in most states. Oh well; maybe something good will come of this.

What can Joe and Judy make? If they have the distribution to make 4 , you’ve already won the board; but this is unlikely. Spades rate to be 3-2 (else you’d surely be doubled) and two clubs will probably cash, which leaves only nine tricks available in hearts. Therefore, your teammates are likely to be plus 140, so your window to win the board is to go down no more than two tricks (minus 100). Consider this likely layout:

 4 9 6 5 2 5 4 8 7 5 4 3 9 4 J 10 7 A K J 10 2 A K J 7 5 Q 3 Q 9 8 7 6 10 9 J 10 8 3 A K 8 4 3 Q 6 2 A K Q 6 2

Suppose you ruff the heart and lead ‘em from the top (Line A). After cashing A-K and A-K, you lead the Q. All would be fine if Joe ruffs; but it should be obvious to pitch. When you next ruff a club, Joe pitches again and it’s your last trick. Joe will gain the lead in diamonds, draw the remaining trumps and claim. Down three; minus 150, and a board-a-match disaster.

What if you draw only one trump? Suppose you win the A, A-K, then lead a low club (Line C). Still no good. Joe can ruff with the 10; then three rounds of diamonds lets Judy ruff with her last trump; and a fourth club gives Joe the J. Same result; down three. Other combinations of spade-club plays are also futile against accurate defense.

As is often the case, players are enamored by high cards. You must also appreciate low cards, especially when playing with Fritz as you’ll find plenty of them in dummy. Instead of leading either black suit, you should be leading diamonds (Line D). What’s theirs is theirs; Joe can do nothing to hurt you. If he shifts to a trump, just win and lead a second diamond; if he continues trumps, win and cash your top clubs; then when clubs fail to break, just give up a diamond to establish a trick in dummy. All you lose are three diamonds, a heart and a spade; down two.

Line F (pitch a diamond) deserves second place. The obvious danger is that the defense may lead three rounds of diamonds; then you’re in trouble if the same hand is short in both diamonds and spades. Note that in the diagram Judy will uppercut you with the Q. Even so, this still offers a better chance for eight tricks than ruffing and leading black suits.

Among the spade-club plays, there’s not a great deal of difference. Lines A and B (cashing A-K-Q) deserve the edge as they produce nine tricks with clubs 3-3 and diamonds blocked, however unlikely. Choosing between Lines A and B is like splitting hairs, so I let the voting decide. Similarly, between Lines C and E.

Leif-Erik Stabell: I will have to settle for minus 100 and hope it is enough. Anything else leads to minus 150 if West is 3=5=3=2 (as expected).

Tong Xu: It is good news if I cannot win two club tricks [then 4 makes]. Diamond plays will break their connection if West has 3=5=3=2 shape. Only two down.

Gareth Birdsall: If opponents continue hearts I will be able to elope with most of my trumps. Otherwise, I should have enough trumps to keep control when I have established side-suit winners.

Julian Pottage: Nonvulnerable, I can afford two off if teammates are plus 140; but I must avoid three down. Trumps must be 3-2 (to give me a chance and because nobody doubled)…

Lajos Linczmayer: The goal is to win [at least eight] tricks, and I can win nine if West has J-10-x A-K-J-10-x-x A-K x-x.

Gabriel Nita-Saguna: This looks like the only line that avoids either losing too many separate trumps or a trump promotion. Opponents could try to make it more difficult by repeatedly playing hearts; but I still have resources to end up with eight tricks, which is my goal on this board.

Frances Hinden: The target is eight tricks. … I don’t want opponents making too many trump tricks; but I can’t afford to draw trumps myself yet.

Zahary Zahariev: I think spades are 3-2 (no double) and clubs 4-2 (if opponents can make 3 for 140). [If] West has a hand like J-10-x A-K-10-x A-K-10-9 10-x, this is the way for eight tricks. For example, East wins and returns something; I cash A-K, A-K-Q and give East the fourth club. Now she has no diamonds, and I’ll take eight tricks.

Bill Erwin: My objective is to hold the loss to down two — minus 100 to beat a presumed 140 by my teammates. Playing clubs risks losing three diamonds, one heart, and two high ruffs when clubs are played (either by me or by East, or both). Playing diamonds, hoping for a 3-2 break will set up Fritz’s suit — justifying his optimistic bidding!

