Squeeze endings Larry Hammick larry@hammick.com ;;;;;;;;;; from 2001.03.01 Contents ;Introduction ;Notation ;Terminology of squeeze play ;Rectifying the count ;Squeeze assets ;Vienna coup ;Transferring the guard ;Simple squeezes Z ;;Automatic twin-entry squeeze ;;Showup squeeze ;;Simple squeeze with split menace ;;No-loser simple squeezes ;;Crisscross squeeze ;;Trump squeeze ;Secondary simple squeezes ;;First kind of secondary squeeze: congestion ;;Second kind of secondary squeeze: demotion ;;Third kind of secondary squeeze: busy loser ;;Unblocking against secondary simple squeezes ;Double squeezes and their relatives ;;Double squeezes Y ;;Either-Or squeezes (at single dummy) ;;Reciprocal squeezes R ;;Guard squeezes G ;;Compound squeezes ;;No-loser double squeeze ;Triple squeezes and progressive squeezes ;;2-loser varieties T ;;Defending 2-loser varieties ;;1-loser varieties ;;Three menaces at the table ;Clash squeezes ;Squeeze throw-ins E ;;Throw-ins ;;Simple squeeze throw-ins ;Stepping-stone and winkle squeezes B ;Specialized menaces ;;Pinning menaces X ;;Vice menace V ;;Two-trick menaces ;;Unblockable menaces ;Control pressure, or mock-squeezes ;Unclassified endings ;;See-saw squeeze ;;Overtaking trump squeeze ;;Backwash (trump) squeeze ;;One-suit squeeze ;Introduction This article describes all the commoner squeeze endings, and looks for general formulas which describe them all. The analysis is mostly of a double-dummy nature; we don't have much to say here about the diagnosis and planning of squeezes at the table. For most of the uncomplicated squeeze types, exhaustive tables of the variations have been worked out by other writers. These tables are included, slightly tidied up in some places. Only one or two new positions appear. The other aim of this article is to help isolate the constituents from which all squeezes are built. As more and more varieties of squeeze play have been discovered, the practice has been to give each one a name: see-saw squeeze, winkle squeeze, pinning squeeze, etc. But the assets and liabilities that make up any squeeze can combine in such a great variety of ways, that we will aim to analyse the constituents and try to find formulas describing how those can add up to a trick, rather than just enumerate positions and give each one a name. To this end, several new ideas appear in this article, including: 1. An intelligible analysis of the different ways in which a squeeze can function (or fail to function) "without the count". 2. The notion of a pseudomenace, which clearly distinguishes a squeeze throw-in from a squeeze proper. 3. The 4-item formula for double squeezes and related types. 4. The generalization "strong menace", with an explanation from basic principles of how it makes possible such things as a squeeze against both defenders in the same two suits. Not new, but worth repeating, is a set of arguments against regarding the "squeeze card" as something fundamental. It is said that most squeezes, since they rarely occur at the table, are of little interest to the practical player. But how many practical bridge players do you know? We all play the game because it is interesting, and squeeze theory is (I hope you agree) interesting. ;Notation When we diagram a hand in several rows, one above the other, the highest row is spades, the next highest hearts, then (if more than two rows) diamonds, then clubs. The letters CDHS refer to the four suits. "HK" for example, is the king of hearts, and "ST" the ten of spades. When we say "South plays off DKA" it means he plays off the diamond king, then the diamond ace. When we speak of declarer and dummy, that means South and North, as usual, but that is only for convenience of language; the ananlysis is of the double-dummy or post-mortem kind, unless we explicitly say "at the table" or the like. ;Terminology of squeeze play Here are two endings to help illustrate the terminology. Z1 AJ Z2 AJ K - - 2 KQ KQ A A - - x x x K A A South leads DA. North leads D2. Menace (or "Threat card"): Any of the constituent non-winners in a squeeze. In the above endings, SJ and HK are menaces. Guard: A holding which prevents, temporarily at least, one of the menaces from taking a trick; in the above endings SKQ and HA are guards. Entry menace: A menace accompanied by a winner which faces at least one small card (so that the winner might serve as an entry). SJ above is an entry menace. Single menace: A menace other than an entry menace. HK is a single menace above. Squeeze card: The card (normally a winner held by declarer or dummy) on which a defender has to choose one of two or more costly discards. DA (not D2) above. Idle card: Any card which can be discarded at no cost. Positional squeeze: A squeeze which, like Z1 above, can operate against one opponent but not the other. In Z1, if East's and