[GaryFisch]

This hand was not actually played, but is an interesting exercise.

Scoring: IMP

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You reach 7NT played by North. The bidding is unimportant, but it might go like this:

South North

1♣  2♠
3♦  3♥
4♣  4NT (RKCB)
5♠  5NT (No. side K's)
6♥  7NT - All Pass

East leads a diamond. You win the A, cross to hand with a club, cash ONE spade, throwing a diamond from dummy (optional, but more than one would squeeze the dummy). You have 12 high card tricks, and the 13th can come in spades, hearts, or clubs, plus there are squeeze possibilities up the wazoo.

First, which entry do you use to the clubs?

Second, how do you continue if East shows out of on the third club? If West shows out?

Third, is there a 100% line?

In answer to the first question, it looks right to play the diamond now, keeping the finesse opportunity intact. However, the heart is the percentage play. To see why, let's do an analysis starting with the heart and then looking at the diamond play. If you want to skip the analysis, I offer an intuitive argument that you could use at the table, in real time, to find the best play.

Suppose you play a heart to the K. Assume all have followed low so far. You cash two more clubs, discarding spades from hand. If both follow, you have your 13th trick and can claim. So what happens if East shows out on the third club?

Let's say East throws a diamond. Cash the last high club, East throwing another diamond. Get back to hand with a heart and cash the third heart (if you haven't already done so). You succeed when either major is 3-3, or the ♥J falls, or East holds exactly 4 spades and 5 diamonds, when East is squeezed. You also succeed when East holds both red suits. West must guard both black suits, so will have to discard a diamond from 4-4-3-2, giving you a double squeeze, or you have a simple squeeze on East if East started with 5 diamonds. However, you fail if East holds length in both majors, or if East has 5 spades and 4 diamonds, as long as West holds the Q, J, or 9 (East discards a spade and 2 diamonds, and West keeps the third diamond behind dummy).

So far not looking so good for this line, but let's see what happens if West shows out on the third club. If East holds length in spades as well, he is squeezed in the black suits on the play of hearts. If East holds the long hearts and West the spades, either West is squeezed in spades and diamonds or there is a double squeeze. Say West started 5-2-4-2. West can throw a spade and a diamond on the clubs, but must discard another diamond on the third heart. Now cash a top spade. Poor East is squeezed in three suits. A heart or club is immediately fatal, so East discards a diamond, but now you come down to ♦K7 in the dummy. The 8 to the K pulls the remaining diamonds, and the ♦7 is the fulfilling trick.

If East holds length in both minors, then East is squeezed in the minors, which may in fact be a double squeeze (West must discard a diamond from 4-4-3-2). And again, you give up nothing if either major is 3-3 or the♥J falls. So the heart to the K is 100% certain if East has the long clubs.

Now, going back to the diamond line. How does this compare when East shows out of clubs? When West shows out?

Well, you certainly gain when East holds both majors, since you cash all of dummy's minor honors to squeeze East, and you don't lose if East has both reds either. You don't have any more squeezes, but when you cash out the black suits and see East throwing diamonds, you have near certainty that the heart finesse is working. You DO lose in the specific case of East holding 4-5 (or longer) ♠-♦, since you no longer have the entries to squeeze East in these suits. Overall, diamond to the K first works better if East has short clubs.

Now let's look at this second line when West has short clubs. Remember, the first line was 100% in this case. The second line, not so. You've lost the ability to play for the double squeeze, so all you have is the simple squeeze on West in the majors or in ♠-♦ and the regular breaks. This means that you will go down whenever West started with ♥-♦ and also when West started ♠-♦ as long as East has three diamonds, one of them being the Q, J, or 9.

So overall, while both lines have excellent chances of success, the heart line is slightly better.

Now for the intuitive argument. You should use the heart entry first, because the heart suit has a chance of producing the 13th trick on its own, while the diamond suit does not, and this chance isn't greatly reduced by giving up the heart finesse (the chance of the J falling is 50% a-priori). Therefore, when all the normal plays have been exhausted, you will need the diamond K as an entry so that dummy's threats - in hearts, clubs, AND diamonds, stay active as long as possible.

[Vilgan]

Fun hand. Harder part is figuring out what situations cause the squeeze to fail.

It seems like if east guards spades and west can guard diamonds (likely both can) and either hearts or clubs, the squeeze fails.

The other scenarios all lead to a successful squeeze I think. Of course if the J of hearts drops that makes life easy too.

Fun Hand

[xcurt]

GaryFisch, on Apr 23 2008, 03:00 PM, said:

So far not looking so good for this line, but let's see what happens if West shows out on the third club.  If East holds length in spades as well, he is squeezed in the black suits on the play of hearts.