Len Vishnevsky: Teammates minus means we lose the board; and if 4 makes, we win. So I will assume they have plus 110 or 140, and try to take eight tricks. With spades 3-2 and clubs 4-2, I can ruff and duck a diamond… and take three spades in hand, A-K, one ruff in dummy, a long club, and either the Q or an extra ruff in dummy. …

Charles Blair: If East wins, I will later cash A-K and A-K-Q, then throw her in with a club. West’s failure to double 4  suggests 3=4=4=2 shape.

Weidong Yang: If opponents can make 3 but not 4 , the task is to avoid down three. This handles more cases than other lines.

John Reardon: My aim is to go two off when teammates are making 3 . West may have something like Q-10-x A-K-J-x-x A-J-x J-x, and I must avoid losing two trump tricks by a promotion on the fourth club.

David Cochener: Set up dummy’s long suit, planning to lose three diamonds, a heart and a spade to beat 3  making 140. Give West Q-J-x A-K-J-x-x A-J-x 10-x.

Andrew de Sosa: Assuming spades are 3-2 and clubs 4-2, Joe and Judy can make 3 ; so I must hold this to down two. Trying to set up clubs poses a serious risk of down three because the lack of entries prevents drawing two rounds of trumps [early]. Starting diamonds immediately allows either diamonds to be set up (assuming a 3-2 split) or forces opponents to concede an eighth trick via a ruff-sluff.

Marcus Chiloarnus: Hope is the dream of the waking man.

One man’s hope
is another man’s hopeless:

Amit Raturi: When in hopeless contracts, play hopelessly.

Sandy Barnes: For opponents to make 4 , we must be able to cash only three black tricks (likely two spades and one club). This will keep control of the hand and establish the long diamond.

Manuel Paulo: Consider this West hand: Q-J-x A-K-x-x A-K-10-9 x-x; East-West can make 3 . If our teammates scored normally (plus 140) I need eight tricks (minus 100). With the diamond suit blocked, East-West cannot cash three diamonds and promote another trump trick.

Richard Aronson: Again, a phantom sacrifice means spades and clubs split reasonably well; but it could be 3-3 clubs and bad spades, based on the double. Any pulling of trumps could lead to down whole bunches; so I lead diamonds. Down two could win the hand against a heart partscore making…

Tim DeLaney: If West has a singleton club or four spades, our teammates will make 4 easily; so I assume West is 3=5=3=2. … I cannot set up clubs and get back to cash the fifth one after my hand is shortened; so I play to set up diamonds. I must get an eighth trick to avoid minus 150.

Jack Rhatigan: Definitely discover what time today partner took up bridge.

Dale Rudrum: I’ll try and develop some diamonds first.

Pat Rich: Punt, and begin reducing the opponents’ communication. Maybe they’ll make a mistake; maybe I’ll win the LOTTery. I’m playing to hold my black-suit losers to one for down 100 without losing my communication.

TopMain

## Problem 6

Board-a-Match N-S Vul

 WestJoePassPass NorthFritz1 5 EastJudy4 All Pass SouthYou1 Dbl

 5 South A 5 4 3 J 10 J K Q J 10 9 8 Lead: 2 East plays Q Q 10 2 6 5 4 A K 10 A 5 3 2

East next cashes the K (West pitches 8) then leads the 9. West has two trumps. Your play?

A. Win A; K-Q; A-K108512
D. Win A; lead all trumps912919
C. Win A; K-Q; run J622533
F. Duck (let East win 9)4619
B. Win A; K-Q; A; ruff heart3639
E. Cover with 10 and let West win jack212718

Were it not for the previous boards, you might sympathize with Fritz’s decision to bid 5 ; but now you know better. No matter what it takes, he’ll find a way to put you minus. C’est la vie. I suppose the same contract might be reached at the other table, so holding it to down one will maximize your chances to win or tie the board.

Joe’s spade discard on the second heart is almost surely from five cards.* Therefore, East’s 9 is a singleton, so you can quickly dismiss Line E, which leads to an immediate spade ruff.

*It is true that Joe might be playing a deep game, but it is quite unusual to pitch a spade from four spades and six diamonds. The possibility increases, of course, with the skill of the defender since the fourth round of spades rates to be insignificant; but even on an expert level, I doubt it would happen more than 10 percent of the time.

