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Which Squeeze 6 with "Solution"
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This is the followup to the problem posed here.

North
A7654
4
K1075
QJ3
South
KQ109
AKQ97
A4
A2
W
N
E
S
2
P
2
P
2NT
P
3
P
4
P
4NT
P
5
P
5
P
6
P
6
P
P
P

Matchpoints.  10 led to Jack, King, Ace.  East shows out on the K, how do you play?

North
A7654
4
K1075
QJ3
South
KQ109
AKQ97
A4
A2
W
N
E
S
2
P
2
P
2NT
P
3
P
4
P
4NT
P
5
P
5
P
6
P
6
P
P
P

Clearly the aim is to make 7.  And, it should also be pretty clear that our main threat is to establish the long heart with one ruff.  So, the "which squeeze?" question is about contingency planning for a 5-2 (or worse) heart break.

One excellent line, advocated for in the comments by Richard Pavlicek, is the compound squeeze line.  Take 2 hearts (not 3!) pitching a diamond, ruff a heart.  This will confirm the heart distribution and put us in a "post" compound ending.  I say "post" because in the presumed ending East has already been squeezed twice, but we are only now taking stock to choose which double squeeze to finish with.  It will look like this, with the lead in North:

North
K107
Q3
South
Q9
A4
2

(If West showed up with 4 spades and 5 hearts, I don't see anything better than playing them for QJ(x) as well and playing Q)

East will be proved to have 2 remaining hearts and thus at most 3 remaining minor suit cards.  This means they can't stop both minors.  To prepare for a double squeeze, keep dummy's winner in the suit East still stops and cash the other and then cross to A.  Somewhere along the way, East will be squeezed again, and then Q will squeeze West.  One possible way for this to play out, if East unguarded diamonds would go like this:

West
J98
98
North
K107
Q3
East
J10
Q
76
South
Q9
A4
2
W
N
E
S
P
6
P
P
P
D
6 West
NS: 0 EW: 0
K
Q
4
8
1
1
0
7
6
A
9
3
2
0
Q
8
10
10
3
3
0
2
9
Q
7
1
4
0
3
5

In practice, this should be easy at the table.  East will have made 4 discards, and perhaps even more revealingly, West will have made one too (aside:  otherworldly compound squeeze defense requires West to unguard a minor asap, at least some of the time). 

But, consistent with the theme of the "which squeeze?" series, we must look for alternative squeezes that may be as good or better.  Suppose East discards 2 in each minor.  This is probably not from an original 0=5=4=4 as it gives up both stoppers, instead it rates to be from 5-3 in the minors one way or the other.  Without trying to read too much into the lead, or the choice to cover at trick one, if you observe this, it is more likely to be from 5 clubs than from 5 diamonds, which means the compound squeeze line requires the K next, as shown in the last diagram.  

However, the last diagram also points to another possibility.  It is not necessary to complete a double squeeze with the E/W cards as shown.  If East has discarded to this ending, we can also just pick up the diamonds with a finesse.

West
J98
98
North
K107
Q3
East
J10
Q
76
South
Q9
A4
2
D

If East has discarded to this ending, we can also just pick up the diamonds with a finesse.

This suggests an alternative:  the guard squeeze.  If there's still ambiguity about which minor East stops, you can defer the decision by cashing Q regardless, then A to reach this powerful ending:

North
K10
3
South
Q9
4

None of this stuff is all that practical, but if I were to elevate one fancy squeeze ending to the practical division, it would be this.  A possible-tenace and a menace opposite a recessed menace and a link can handle almost anything.

In our present case, East is still known to have 2 hearts, and thus only one minor suit card.  If it's a diamond, then we're playing along the compound lines where we judged (correctly) that East released clubs.  The earlier Q play extracted a diamond from East, isolating the stopper with West (not that we needed to know this at the time: focus on the decision points, not the actual squeeze points), and now Q will squeeze West in the minors.  If instead East has a club, we've failed at the compound line, we should have kept Q (as an entry in the doubly-stopped threat suit) and cashed K instead.  However, if East was also dealt a diamond honor, we can just cash Q and take a diamond finesse.

There is almost no guessing here:  regardless of what we think is going on, we play Q and pitch the club unless it is good.  And then play a diamond (unless the 9 is good).  If West follows low, we finesse.  That last step is a guess, though. 

Another important way to reach this ending is when East pitches 3+ clubs on trumps.  In either line, we cash Q next.  If East follows to this, then they can no longer stop diamonds, but they may still stop clubs. 

Which of these lines is better?  I don't know, but here's part of it:

First, I'm assuming that if East pitches 3 or more clubs, everyone will cash out clubs and face the same ending.  Or if East pitches 2 plus diamonds including an honor, everyone will cash K, A and again face the same ending.  So, we're comparing scenarios where East pitches 2+ diamond spots and "compounders" cash out diamonds hoping for a double squeeze around clubs, and "guarders" cash Q and A hoping for a double squeeze around diamonds OR, when East retains a club stopper, a guard squeeze picked up with a diamond finesse at trick 12.

The guard squeeze line gains against unlikely shapes like 0562 and 0571 when East pitches 3 diamonds and compounders have mis-guessed.  Perhaps the cover at trick one makes these less unlikely?  It also gains against the more plausible 0553 if East pitches 2 from each minor and the compound line mis-guesses and cashes K, ending all hopes.  Given that we're contingency planning, that layout and defense is a material pickup, I think. 

On the other hand, 0535 is more likely, but guarders have compensation most of the time (at least a priori), i.e. as long as West doesn't have both diamond honors.  0535 where West does have both is the main pickup for compounders.  Exact odds would require assumptions about East's discarding strategy, but this would tend to favor compounders, probably quite materially, as East will in practice never pitch 2+ diamonds from Qxx but frequently will from xxx.

And there's still one final catch.  If East started with something like -/Jxxxx/QJxx/Kxxx and has the foresight to pitch 2 diamonds and 2 clubs, the compound line will drop the diamond honors and get home easily, while the guard line will lose a finesse at trick 12, and to add additional insult, go down.  Without knowledge of South's 5th heart, though, this is an impossible defense.  

 

My bottom line:  in problems like these, the guard squeeze is often superior.  It has less stringent entry requirements (particularly useful when dealing with a psuedo-compound) and defers any guessing until very late in the play.  In this particular case, though, it seems about a toss-up, and I lean towards the compound.

Perhaps the problem would be better had East ducked at trick one.

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