I think I agree with playing DA, CA, HK, CKQJ, HAQ, SA, reducing to

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However, east has both black suits, you cannot squeeze him unless he needs to keep red card(s) since you have no entry in either thread suit.

Let's analyze this in more detail...

Since three of the suits can only be guarded by one opponent we can make the following payoff matrix, given that S are not 3-3, H are not 3-3, the HJ does not come down, and C are not 4-3, according to what east guards.

black suits: you cannot make this hand, no threat over west, who keeps --, J, xxx, --.

pointed suits (diamonds 7-2 or worse): east is positionally squeezed in the pointed suits

pointed suits (diamonds not 7-2 or worse): you cannot make this hand, no threat over west, who keeps --, J, xx, T.

major suits: oops, we needed to cross in diamonds, not hearts , east keeps Jxx, J, --, -- and west --, --, xxx, T. The OP indicated we make in this case, but we don't since we again have no entry in either thread suit. We can get to KQx, AQ, --, -- facing --, Txx, x, x but that's not good enough.

red suits (diamonds not 7-2 or worse): west has to keep Jxx, --, --, T, so we get to positionally squeeze east in the red suits anyway, now. Non-simultaneous double squeeze with an extended menace, nice

red suits (diamonds 7-2 or worse): east is positionally squeezed in the red suits

minor suits (diamonds not 7-2 or worse): we needed to cross in diamonds, not hearts allowing us to squeeze west in the majors

minor suits (diamonds 7-2 or worse): east is positionally squeezed in the minor suits

Hands where east has three guards are not material to this analysis. East cannot have the major suit guards and the club guard since he led a diamond. East cannot have the only diamond guard and two other guards since that implies a 15-card hand.

Ignoring the possibility of using the HT8 to force a 4th heart trick on power, we go down when we might have made when east has 44,+ in the majors including the HJ, and when east has 3-6 diamonds and 5+ clubs, and 2 or fewer hearts, and 2 or fewer spades, and no HJ.

Good analysis. I might try to do the payoff matrix for the other line later, but one is enought for now.

What's the slow play penalty in this event?

[inquiry]

You have four squeeze suits, but your entry conditons are horrid.

As far as the threats

• only one opponent can stop spades (if suit is not 3-3)
  
• only one person can stop hearts (if suit is not 3-3, and the Jack can be hooked if with East)
  
• Only one person can stop clubs (if suit is 5-2 or worse)
  
• Both may stop diamonds, and for possible quard squeeze the diamond spots in diamonds are foul. I would love to trade the 7 for the 8.
  
  The entry conditions are damn hurtful for most of the simple squeeze.
  
  For instance, there is no simple RED suit squeeze on West even if he has long diamonds or all the diamond spots, as he is behind both threats.
  
  There is no Club-heart or club-diamond squeeze on West either, for the same reason. Even if West has the C-D-H stopper, he can not be three suit squeezed, becasue he is once again, behind all three threat cards.
  
  Likewise, there is no CLUB-Spade simple squeeze on anyone as neither threat suit has an entry into its own suit.
  
  Nor can there be a Diamond-Spade on West unless the last squeeze card is the heart Q. In fact the simple squeezes taht work are fairly few. However, should you have a ♦-♠ type ending on West, that means in theory you have a simple heart hook on East or a club-heart squeeze on East.
  
  Also an unlikely D-Heart on East (but then the heart hook works), A spade-heart squeeze on East, but then the heart hook works.
  
  Squeeze on West all have to include spades. And it works out that if West has to keep four spades, All the five card endings resullt in death for his partner. Imagine his last five cards...
  
  West (hand behind the spade void)
  ♠JT98 ♥J == a major suit simple squeeze if you kept heart entry to dummy. This one might be hard to read, but you will get it right per force.
  sp]JT98 ♦J == his partner is squeeze in hearts/clubs, of you kept a heart entry
  sp]JT98 [ck]T == his partner is red suit squeezed, which ever red entry you kept
  
  So you will always make when West has four spades, as long as you keep the heart king as an entry. Your last five cards are 4♠ and a red suit with entry opposite it. Of course, you also always make if spades are 3-3 (trivial case).
  
  Since the winning cases where WEST held four spades all started using the diamond as early enty, let's imagine that it is East has the four spades. Here things are not as bright.. His last four cards could be...
  