West's hands were swapped, the squeeze would not function. Automatic squeeze: A squeeze which, like Z2, works equally against either defender (whichever guards the menaces), or (if both are involved) works whenever their two hands are interchanged. Simple squeeze: A squeeze in two suits against one opponent, i.e. a squeeze which uses menaces in only two suits, both of which are guarded by the same opponent. Some writers say "simple squeeze" where we say "positional squeeze". Z1 and Z2 illustrate two quite different principles on which squeezes function. In the positional Z1, third hand has the same length in each suit as the squeezed defender. In fact, third hand is squeezed as well as second hand, but the defender is handicapped in that he must choose his discard first. In such cases, third hand tends to discard from some suit which the defender _kept_. Automatic squeezes like Z2 exploit the fact that declarer has mismatching length in his two hands, and a defender has not enough cards to match the length of _both_ enemy hands. In an automatic squeeze, if third hand cannot follow suit to the squeeze card, then declarer knows what he will discard on it irrespective of second hand's play. It is therefore convenient, in discussing automatic squeezes, to omit the squeeze card and third hand's card from the diagrams, and to use instead what is called a "squeezed position". Thus Z2 could be abbreviated to: Z3 AJ - KQ A x K Squeezed position by South. The tradition is to regard two positions as distinct when the only difference between them is in the location of the squeeze card. In this respect, the old notion of squeeze card can complicate, rather than simplify, the study. This is especially true of automatic endings. If, at the table, you think in terms of what cards you will come down to, and which hand you will be in, then you will have fewer positions to remember and you won't need to know on which trick the squeeze occurs. The general notions used in the study of squeezes, like so many other general principles in bridge, break down and require modification in advanced cases. For example, the squeeze card need not be a winner; it may be a loser, or even a card led by an opponent. There are squeeze endings in which no single squeeze card can be identified. There are variations in which the entries and positional factors are different from the norm, but declarer has compensation of some sort. The card that gets wrung from a defender need not be a winner (or a card which protects, say, a king) but a necessary exit card; or it may be a card whose loss creates an entry rather than a trick for the declarer. It may be a loser which, when discarded, gives declarer a count of the suit and thus enables him to drop an honour in the other defender's hand. There are various hybrids of squeeze endings and throw-ins. And so on and so on. ;Rectifying the count The commoner squeezes usually will not function until declarer is in a position to take all the remaining tricks but one. In this majority of cases, until that condition is met, the defender will have an idle card. Therefore, declarer will often go out of his way to concede inevitable losers until he can take all but one of the remaining tricks. But this all-but-one rule is not always accurate. It doesn't matter how many losers declarer has; the squeeze card produces a trick if and only if the defender has no idle cards. We will later discuss three different ways for that to be the case when declarer has more than one loser. The purpose of rectifying the count is to remove idle cards from a defender's hand, not to get rid of one's own losers. Indeed, when declarer plays off several winners in succession, ending with the squeeze card, he is simply removing the defender's idle cards. When the idle cards run out, the squeeze clicks in. ;Squeeze assets The assets which comprise any squeeze are traditionally listed something like this: -- At least two menaces (suitably positioned, in some cases), including at least one entry menace -- A squeeze card (assumed to be a winner) -- Necessary entries, including at least one entry opposite the squeeze card -- Timing (i.e. a rectified loser count of one) In the more advanced endings the ingredients are less simple, but we can still speak of three kinds of asset: Menaces Communication to the menaces Timing There are three basic kinds of menace: 1. An almost-high card, guarded by one or more enemy high cards. 2. A small card which, by reason of length in the suit, needs to be guarded. 