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Top of Nothing

Last night at the club I was West as my opponents routinely bid their balanced hands to 3 NT. A club lead was unattractive, especially at matchpoints, and my majors bore omens of “never lead from a jack.” Therefore, I led top of nothing in diamonds. Argh! Turns out my lead allowed declarer to win a diamond trick that he could not have won on his own. Oh, well. I would have lost at poker, too. My full house (jacks over eights) would easily beat North but would have lost to South.

3 NT  Dummy


 
None Vul

West

Pass


North

3 NT


East

All Pass


South
1 NT*

*15-17
S J 7 4
H J 6 4
D 8 7 4
C A J 8 6
Table


 
Lead: D 8


 Declarer

Construct a layout consistent with the auction and story. Multiple solutions exist. A further goal is for North to have the worst possible poker hand, and South the best possible poker hand. (Outcome of 3 NT is irrelevant.)

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Tim Broeken Wins!

In August-September 2011 this puzzle was presented as a contest, with 38 participants from 16 locations. Thanks to the dwindling few who entered — if the trend continues I may have to bring Fritz out of retirement — and congrats to the eight who submitted valid constructions. Correct solvers are ranked by the worst North poker hand, the best South poker hand, and lastly by date and time of entry.

Well, what can I say. Another record broeken, as Tim comes through with a fourth win in this series. Not only that, but he topped the construction I had in mind when creating the puzzle. Evidently, my plan to flood the dikes using kelp beds isn’t working, so it may be time to send Fritz on a Dutch bridge holiday — the sight of him alone could reduce bridge interest by 50 percent.

RankNameLocationNorthSouth
1Tim BroekenNetherlands3322ATTTTA
2David BrooksAustralia3322A5555A
3Aurelien BoutinFrance3322A5555A
4Leigh MathesonAustralia3322A5555A
5Dan DangBritish Columbia3322AKKKAA
6Jim MundayMississippi3322AKKKQQ
7Tony NorrisMassachusetts6655ATTTTA
8Richard SteinCaliforniaQQ33AKKKAA

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Solution

When preparing the entry forms for this contest series, I try to keep the presentation brief so the page will redisplay in place, rather than require scrolling. Occasionally this leaves an ambiguity, or a loophole I didn’t foresee. In this case, “…let declarer win a diamond trick that he could not have won on his own.” was intended to imply after any of the other three plausible leads. But I didn’t say that, and some respondents assumed that if one or two of the other leads would stop the extra diamond trick, the solution was valid.

Rather than enforce my intended implication, I decided to compromise. If at least two of the three plausible lead alternatives (S 4, H 4 and C 6) would prevent the extra diamond trick, I accepted the solution as valid. But if only one other lead would do it, the solution was… well, accepted by my new trash can.

Bridge-Poker 101

Choosing the best poker hand from a bridge hand has some curious quirks, as many — excuse me, few — probably discovered with this puzzle, most notably in regard to the worst poker hand. I’ll yield the helm to “Diamond Jim” on the mighty Mississip’:

Jim Munday: Given that straights and flushes are legal, North must be 4-4-3-2 or 4-3-3-3 and have no fives or tens. Thus, two pair must be present at a minimum. Twos and threes are the worst. I could not construct a 10-HCP hand without an ace [kicker] or a higher two pair.

Thanks, Jim; now you can reboard your riverboat. More specifically, fives and tens are the only two ranks that can be removed to spoil all straights. For instance, if you removed a jack and a six, which may seem adequate to a bridge player, you end up with a wheel: 5-4-3-2-A.

As to the best poker hand, the West cards allow only two straight flushes (D A-K-Q-J-10, D K-Q-J-10-9) which are ruled out by the puzzle’s basic condition. Next best is four-of-a-kind, of which kings, queens, nines, threes and twos would ruin North’s worst hand, the primary goal. Therefore, South should have four tens, four fives, or a full house higher than West’s.

Speaking of bridge-poker trivia, here’s a poser: What is the highest poker hand that cannot be the best in a bridge hand? [Answer at end]

While lacking in the poker department, I liked the following construction because of its subtle diamond layout. I liked it even more because another Richard provided the explanation — now if he could only explain why he missed my Toughest Beer in Bridge fest, clearly in his honor.

