Puzzle 8K53   Main

The Three Trick Gainer

  by Richard Pavlicek

Most players are familiar with the progressive squeeze to gain two tricks; but is it possible to gain three? More specifically, can a squeeze gain three tricks without losing the lead? The answer is yes, as illustrated by this deal from New Zealand Bridge, circa 1974. South can win only 10 tricks at the start (note the blockages) but West is squeezed for all 13.

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

Alas, the deal is flawed because 7 NT only makes with a club lead. Indeed grossly flawed, because in real life a club would be West’s last choice of leads. A challenge for you:

Construct a deal where South can make 7 NT against any defense without a finesse, with only 10 cashable tricks at the start.

“At the start” means after West’s best lead; so if West were endplayed at Trick 1, anything gained by that lead already belongs to declarer. “Without a finesse” means declarer cannot vary his play based on a defender’s play in the same suit, except as South at Trick 1.

Multiple solutions exist. Further goals (tiebreakers for the August contest) are to have the fewest North-South HCP, and lowest North-South rank sum, in that order of priority.

Edouard Bonnet Wins

In August 2011 this puzzle was presented as a contest, with 46 participants from 17 locations. Thanks to the brave souls who entered, and congratulations to the 10 who constructed a valid deal to fulfill the conditions. Ties are broken by the fewest N-S HCP, the lowest N-S rank sum, and lastly by date and time of entry.

The first of three to submit the optimal solution was Edouard Bonnet of France. That’s “Edward” to most of us, but the French continue to stockpile their consonants and insert vowels of mass confusion. I mean, look at what they did to a simple “yes” with oui, and I don’t think anyone can spell hors d’oeuvres without looking it up first (as I did). All the makings of a Conehead conspiracy, but I digress.

USA in Top 10! Czech Republic loses!

After my carefully crafted subtitle, readers might have no need to peruse the leaderboard. Oh well. Thanks to Mississippi and its newfound resident (formerly of California) for saving us from oblivion.

Winner List
1Edouard BonnetFrance25188
2Pavel StrizCzech Republic25188
3Dan DangBritish Columbia25188
4Tim BroekenNetherlands25189
5Jonathan MestelEngland25189
6David BrooksAustralia31192
7Paul BardenEngland31194
8Gareth BirdsallEngland32193
9James LawrenceEngland33196
10Jim MundayMississippi34204

Puzzle 8K53   MainTop   The Three Trick Gainer


A few solvers tried to skirt the essence of the puzzle by having West endplayed at Trick 1, thereby gaining a trick, so the squeeze only needed to gain two tricks. Sorry, no shortcuts. While I neglected to define “at the start” in the original puzzle (now clarified) the great majority of respondents correctly interpreted my intent.

A three-trick-gaining squeeze (without losing a trick) is extremely rare, because if declarer has three losers, the defender has three extra cards, which allows him to retain stoppers in three suits. The crux of this rare squeeze is a blocked position in two suits, as represented by the majors in the example, such that declarer would have only two losers if he could reach all his winners. Further, all three threat suits require an extended threat (two or more threat cards) so the initial squeeze gains two tricks. The third trick can then be gained in typical fashion by a simple squeeze.

To succeed against any defense, the main hurdle is to prevent the removal of either blocked threat-suit position. Rather than A-9-8-2 opposite a blank king, where one lead will destroy it, declarer needs something like A-x-x-x-x opposite K-Q, where one lead is harmless. Below is a valid construction by David Brooks (Australia):

7 NT SouthS A 5 4 3 2TrickLead2nd3rd4th
H A 5 4 3 21 WS J26K
D 3 22 SH K826
C 23 SD A62J
S J 10 9 8TableS 7 64 SC AK25
H J 10 9 8H 7 65 SC QS 8H 36
D 9 8 7 6D Q J6 SS Q937
C KC J 10 9 8 7 6 57 SH Q9A7
S K Q8 NS AC 7C 310
H K Q9 NS 5C 8C 4H 10
D A K 10 5 410 NS 4C 9D 4?
Lead: S JC A Q 4 3West is squeezed

Many play sequences exist. To verify the success after any lead, Tricks 1-4 consist of winning a top card in each suit. At Trick 5 West is triple-squeezed, and the path shown assumes he abandons spades; so cash the S Q then overtake the H Q. The good spades are then cashed, and at Trick 10 West is squeezed in the red suits. Obviously, if West abandons hearts early, the play is mirrored. If West instead abandons diamonds, running that suit will squeeze him in the majors.