3. A ruffing menace, i.e. two small cards facing a ruffer. When dummy goes down and declarer counts his tricks, he notices the first kind and thinks about leading toward them: AQx or Axx xxx Qxx But such almost-high cards may also be useful in a squeeze or throw- in, or a combination of the two. As for the second kind, a long card might get established by itself if neither opponent can cover it: Axxx Kxx But if one opponent can cover it: Axxx Kx a second menace is required, guarded by the same defender. If both can cover it: Axx xx there may yet be a squeeze if two other menaces are available, one against each opponent. A guard behind a menace tends to be more valuable than one in front of it, because then the hand with the guard will be discarding first. When a menace is behind the guard, the menace is described as "well- placed" or the like, and the guard as "unfavourably placed", and vice versa when the menace is under the guard. ;Vienna coup Consider this ending: AJ A x - KQ x Kx Jx - A - - x Qx - A South is on lead. If declarer had played off HA ealier, he could cash CA, throwing North's diamond, and take the balance by means of an automatic squeeze. But as it is, if South cashes CA, West can throw his small heart; this establishes the Q, but the Q cannot get cashed owing to blockage. The playing off of a winner opposite a single menace, to avoid such blockage in the endgame, is called the Vienna Coup, after a double-dummy Whist problem of the 1800's. ;Transferring the guard We will have occasion to mention this technique later. AKx A9x Qxx Txx Qxx Txx J9x KJx If West is known to have the Q, or if declarer can only squeeze East, South can lead the J, forcing a cover, and winning in the North hand. This establishes the 9 as a menace against East. QTx Ax North leads the Q, forcing a cover, and hopes that West has the J. QTx A Declarer cashes the ace and later leads the Q, to be covered and ruffed. If entries are a little short for that move, you can try leading the Q toward the bare ace in the closed hand! ;Simple squeezes A "simple squeeze" is a squeeze in two suits against one opponent. Z1 and Z2 above are the commonest endings, but there are several others. ;;Automatic twin-entry squeeze Z4 A9x - QJT A Kx K Squeezed position by North. (If by South, this reduces to Z3). Here the single menace is under the guard and is in the hand opposite the squeeze card. But this automatic squeeze still functions because of a compensating extra entry in the form of a "twin entry menace". Since declarer may always continue with a spade to the king, Z4 and Z3 are in a sense the same. The automatic simple squeeze is commoner than the positional and easier to play. Declarer needs to watch only for the discard of cards higher than his single menace. If the single menace is not a winner by trick 11, he takes (in this example), K then A of spades and hopes that the last spade is good. ;;Showup squeeze AQ K - xx - A South is on lead. At double-dummy this would not be a squeeze at all. But let's suppose West is marked with the master heart, perhaps because East has shown out of hearts. The DA brings something other than HA from West, and HK is discarded. When West follows to the next trick, declarer knows that he must go up with the ace, since West's last card is a heart. The showup squeeze occurs at the table relatively often, sometimes smoking out an offside singleton K or doubleton Q. It exemplifies how pressure can extract _information_ rather than an outright trick. Some writers call this a "count squeeze" if the finesse is off and a "showup squeeze" if it is on, but the distinction seems unimportant. ;;Simple squeeze with split menace Ax The squeeze card is DA. SAx is not an entry K menace in that both defenders may guard it. But - with Qx opposite it constitutes a menace against Kx West's king. Since a split menace occupies two A cards in each hand, a single menace must be - opposite the squeeze card; therefore, a 1-loser Qx squeeze which depends on a split menace cannot be - automatic. A ;;No-loser simple squeezes Even when declarer has enough winners for all the remaining tricks, blockage may necessitate a squeeze. J1 AT J2 AT J3 A K - Kx - - - QJ QJ QJ A A A - - - K K KT x K - A - A South leads DA. Squeezed position South leads DA. by either hand. J1 is only trivially different from Z1, in that it plays just as if SK were a loser. J2 is likewise the same as Z2 except that it now works even if the lead is with North. In J3, called the "jettison squeeze", if West throws a spade, SA is discarded and the South hand runs, while if West throws HA, a heart is discarded and the North hand runs. ;;Crisscross squeeze Qx Jx A A Kx KQ Kx KQ A A Qx Jx Squeezed positions by either hand. Declarer takes the remaining tricks, provided that he can read which suit has been unguarded. This infrequent ending is an odd one in that there is no entry menace of the usual form, nor any single menace. Off the topic, the crisscross squeeze is not the only case in which a player can overcome blockage in one suit by deliberately blocking another suit. Example: Txxx AKx ATx xxxx KTx