  ♠JT98 ♥J ==you make as long as you kept heart king as entry
  ♠JT98 ♦J = you are doomed** if ♥J hasn't fallen and ♥ are not 3-3
  ♠JT98 [ck]T = you are doomed if ♥J hasn't fallen and ♥ are not 3-3
  
  **NOTE: If EAST held four spades and five plus diamonds you could make by preserving a diamond entry and using up your heart entry. This is the only time the alternative line of diamond early "wins out over" low diamond. Also see evidence belwo that when east is long in both black suits, you do not make if hearts are sour, despite comments by others.
  
  Also, even if EAST has four spades, if he also has four clubs, and four hearts, starting diamonds will squeeze him (3 suits), but if he has 4D. 5C, and 4S, starting hearts wll not, as he can throw away three diamonds, if you try to cash teh last diamond you cut off yoru entiries...
  
  
  What this means, and what you should be able to see quickly is:
  
  [list]
  
• No S-C simple squeeze on anyone due to lack of entries in either threat suit.
  
• Very small chance of spade-diamond simple squeeze on anyone, someone needs five diamonds, or the QJ9 third or fourth.
  
• All double squeezes require West to have spades, and these reduce to simple squeezes almost immediately (see above).
  
• Any double squeeze with East having spades fails because no threat card "over" West.

So to answer the original questions, I don't care who is long or short in clubs, it is spades I worry about. There is no 100% line. I prefer to preserve the heart entry and to use the diamond entry. Preserving the heart entry works 100% of the time WEST quards spades, and when EAST quards spades and hearts (failing when the hand can be made only when EAST quards spades and diamomnds). Preserving the diamond entry fails when WEST stops both majors, and fails when EAST quards spades and hearts.

Note, the question about what to do when East or West has clubs is really non-material. The key suit here is spades because it MUST be a threat suit against West or you have no way to "squeeze" him. If you focus on the spade suit, the sequence of plays is much easier to unravel. Far easy to unravel than to try to explain.

=======================================

Let me address some of the comments by GaryFisch, the original poster, who reached a different conclusion that I did. He tried to explain using the heart king as a trick three entry to the clubs as the "percentage play" using a West unlikely 4♠ and 5♦ to "intuitively" argue that the "precentage" play, using the heart entry to dummy so you could execute a spade-diamond squeeze on EAST (and also gain perhaps by dropping the jack of hearts).

Here he overlooked the obvious. If EAST has 4♠ and 5♦, then the slam is cold if you perserve the heart king. If he has 4♣, the hand is laydown, if he has 4♥ the spade=heart squeeze works as well as the spade-diamond. In fact, West is under the gun of a three suit repeating squeeze, when you only need one extra trick!!!

GaryFisch fiurther stated that low to the heart king was a 100% line when "west' was short in clubs. This is demonstratable untrue. Let's imagine west holds, for instance. short clbus and short spades. Gary Glibbly announces "then if West shows out on the third club. If East holds length in spades as well, he is squeezed in the black suits on the play of hearts."

While this is true, the entry conditions are fatal to the squeeze. Lets see how this fails...

Here when you cash your top two hearts to "squeeze" east in the black suits, he throws his diamond. Now whenever you play a diamond to king, he can throw a spade and collect his club trick. nOTE HEART TO THE KING EARLY HERE ALSO FAILS

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He ALSO gave the following "intuitive" explaination for why a heart is better than a spade..

Quote

Now for the intuitive argument. You should use the heart entry first, because the heart suit has a chance of producing the 13th trick on its own, while the diamond suit does not, and this chance isn't greatly reduced by giving up the heart finesse (the chance of the J falling is 50% a-priori). Therefore, when all the normal plays have been exhausted, you will need the diamond K as an entry so that dummy's threats - in hearts, clubs, AND diamonds, stay active as long as possible.

Let's shoot intuitive down? If hearts are 3-3 or the jack is falling, you don't have to play them at trick three to take advantage of that fact. Second, having a random diamond entry to the "heart, club, AND diamonds threat is of use only if diamond is the threat card. What I mean is a diamond entry to the heart threat or the club threat is, well, useless, as those are the failing cases (without a valid diamond threat). Simple squeezes require an entry in their own threat suit (or in the case of a criss-cross simple, each threat suit has an entry in the threat suit of the other hand). So saving the diamond entry only works when diamond is one of the threat cards. By starting with the heart, you fail anytime a heart/spade squeeze would have worked against either opponent. By starting diamond, you fail only when you have a diamond/spade squeeze against EAST. Starting diamonds will also work if EAST has spades, hearts, and clubs, but that is redundant, starting hearts there will not.

Gary;s proofs were hard for me to follow, maybe I got lost because they kept jumpting around to the odds of droping and honor or a suit splitting three-three. These endings seem much easier to analyse by hand type, entry conditions, etc. Accepting that if clubs run, spades run, heart run, or heart jack drops, then the slam makes.

