[mpefritz]

Scoring: MP

6NT South, no interference

♠ T-3-6-Q
♣ K-5-6-2
♣ J-Q-A-3

??

---

Here's a MP hand from the other day. I have shown all 4 hands. There is a heart double squeeze line that works here for 7, but is it best when you play out the hand and find West with 5 spades or should you have tried for a diamond double (both of which might develop guard components against West)? Please state what cards you should play after the favorable club lie is found.

fritz

p.s. Extra Credit : Does your answer change if South has only small hearts (i.e. AK654) and is missing the QJT987?

p.p.s. Don't come looking to me for answers. I'm not quite sure what is best, although I have some thoughts.

[cnszsun]

After ♣K, ♣J to A, cash two top ♠ to find ♠ distribution, you must decide paly a double squeeze line or a compound squeeze line.
For double squeeze line: only assuming East has both ♦ K and Q, then you can cash ♥A (optional) and ♦A (necessary), run ♣ and ♠ winners, squeeze automatic happens. You can also assume East has more than 4 hearts, then you should cash ♥ honours rather than ♦ honours, double squeeze also works.
For compound squeeze: you lack entry return to dummy, so you have to depend on double guard squeeze, but you still have to guess which suit is split as you wish (East holds only one ♦ honour or only one ♥ honour), then cash another suit's honours before running long suit winners.
So, no matter which line you choose, playing sequence is the same. you must decide to cash ♥ honors or ♦ honor, then run ♣ and ♠ suit.
I believe i will cash ♥AK, then run ♣, east is possible to hold more ♥ and ♦ honours is more easy to be split. unfortunately, my choice will fail with the actual layout.

[inquiry]

If EAST/WEST would be so kind as to tell you how their red suits were split, this hand is laydown. There are five basic positions, all of which result in a successful squeeze.

Case I: west has 4+♥'s (major suit simple squeeze)
Case II: East has 4+♥'s (double squeeze, ♦ both suit)
Case III: ♥ 3-3, EAST with ♦KQ (double squeeze, ♥ both suit)
Case IV: ♥ 3-3, WEST with ♦KQ (simple ♠-♦ squeeze on WEST
Case V: ♥ 3-3, with ♦ top honors split between hands (compound quard squeeze)

Case I and III requires you to cash the ♦Ace before running all black winners
Case II, IV and V require you cash both ♥ honors before running black winners

This looks like 3 case to 2, suggesting cashing ♥ honors is best play, but are these five cases equal chance? ANd what clues can you get.

First thing, win ♣Ace and cash two top ♠s (not all three) throiwng something like a ♥ ad ♦s. East has to find a pitch, assume the uselss ♣. Did west give a suit preference signal in the ♠ suit? Next play a ♥ to your hand, and did anyone show a ♥ count you believe. The postiion will be...

---

IF your opponents are not trustworthy in their signals, all you know is that WEST began with 7 black cards to EAST's 5. This affects the odds. The odds for the five cases above (roughly) with the known black card split, will be

Case I West with 4+♥'s is only 15.6%
Case II East with 4+♥, is a whooping 46.1%
Case III ♥33, EAST with ♦KQ = 11.6%
Case IV ♥33, WEST wtih [DI[KQ = 6.3%
Case V, ♥ 33, ♦ honors split = 20% (all calculations estimates based upon 7-5 black suit splits).

So playing ♥ AK wins in case II, case IV and case V, this totals about 73%, while cashing ♦A wins in case I and III, or about 27%. Of course, you may not be willing to risk the slam for the guard squeeze in case V. I like playing "reliable" opponents on these hands, but without such a fortunate circumstance, I will play the ♥AK.

The quard squeeze ending (case V), btw looks like this on the next to last trick...

---

On the last ♣, EAST and south will throw ♦, but what is WEST to do? Not a ♥, or ♠ACE squeeze EAST in the red suit, not a ♠ or the small ♠ will be good, so he will throw the ♦Q. Now, the ♠ACE for a ♥ discard, and a ♦ hook. Note if you cash the ♠A before the last ♣ this ending will not work (west will have a defense, no matter what you do).

So on the given hand, sadly, I would probably go down, as I would be cashing two top ♥ if no other clues set me straight.

Ben

[mpefritz]

There is one more case:

West with 5=4=Hx=2 (note if 5=5=H=2 you will find out as you cash 2 top hearts, then diamond hook is a guarantee) as played under the proposed diamond double line.

In the 4 card ending West is reduced to 98=Q=H=void and must pitch something on the last club, while declarer keeps void=8=AJ=void.