A AKx xxxxx North lead HK against 3NT. West takes the second round, South following. West now ducks a club and has 9 tricks whenever clubs are 3-2. He cannot afford to play off CAK first. For more on this topic, see the article about the "crisscross duck" at hammick.com. ;;Trump squeeze The trump squeeze is like a crisscross squeeze, and likewise automatic, but uses a blocked menace in only one hand, and a "ruffing menace" in the other. A ruffing menace is a pair of losers of which one might get established by ruffing. - - KQ KQ AK A - - - - Ax Ax Qxx Kx - - x (trumps) x (trumps) - - Jxx Qx - - Squeezed position Squeezed position by South. by North. The trump squeeze is usually diagrammed as on the left. If the defender bares his HA, it is ruffed out and HK cashed; for this, two entries are needed to the hand opposite the last trump. Since South will continue with a diamond to dummy irrespective of what the defender discards, we may use the simpler diagram on the right. One entry will be in the blocked suit; the other is normally in the blocked suit or the "fourth" suit, but may be anywhere: -- A Ax A AQT KQ -- -- -- -- Kx Kx KJx Ax -- -- xx (trumps) xx (trumps) Qx Qx x -- -- -- Declarer leads a trump and, at left, discards dummy's small heart. Although the trump squeeze is automatic, it is seldom used except against the player sitting under the long trump hand, most often declarer's right-hand opponent. The reason is that that defender would, in commoner squeezes, have the advantage of playing fourth hand to the squeeze card if, as is usual, the squeeze card is a trump. A rare variant of the trump squeeze uses two single menaces instead of one ruffing menace. (It is not strictly a simple squeeze.) - - K Kx K Kx A Ax - - A Ax A Ax Kx KQJ x (trumps) x (trumps) - x - x Qx Txx Squeezed positions by either hand. The variation at right shows that the squeeze is still feasible with an additional loser in any side suit, or any several side suits. Only one entry (the one in the blocked suit) is needed. Another rare variation, known as a "scissors movement", uses no blocked menace at all, but a ruffing menace in each hand. x x Axx AKxx x x x x - - - - xx KQJ xx QJT9 xx KQJ xx KQJ Ax - Axx - xx xx x x Axx Axxx - - Spades are trumps and North is on lead in these two diagrams. At left, declarer has 5 of the last 6 tricks, and might hope to establish a long card in the course of the crossruff. However, East controls both hearts and diamonds. At right, declarer has 6 of the last 7. This time East does not guard the long diamond, but with only one trump in dummy, declarer would need to lose a diamond before he could score his long card. In both positions the winning play is to ruff dummy's club! East is squeezed by this seemingly unconstructive move. The squeeze may occur on the play of a winner in the "fourth" suit, and also works in a crisscross configuration: x xxx A - - KQJ KQJ - x (trumps) A xxx - Squeezed position by either hand But a 2-loser variant of the scissors movement can, in general, be defended; by leading the "fourth" suit, the defence can compel declarer to use up a ruffer without helping to establish either of his side suits. x x Axx AKxx x x x x - - - - x KQJ xx QJT9 x KQJ x KQJ Axxx - Axxx - x x x xx Axx Axxx x - At left, declarer has 4 of the last 6. Hoping for a squeeze, he leads out his club loser, on which East discards (say) a heart. West wins and leads back another club, on which East discards a diamond. Whichever hand declarer ruffs in, he still has only four tricks. At right, likewise, declarer leads dummy's club and discards a heart while East weakens either of his suits. West leads back another club and East weakens the other suit. Declarer still has only five tricks. ;Secondary simple squeezes ;;First kind: congestion There is no exact agreement on the use of the term "secondary squeeze", but, for us, it is any ending in which a trick is lost after a squeeze occurs. When attempting a squeeze in two suits, more than one loser is a defect of _control_. Compensation, of a control nature, which allows the squeeze to function anyway, may exist in several forms. The first possibility is that the squeezed defender is the only one who can cover declarer's additional losers. Since anything he throws _promotes_ one of declarer's cards -- though not necessarily to winning rank -- he has no idle cards. Below are a few illustrations of this "congested" or "first kind" secondary squeeze. AJ Kx Qx AKx - - KQ Ax AK QJT9 - - xx - x xxxx A x (trumps) South leads DA. Squeezed position by either hand. A A9x AJ Txx x xx KQ QJT KQ KQJ AK KQJ Jx Kx x Ax QJ ATx Three squeezed positions by either hand. In all the above cases, the defender may hold a side winner instead of a second heart trick. But he may not hold a loser opposite a winner in his partner's