With threat cards in three suits, it is tempting to follow Line D and run your trumps. Somebody will be hurting in the end position, and you can succeed against any distribution. For example:

 5 A 5 4 3 J 10 J K Q J 10 9 8 K J 8 7 6 2 9 7 6 5 4 7 6 9 A K Q 9 8 7 3 Q 8 3 2 4 Q 10 2 6 5 4 A K 10 A 5 3 2

Before the last trump is led, the position will be:

 North leads 5 4 3 — J 9 K 7 — 9 7 6 — — A 9 Q 8 3 — Q 6 A K 10 —

On the last club, Judy must pitch a heart; you let go the Q, and Joe pitches a diamond. Next lead the J to your ace and exit with a heart to endplay Judy. If Joe held the Q, you could just as easily endplay him* by keeping your Q instead of the low heart. You’d probably guess it right at least 70 percent of the time, but there is no lock.

*Actually, there is never a need to endplay Joe, as he is obliged to keep two spades (else you could throw him in and succeed no matter who held the Q) so he must always unguard the Q if he has it; while Judy must come down to one heart and two diamonds. Hence, after you exit with a heart, you have the option to fly with the K if you think Joe has the queen. Nonetheless, you still have to guess.

Based on the inferred spade lie, there is another play that will succeed no matter who has the Q without a guess. After winning the A, cash two trumps and both top diamonds (Line A) then ruff the 10 in dummy. Cross to your A to reach this ending:

 South leads 5 4 — — J 10 K 7 6 — 9 — — A 9 8 Q — Q 2 6 — 5

Next lead the 6 and pitch a spade from dummy. Judy must now give you a ruff-sluff to eliminate the other spade loser. This only fails if Judy produces a surprise spade in the end — nah, she’s too sweet to do something like that.

Note that if Judy tried to prevent the endplay by leading a third heart instead of the 9, this wouldn’t help. After drawing trumps, you could simply lead a low spade to the 10 (with or without eliminating diamonds) for an easy endplay against Joe.

Evidently, the correct play on this problem comes down to a judgment call. Which is more likely: Guessing who has the Q? Or Joe having five spades? I think the latter, so Line A gets the top award; and Line D, a close second.*

*Several respondents suggested that West would (or might) have bid over 1 with K-J-8-7-6 at the vulnerability. Certainly, some players would — I won’t tell — but lacking any information about Joe’s style, you should assume he follows the system guidelines, which dictate a pass. The only other high card West could have is the Q, which would not justify a 1  overcall; and the spades hardly qualify as a “strong five-card suit,” with which the system would allow a weak 2  bid.

Other plays are clearly inferior. Line C (run the J) bucks at least 5:4 odds on the location of the Q. Line F (let East win the 9) may seem cute, but East should shift to a diamond to break communication; then the only real hope is to take the finesse, with the ignominy of going down three if it loses (spade ruff).

Line B ( A, K-Q, A, ruff heart) seems to lead nowhere, but it does allow an eventual endplay if East holds the Q and a singleton spade. Line E (cover with 10 and let West win jack) must be rated worst, as down two is imminent with the likely spade ruff — though if spades happen to be 4-2, it offers a lock for down one by a double squeeze.

### Comments for A. Win A; K-Q; A-K

Leif-Erik Stabell: I could try to endplay the player with the Q (Line D); but it must be better to try and guess whether West has four spades (Line E) or five (Line A), since I might have to do that anyway. If my calculation is right, West is a 5:4 favorite to hold only four spades (don’t know at this stage how clubs break…) which indicates Line E is best. But how often will he discard the 8 from various holdings? It should be automatic with K-J-8-7-6 and can hardly cost with K-J-8-7… But with K-J-8-6, it might cost a trick… So that should tilt the odds in favor of Line A… On the other hand, why have I been dealt the 10 if it is of no use? :)

Tong Xu: I do not think West pitched the 8 from four cards. I will try to use my third heart for a throw-in against East.

Julian Pottage: Very close between this and Line D. This is 100 percent if the 9 is a singleton (East will have to give me a ruff and discard after winning the third heart). With Line D, I will have to guess who has the Q, and may have to guess shapes as well.