The other question involved in this hand is whether or not you'd believe the diamond situation enough to hook the diamond at trick 12 when West pitches a diamond honor? I'm not sure I would - but would if in 7NT. There also seem to be restricted choice position against the heart honors (as well as diamond honors) that may sway your end game decision.

fritz

[inquiry]

mpefritz, on Feb 24 2004, 07:39 AM, said:

There is one more case:

West with 5=4=Hx=2 (note if 5=5=H=2 you will find out as you cash 2 top hearts, then diamond hook is a guarantee) as played under the proposed diamond double line.

In the 4 card ending West is reduced to 98=Q=H=void and must pitch something on the last club, while declarer keeps void=8=AJ=void. 

The other question involved in this hand is whether or not you'd believe the diamond situation enough to hook the diamond at trick 12 when West pitches a diamond honor?  I'm not sure I would - but would if in 7NT.  There also seem to be restricted choice position against the heart honors (as well as diamond honors) that may sway your end game decision.

fritz

If west has 4♥, the ♦ honor is inconsequential. If WEST has both, he is three suit squeezed, and you can't go wrong, if they are split or EAST has both, no problem either, this reduces to a ♠-♥ simple squeeze (east can have only two ♥). Similar agruement goes if EAST has 4♥, it doesn't matter who has the ♦ honors, if they split, it is a double squeeze, if EAST has the both of them, you have a red suit simple squeeze against EAST played as a double squeeze (but really the ♠ threat is inconsequential).

So there is no need for a case where WEST has 4 ♥ and a minor honor. For simplicity, there really is no need to consider the hand where WEST has specifically T98xx QJxx KQ Qx... because you really can't misplay.

The next question is rather you would risk the ♦ hook at matchpoint in 6NT in one of the following two endings (if no, you lose one of the working cases... the quard squeeze)..

West
5S-2H-DKQxx-CQx, versus
5S-3H-DQxx-CQx

AT imps the answer is a clear no, I would not risk my slam for the hooked needed for the quard squeeze. At matchpoints I risk my contracts frequently, and restricted choice and other odds favor going for the guard squeeze. You already mentioned the restricted choice favoring the hook. And secondly, in a fairly good game, many will play for one of the double squeeze and some will guess right, but few can manage to remember NOT to cash the last ♠free winner before the last club (necessary for the quard squeeze). So if you happen to catch the quard squeeze position with 3-3 ♥ you are likely to get a top or be tied with a very small group for a top. Unless it is a truely expert game if the guard squeeze is the one working, experience suggest you will get 10.5 to 12 on a 12 top going for it.

I am a little confused by your 55H2 hand.. (giving west, say...)

---

If I cash two rounds of hearts, and discover WEST had five, there is nolonger a ♥-♠ squeeze on WEST, because of no entry to either hand in either threat suit (major). You suggest cashing the second heart discovers the bad split in time so that the "diamond hook is quaranteed", but that singleton ♦ will always stand in the way. Against such a distribution, you must cash your ♦A and keep a ♥ entry to hand...unless you are going back the guard squeeze again in that discussion. Where the ending would be (note same ending I showed earlier, except with "full and accurate count" also note, yet again, MUST CASH the ♣ winner, not the ♠winner in this four card ending (try it both ways to see why).

---

Anyway, the odds of when you can make still stand. If EAST has 4+♥, cash ♥AK. If WEST has 4+♥ cash ♦A, otherwise, if EAST has both ♦ honors, cash ♦A, if WEST has both ♦ honors, cash ♥AK, and if ♦ honors are split, cash ♥AK. This is just immutable mathematics. Figuring out which one exist is up to you, but the odds are stacked in the favor of cashing the ♥AK, just doesn't work on the actual double dummy layout.

ben

[mpefritz]

Ben,

Thanks for the analysis. I defended this hand in an minor tourney and everybody in some number of NT cashed the 3rd club at trick 4!?! I, however, never make a less than optimal play online

My 5=5=H=2 comment was only that if you play the (correct) line of cashing ♥AK you will make 7 on this shape also on the compound squeeze, without having to worry about whether West started with KQ of diamonds (complete count known). I was only trying to mention a case where West had 4+ hearts and showed up with a diamond honor where you'd be 100% sure the hook was going to win (once you cash the club at trick 10).

In cases where West pitches a diamond honor at trick 10, and the full count isn't known, the diamond hook does seem somewhat dicey as you have already beaten all pairs in 6C and NT less than 6. Both red suit's discards may give conflicting RC information. Just my thoughts.

thanks again,

fritz