hand, unless we also put restrictions on that hand. Declarer needs a little extra communication to any hand containing a menace against which the defender has two guards (hearts, in these diagrams). And lastly, there is a restriction on declarer's control: ATx On DA, West throws a heart, promoting South's 9. xxx Declarer ducks a heart, but West establishes two x spade tricks, and will also get two hearts KQJ before declarer can cash H9. That leaves declarer KQJT only the three tricks that he started with. - xx A9xx A The control formula for congested squeezes seems to be this: Declarer needs at least as many winners (including the squeeze card) as losers in the two suits. At the table, the declarer usually cannot tell that the defender to be squeezed is also saddled with some other high card for which his partner has no equivalent. Since that is usually not the case, it is advisable of rectify the count whenever one's control permits it. ;;Second kind: demotion L1) KT L2) KT K - - x QJ Axx QJ Axx A - A - - - - - x x x K A A South leads DA. South leads DA. A squeeze turns one trick into two, despite two losers. These positions are Z1 and Z2 modified as follows: the defender without the guards (East) has been given a trick in the suit of the entry menace, and the rest of that suit has been demoted by one rank. L3) x L4) x L5) K AJ AJ AJ ? - - KQ x A - A - KQ xx KQ xx KQ xx - A - A - A AJ K - x x - x x x?? In each case South leads a diamond. In these cases we have demoted the squeeze card rather than a menace. The above positions illustrate what we call a "demoted" variation of other positions, which now function with two losers. This type of secondary squeeze requires restriction on the hand of the weak defender (i.e. the one without the guards). Declarer's entries must be able to withstand any exit available to that defender. Any single menace, in particular, must be accompanied by a control unless the weak defender has none of that suit. L3 is an automatic position, derived from the automatic simple squeeze Z3 by upgrading the single menace to an entry menace. L4, with a single menace and no accompanying entry, is positional; moreover, there must be a small card opposite the single menace and fourth hand must be void of that suit. In L5, there need be no small card opposite either of the menaces. L6 x Now South has an entry as well as a A9x control in spades, and gets a fourth trick x even if East is already on lead; but if KQ x East were on lead and had two spades, he QJT xxx could kill the squeeze with a spade lead. - A AJ Kx x Here's a subtler one: 1) AJx 2) AJx K K - - K9x Qxx KQ9 A - A - x - Txx Txx - - A A In (1), South leads DA, and the squeeze works without the count even though East covers one of the losers. In (2), West alone covers the extra loser, but the squeeze fails. To understand this odd behaviour, I think (1) should be regarded as a demoted version of the simple squeeze with a split menace: 3) AKx 4) AQx K K - - QTx KTx A A - - Jxx Jxx - - A A (3) is just the simple squeeze with a split menace. (4) is equivalent, at least at double-dummy. And (1) is obtained from (4) by giving East a trick, the SQ, and demoting the lower cards. ;;Third kind: busy loser When a menace has an extra loser with it, a defender may find himself stuck with a busy loser in that suit, as here: Kx Kx QJT Ax A9x x Squeezed position by either hand. If East discards his small heart, declarer ducks a heart, setting up the king. This busy-loser phenomenon is the third way in which a squeeze can function without the count. We will use the same term "busy loser" for the small card that accompanies declarer's menace. Generally, simple squeezes can function in third-kind variations provided that the declarer's communications allow him to concede the busy loser after the squeeze occurs, and get back to the hand which contains the newly-established menace. The simplest cases: 1) AJ 2) AJ 3) AJ Kx x xx - x - KQ KQ KQ Ax Ax Ax - - - xx x x x Kx Kx A A A South leads DA. (No squeeze) South leads DA. (1) is a variant of Z1, and the extra loser makes little difference. (2), derived from Z2, fails: West throws his small heart on DA and, while HK can be set up, it cannot later be reached. (3), also based on Z2, works, but is no longer automatic. For a variant of Z1 or Z2 to work in a third-kind modification, the requirements are: -- in the hand of the squeeze card, at least one card of each menace suit. -- an entry in the hand with the single menace, or two cards opposite the single menace. The ending is automatic only in the former case and only if the menaces are in different hands. Two more examples: A9x Ax x Kx - QJT Kx Ax Ax - Kx Qx Kx x A Squeezed position South leads DA. by either hand. Not only a single menace, but an entry menace, may have a busy loser appended to it. But since declarer may then need to duck a trick to the weak defender, there are restrictions on that hand as well: AQx x x JT9 Kxx x KQ x - xx AJ A East's third spade is busy: if he discards it on DA, declarer ducks a spade and takes the rest. This position is automatic, but if the defenders' hands are swapped, declarer has a finesse for the fourth trick, and the squeeze does not produce the fifth. It is incorrect to think of a busy loser as an exit card; declarer will never benefit from an opponent's lead. ;;Unblocking against secondary simple squeezes On defence, failing to unblock can give declarer the control he needs for a congested squeeze. 