This type of analsyis will frequently suggest keeping a suit like diamonds as a double threat suit. But with three threat suits in teh same hand, there is a huge tradeoff. The finessee position in hearts, make keeping heart entry at least twice as good as keeping the diamond entry (when you throw out all the hands on which either line works).

[suokko]

Here is 2 possible lines after ♦ lead.

1st:
♣A
♦K
♣K
♣Q
♣J
♥A
♥Q
and then running ♠ in ending

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2nd
♣A
♥A
♥K
♣K
♣Q
♣J
♥Q
and again run spades in ending

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2nd line is clearly superior because you have a lot higher chance to win the last trick with ♦7 (When ever there is double squeeze).

For per cents. First line wins because it allows squeeze against LHO when she holds both majors at least 4-4 while 2nd line allows squeeze only if LHO is 4=2=5=2 (or similar). In all other cases both lines will make or fail only depend on opponents cards.

PDF file includes squeeze details. It assumes that HJ is in 4 card suit (naturaly)

[inquiry]

suokko, on Apr 24 2008, 07:26 AM, said:

2nd line is clearly superior because you have a lot higher chance to win the last trick with ♦7 (When ever there is double squeeze).

For per cents. First line wins because it allows squeeze against LHO when she holds both majors at least 4-4 while 2nd line allows squeeze only if LHO is 4=2=5=2 (or similar). In all other cases both lines will make or fail only depend on opponents cards.

PDF file includes squeeze details. It assumes that HJ is in 4 card suit (naturaly)

You suggest that line 2 is superior because it gives you a chance to make the diamond 7 when WEST has spades and EAST guards either clubs or hearts (both stop diamonds). In fact, if WEST has spades, line one works 100% of the time without need for double squeeze. To see why, lets look at hands where EAST stops clubs, and hands where EAST stops hearts.

For these examples, 4=4=4=1 would mean precisely one club, but 4=4=1=4 would be precisely one diamond, 1=4=7=1 would be precisely 1 spade, 4 hearts, 7 diamonds and 1 club. Anyone with 4 hearts will always have the jack to prevent the hand from being the trivial case.

WEST
4=4=3=2 Line two double squeeze works, but so does line one. For line one, WEST is subjected to a heart/spade simple squeeze. No advantage either line

WEST
4=4=4=1. Line one is again a major suit simple squeeze, line two still works as a double squeeze.

WEST
4=2=5=2 Line two is no longer a double squeeze, but it does revert to a simple ♠-♦ squeeze on WEST and works. While line one works without worrying about WEST since it results in a ♣-♥ simple squeeze on EAST (east has to be 2-4-2-5)

WEST
6=2=3=2 Line two works, because EAST is squeeze in three suits (hearts, clubs and diamonds). Line one also works because of the same squeeze (it is a simple heart/club on EAST)

WEST
4-0-4-5, Line two works (because you cashed high heart first) as it exposes the heart finessee. Line two works because the heart finessee is easily found after WEST shows up with four spades five clubs and at least two hearts.

WEST
4=1=3=5 Line two works even though it is too to take the heart finesse after the distribution is discovered because the double squeeze works (you can ignore clubs), but again, line one also works, since WEST will show up with five clubs and four spades and at least two diamonds, the heart hook is 100%.

WEST
4=1=2=5 Line two works, as EAST is squeezed in the red suits, line one works on a squeeze or a finesse of EAST.

WEST
4=4=0=5 I guess this one doesnt exist, as the void would have been discovered at trick one. But, if it did, the squeeze would not work as you would need the heart entry to squeeze WEST, the diamond would do no good.

WEST
4=5=2=2 Either line works. If you start with the diamond (line one) you end up with a major suit simple squeeze on WEST, if you start with a heart, you end up with a minor suit simple squeeze on EAST.

Thus, anytime WEST has spades, either line works. This voids the argument that line 2 is superior because of the double squeeze threat.

The problems arise when EAST has four spades. Here are the shapes of interest. The bold number shows which lines works... a happy face, means that line works, a sad face, that line does not.

WEST
0/2=4+=5+=0/2 Line 1 , Line 2
2=2=4=5 Line 1 maybe on heart play , Line 2
2=1=4=6 Line 1 , Line 2
2=1=5=5 Line 1 , Line 2
1=4=3=5 Line 1 , Line 2
2=0=5=6 Line 1 , Line 2 (but only suokko's improved cash one heart before heart to king)
2=0=6=5 Line 1 , Line 2 (but only suokko's improved cash one heart before heart to king)
0/2=4+=0/2=5+ Line 1 , Line 2 (a spade - diamond simple on EAST)