David Brooks: I am sure you can do better, but if I spend any more time on this I will be doing the next problem waiting in the divorce courts.

Probably a wise decision, but if you decide to set your priorities straight, PavCo Attorneys Down Under will represent you pro bono.

Leaping tall buildings in a single bound

I especially liked the next entry from Tim Broeken (Netherlands), this series’ most formidable solver with three wins to date. Not only does it reduce North-South to a mere 25 HCP, but the squeeze occurs in a single bound — three tricks gained at once. Further, if West chooses, the squeeze can occur on the opening lead. East is the victim:

7 NT SouthS A JTrickLead2nd3rd4th
H A J1 WD KA5C 3
D A Q J 10 4 3 22 NS A72K
C A 23 NH A72K
S KTableS 10 9 8 74 NC AH 8S 34
H KH 10 9 8 75 ND Q6S 4C 5
D KD 9 8 7 6 56 ND J7S 5C 6
C K Q J 10 9 8 7 6 5 4C7 ND 108S 6C 7
S Q 6 5 4 3 28 NH J93C 8
H Q 6 5 4 3 29 NS J8QC 9
DDeclarer succeeds
Lead: D KC 3

If West leads a non-club, North wins the S A, H A and D A in any order. Note that North’s D 4-3-2 comprises a triple extended threat, as do South’s low cards in each major, provided the club is discarded on the D A. Therefore, when the C A is led at Trick 4, whichever suit East abandons gives declarer three immediate tricks, so all that remains is to cash winners. If West makes his natural lead of a club, he achieves the ignominy of forcing partner to lose three tricks on the opening lead. Ouch!

A similar layout, but majors A-Q-x-x-x-x opposite J-x with blank kings offside, was submitted by this brilliant solver:

Jonathan Mestel: If you won’t let us finesse, we’ll drop ‘em all!

Lowering the bar a notch

While the previous deal contains the absolute minimum N-S HCP, their rank sum of 189 can be lowered to 188 — a trivial difference, but worth gold in these contests. This is accomplished by changing the enemy singleton king in declarer’s non-blocked threat suit (diamonds) to Q-J doubleton, as this winning entry from Edouard Bonnet (France) shows:

7 NT SouthS A Q 6 5 4 3TrickLead2nd3rd4th
H A Q 6 5 4 31 WD 5S 3JK
D2 SD A4H 3Q
C 43 SD 106C 4C 5
S 10 9 8 7TableS K4 SC AS 7H 46
H 10 9 8 7H K5 SD 97H 5C 7
D 8 7 6 5 4D Q J6 SS 28AK
CC K Q J 10 9 8 7 6 57 NS 4C 8J9
S J 28 SH 27AK
H J 29 NS QC 9C 210
D A K 10 9 3 210 NS 6C 10C 3H 8
Lead: D 5C A 3 2continued below…

The play is flexible after any lead. A diamond is most interesting, in which case only three diamonds can be won immediately, pitching one card from each suit in dummy. The C A then triple-squeezes West, who does best to give up a major (spades as shown) and North pitches the opposite major. Cash the last diamond winner to pitch a heart, unblock spades, then cross to dummy with the H A.

Next run spades to reach this ending before the last spade is led:

NT win allS 5TrickLead2nd3rd4th
H Q 611 NS 5C JD 2?
DDeclarer succeeds
H 10 9H
D 8D
D 3 2
North leadsC

On the S 5 South sheds a diamond, and West is squeezed in an unusual matrix. If he pitches a heart, the H Q drops the jack and the H 6 wins the last. If he pitches his diamond, declarer crosses to the H J to win the good diamond. This specific ending is not required to make 7 NT but is just one of various successful finishes.

If West leads a major, the play is easier. North wins the S A and H A, then a club to the ace squeezes West, who must pitch a diamond to avoid losing three tricks at once; then the good diamonds finish him off. North also makes 7 NT, as the only difference could be a club lead, which squeezes West immediately.

The same optimal layout was submitted by Pavel Striz and Dan Dang.

Odd Man Out

Pavel Striz: I would prefer a solution with less than 25 HCP — I am not an odd person.

Entering these contests may suggest otherwise, but don’t worry. I used to be an odd person but not anymore! Thanks to diligent research I have graduated to nut case.

Puzzle 8K53   MainTop   The Three Trick Gainer

© 2011 Richard Pavlicek