1) ATx 2) ATx 3) ATx xx xx xx - - - x x x KQJ xxx KQJ xxx KQJ xx KQx Jxx KQx Jx KQx Jx - - - A - AK - - - - - - xx xx xx ATx ATx ATx - - - A A A In these three diagrams, only the East hand is varied. 1: There is no squeeze; West throws any heart on CA, relying on East to guard the third round. The same would be true if West held HKQJ and East the Txx. 2: Now East has a side winner but the squeeze works. If West throws a heart, declarer ducks a heart (to either opponent) and gets a second heart trick before the defence can get more than two tricks. 3: Declarer makes only his three aces _if_ West throws a high heart under CA. South's menaces are in place, and the squeeze does develop a heart for South, but East makes two clubs, obliging South to discard his new heart trick. In these cases, failing to unblock does not actually create a squeeze that didn't already exist. Instead, the purpose of unblocking is to keep an entry to partner's _side_ winner. ;Double squeezes and their relatives In this group of squeezes, declarer is equipped with menaces in three suits, but both defenders contribute to guarding them. ;;Double squeezes In a double squeeze, one defender guards suit A, the other guards suit B, and they both, or jointly, guard suit C, until alas declarer produces a squeeze card in suit D. Two menaces and a double menace, as it is called, add up to one winner. The suit of the double menace (suit C) is called the "middle" or "pivotal" suit, and we will refer to A and B as the "single" suits. In the diagrams below, the queries denote insignificant cards, which may be in any suit. Except in Y2, South leads CA. Y1 Ax Y2 AKx K - - - - - Kx Qx Qxx Jxx A - A - - A - A - - - - x x - K K K A - Squeezed position by South. Y3 Kx Y4 x K Ax K K - - Qxx Jxx Kx Qx A - KQ - - A - A - - - ? Axx Ax - x - - A A Y5 Kx Y6 x Y7 x Ax AKx K - - Ax x x x Qxx Jxx Kx Qx Qxx Jxx KQ - QJx - A - - A - A - KQ - ? - ?? ? - Axx Ax AKx - x - K K x A A A In the above diagrams (based on Romanet's analysis) we have given each defender an independant stopper in the middle suit, spades. That is the usual situation in practice, but the squeeze is still necessary if we take a small spade from one opponent or the other (not both) and replace it with an idle card such as a club. Y1, Y2, and Y3 are called simultaneous double squeezes, because one trick knocks out both defenders. The last four, in which one defender has an idle card, are called non-simultaneous or interrupted. Y1 is the commonest double squeeze, and the only 3-card variety. It is called a balanced (or just "the") simultaneous double squeeze. It contains the usual entry menace, and a well-situated single menace against each opponent. Y2 is the automatic double squeeze, which works whenever the defenders' single guards are in different hands. To allow room for both single menaces alongside the squeeze card, the long menace must be headed by two winners rather than one: a "recessed menace". Y3 is the twin-entry or "inverted" double squeeze, the latter name referring to the fact that the long menace is with the squeeze card. As in simple squeezes, the twin entry compensates for the location of a single menace under its guard. In this ending, declarer must know (or guess) which of the single suits West is guarding. Y4 is the only 4-card nonsimultaneous double squeeze. The CA squeezes a spade from West. North throws a heart, and now a heart to the ace executes a simple squeeze against East. The upgrade of a single menace to an entry menace overcomes the fact that one menace is under its guard. Y5, Y6, and Y7 are different from others only in the location of the squeeze card. We have put a club in the North hand, but any idle card for CA will do. In Y5, declarer will continue with a spade to the king whatever happens on CA, and then lead HA; the position is now Y1. In Y6, he will continue with a heart to the ace and then lead HK; again we have Y1. In Y7, after CA declarer will take DA, and the position is Y2. A twice-recessed menace is theoretically possible (Kelsey): AKQx - - ? Jxxx Txxx A - - A - - x Kx K A Here is a sort of formula for double squeeze endings: Declarer has three menaces and an