3 NT S A Q 8
H K Q 3
D 10 9 2
C 7 5 3 2
Trick
1. W
2. S
3. N
4. W
5. N
6. W
W 4 L 2
Lead
D 8
S 5
C 2
H 4
C 3
H J
2nd
9
4
Q
K
D 3
3
3rd
J
Q
K
7
10
8
4th
A
2
A
2
J
A
S J 7 4
H J 6 4
D 8 7 4
C A J 8 6
Table S 10 9 3 2
H 10 9 8 7
D Q J 5 3
C Q
Richard Stein
California

S K 6 5
H A 5 2
D A K 6
C K 10 9 4

Richard Stein: North and East cover the D 8 as South wins. Spade up, then a club; Q-K-A. West exits in a major, dummy wins, then a club to the 10. West can win the C J or duck; it doesn’t matter. [See ending]. Declarer runs his majors then endplays West in clubs. West is forced to break diamonds, which are frozen thanks to the D 8 lead. Making four. This is declarer’s best line of play, I believe. On an original major lead, declarer can still make 10 tricks by stripping the majors early, but this is unlikely to happen in practice. South
leads
S A 8
H Q
D 10 2
C 7 5
S J 7
H 6
D 7 4
C 8 6
Table S 10 9 3
H 10 9
D Q 5
C
S K 6
H 5
D K 6
C 9 4

Richard’s concern about declarer making 10 tricks on another lead does not dilute the solution. All that matters in the puzzle is how many diamond tricks declarer can win, and only a diamond lead allows three. For example, on a major lead West can accept his loss in clubs, yielding no extra diamond trick. By the way, my middle name is Frank; I hope this guy’s isn’t.

Dan Dang also availed the frozen-suit-endplay idea but with D J-9-6 opposite D A-K-3, and he improved on the poker hands. Ah, memories of Roger Miller, “Dang me, they oughta take a rope and hang me.”

The next deal is essentially the solution I intended. Besides giving North the worst possible poker hand, it gives South four fives. The diamond lead costs a trick outright, allowing declarer to establish a spot by force.

3 NT S A 8
H K 7 2
D J 9 6 3
C Q 4 3 2
Trick
1. W
2. S
3. E
4. N
W 2 L 2
Lead
D 8
D 5
H 10
D 6
2nd
9
7
3
K
3rd
10
J
4
C 5
4th
A
Q
K
4
S J 7 4
H J 6 4
D 8 7 4
C A J 8 6
Table S 10 9 6 3
H 10 9 8
D K Q 10 2
C K 7
Leigh Matheson
Australia

S K Q 5 2
H A Q 5 3
D A 5
C 10 9 5

The first two diamond leads are covered all around, and East exits safely with a heart. The D 6 is then led to force out East’s remaining honor and smother the four. What does this leave? That’s right, the D 3 is high. If West doesn’t cover the D 5 at Trick 2, declarer simply rides it and smothers the seven later.

While only a diamond lead lets declarer score an extra diamond trick, 3 NT can be made on any lead. After a spade lead (best) South wins and leads the C 9, ducking when West covers. Eventually, the C Q will establish (losing three clubs). The defense has the option to prevent this by shifting to diamonds, which reverts to the original theme (or East can be endplayed if he leads the D K upon winning the C K).

Two others produced the same poker hands (deuces and treys opposite four fives) but with different diamond layouts. Aurelien Boutin had D A-J-9-6 opposite D Q-5, and David Brooks had D J-9-6 opposite D A-Q-5, each with a valid deal construction.

Forty miles of railroad track

I didn’t think four tens for South could be achieved (opposite the weakest two pair in North). My construction attempts focused mainly on obscure card combinations, and I overlooked a clever layout dependent on tempo and entries. Therefore, the winning solution was not in the windmills of my mind — until it appeared from a broeken windmill in nether-nether land:

3 NT S A K Q
H 9 8 7
D J 6 3 2
C 4 3 2
Trick
1. W
2. S
3. N
4. S
5. N
6. E
W 5 L 1
Lead
H 4
S 5
D 2
S 6
D 3
S 8
2nd
7
4
9
7
A
10
3rd
2
A
10
K
5
J
4th
10
2
4
3
7
Q
S J 7 4
H J 6 4
D 8 7 4
C A J 8 6
Table S 9 8 3 2
H 5 3 2
D A Q 9
C Q 7 5
Tim Broeken
Netherlands

S 10 6 5
H A K Q 10
D K 10 5
C K 10 9

Tim Broeken: Going for style points. [Besides a diamond], only the lead of the C A costs a trick.

With a diamond lead, declarer has an easy time to develop three diamond tricks. But with any other lead the task is impossible, because the defense is a tempo ahead. Note that East will duck the first diamond (or cover the jack with the queen) then hop with the ace on the second round. This way, all the spade entries will be wiped out before declarer can unblock the D K.

Answer to poser: The highest poker hand that cannot be the best in a bridge hand is three tens. Any three-of-a-kind requires 11 different card ranks (can’t have another pair, else a full house) and these cannot include a five or ten, else a straight. Three fives is likewise impossible. Note that two pair with fives and/or tens is possible, but only if a third (irrelevant) pair is held.

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© 2011 Richard Pavlicek