Lajos Linczmayer: The goal is to win 10 tricks. East probably has: x A-K-Q-9-8-7-3 x-x-x-x x (with the Q he [might] have covered the J). Then a diamond ruff; club to the ace, and lead the last heart to pitch a spade from dummy.

Zahary Zahariev: Normally, West discards a spade from five cards; so I think East has 9 A-K-Q-x-x-x-x x-x-x-x x. This is the only way for one down no matter who has the Q. Next ruff the 10; cross to hand with the A, and discard a spade on the last heart — East wins and must give me a ruff and discard.

Charles Blair: I am assuming a non-expert West is very unlikely to discard a spade without five; so I can ruff out diamonds and throw East in with a heart.

Andrew de Sosa: Playing Judy for 1=7=4=1 distribution. I plan to ruff the 10, take the A, and (hopefully) endplay Judy with the last heart forcing a ruff-sluff for down one.

Daniel de Lind van Wijngaarden: Only down one when East has a singleton spade, as I can ruff the third diamond, cross to the A and throw East in with a heart…for a ruff and discard. … (Line F looks promising if West has the Q, as I might squeeze West in the pointed suits, but East can break the squeeze by playing a diamond.)

Richard Morse: Then ruff diamond; [cross to the A] and exit with a heart, throwing a spade. I hope East is 1=7=4=1 and gets endplayed.

Jane Marvin: Fritz and I are well matched, I fear.

Gabriel Nita-Saguna: Looks like a close choice. Line A will win without guessing when spades are 5-1, as East will be endplayed in hearts for a ruff-and-discard return. Line D, however, is 100 percent if I guess what is going on, as I can strip-squeeze either East in hearts or West in spades, or I could just cash A-K to drop the unguarded queen.

Frances Hinden: Assuming the K is wrong, this line always comes to 10 tricks if I can read the end position. Other lines all fail against possible distributions: Line A fails if East has a doubleton spade; Line E, if he has a singleton; Line C or F, if West has the Q; and Line B fails [most of all]. So I start on Line D and make a decision later.

Neil Morgenstern: … However the cards lie, I can go just one off; but I have to read the position. If West throws three diamonds and one spade, and East throws four hearts and one diamond, I will have no idea whether West started with 5-5 or 4-6 in spades-diamonds, or who started with the Q. Anyway, [even if I guess right] I was better off defending 4  doubled.

Rainer Herrmann: Strip-squeeze West between diamonds and spades.

John Reardon: I can easily win nine tricks, but the object is to win 10. If East has the Q, Line C is easy; however, West has more diamonds so I choose to play him for the Q. In the five-card ending, North has x-x-x J x; East x A x-x-x; South Q x A-K-10; and West K-x Q-x-x. The last club forces West to throw his last small spade while South parts with the heart; then a spade exit sets up spades in North, so West must concede the rest.

David Cochener: Playing West for four or five spades (the latter more likely) and the Q based on greater length in diamonds. I will either endplay West if he bares the K, or fell the Q if he doesn’t. I hope 5  goes down two at the other table.

Frans Buijsen: Line C works if East has the Q; Line D, if West has it (West will be stripped and thrown in). Since it looks like West has about six diamonds, and East only three, I choose Line D.

Quentin Stephens: Funny things can happen when you run long trumps.

Tom Barczy: Strip-squeeze West, who cannot keep Q-x-x and two spades.

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## Final Notes

Comments are selected from those above average (top 310), 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).

I hope you enjoyed my story — well, I guess not, so next Halloween I better stick to carving pumpkins. Thanks to the courageous souls who participated, and especially those who offered kind remarks about my web site. As you may have noticed in the story, the cemetery had no grave marker for Fritz. So watch out! He may be coming soon to a club near you. Speaking of the devil:

Robert Eachus: I gather that killing Fritz is not a solution. But if I could render him unconscious for a few hands?

Charles Blair: I don’t like Michaels either. Maybe that’s why my partners think my bidding is “on the Fritz.”

Tim Hemphill: This was indeed a ghoulish contest. Down, down, down — they’re coming to take me away!

Roberta Tarr: I’ll drop in to see Fritz tonight as I go for my annual ride on my broom!

Richard Morse:
Oh, the horror of bidding like this
With an unending series of misfits,
Leaving nowhere to go
Against Judy and Joe.
Why don’t you give it a miss, Fritz?

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