extra winner, and each hand contains two of those four items. An "extra winner" is a winner facing a void, or two winners facing a singleton (i.e. a recessed menace). ;;Either-Or squeezes (at single dummy) At the table, a hand may play just like a double squeeze even if the middle suit may not be -- or cannot be -- guarded by both defenders, and indeed may not be guarded at all. xx Ax K x AKQx x - A East has DA but has shown out of hearts. Declarer does not need to guess which opponent guards spades, i.e. which opponent he can squeeze. He cashes CA. If West keeps his hearts he must come down to fewer than four spades. Then declarer crosses to HA. If East keeps DA he too must come down to fewer than four spades, and declarer's spades run. The play is unchanged if we give North three small spades (and no clubs), or just one small. If North has two or three spades, then spades (the middle suit) cannot be guarded by both defenders; if three, it may not be guarded by either defender. But in any event West is squeezed in spades and hearts, or East is squeezed in spades and diamonds, or spades are 3-3. Such variations of double squeezes have been called "Either-Or squeezes". The above example is based on Y7. Here is another, based on Y1. AKxx K - - Qxx - K A Declarer does not know how the spades are distributed but knows that West is burdened in hearts and East in diamonds. He leads CA and claims the balance. ;;Reciprocal squeezes This elegant type is a close relative of the double squeeze. Now there is no fourth suit containing a squeeze card. Instead, each defender is squeezed on the play of a winner in the suit guarded by his partner. R1 Ax R2 x xx AKx - ? Kx Qx Kx Qx Kx - QJx - - Kx - KQ? x Ax A x Ax Ax South cashes HA. South cashes DA. R3 Kx R4 AKx Ax - ? ?? Qxx Jxx Qxx Jxx KQ - KQ - - KQ - KQ Axx x - Ax Ax Ax South cashes DA. South cashes both aces. As in the double squeezes, either defender, but not both, may have one fewer card in the middle suit (spades), and an idle card instead. The 4-item formula for double squeezes remains valid for reciprocal squeezes. R1 is the only 4-card reciprocal squeeze, closely resembling the 3- card double squeeze, with an entry menace and two well-placed single menaces. R2 and R3 are variations of R1 to allow the squeeze card in the same hand as the double menace; declarer will always cross to the table on the next trick. R4 is the (automatic) analog of Y2. The first three positions converge, in a sense, with Y1, and R4 converges with Y2. In each case, one opponent will follow to the squeeze card. If the other lets go of his single guard, the declarer can run the remaining tricks. If we assume that he lets go of a small spade or an idle card instead, the positions become identical with Y1 and Y2. Compared to the double squeeze, the reciprocal requires additional strength in one or both single suits. But I suspect that reciprocals would occur more often if more players were familiar with them. If declarer thinks that a double squeeze is required, he should consider playing off the fourth suit at an early stage. Compelling the opponents to discard may help him place the high cards in the single suits. ;;Guard squeezes In a guard squeeze, the same defender guards both single menaces. But declarer's middle menace is reinforced, and the same defender is also burdened in that suit with a partial stopper which protects his partner from a finesse. Such an ending still works even if the second defender also guards one of the single menaces, in which case it is called a double guard squeeze. Below are the basic positions. In each, the squeeze card is CA. G1 Ax G2 AJ G3 Ax K - Ax K K - - ? ? Jx Qxx Kx Q Jx Qxx A - - KQ KQ - A - - A A - - ? ?? - - ?? KTx x KTx - Ax - - - K A A A G4 x G5 x Ax AKx K - - ? Q Kx Q Kx KQ - QJx - A - A - - ?? - ??? AJ AJ x x - K A A Again the queries denote insignificant cards in any suit. Those cards may comprise a second guard in either of the single suits. (The defender has not enough cards to guard both.) G4 and G5 are intrinsically double guard squeezes, in that they simplify if East does not guard diamonds: South can just cash SA and squeeze one or both opponents with CA. If the 3-suited defender lets go of the middle suit, declarer runs the rest by aid of a finesse. If he lets go of a single suit which his partner does not guard, declarer has the rest on top. And if he lets go a single suit which his partner does guard, the ending converges with a double or a reciprocal squeeze, and no finesse will be needed. The 4-item formula is valid for guard squeezes. The tenace in the middle suit must be such that declarer can win the finesse in the _longer_ hand. AT ATx K K K K - - Jx Qxx Jx Qxx A - A - A - A - - ? ? ?? K9x K9x - - - - A AK At left (a variant of G1) the squeeze fails. At right, declarer cashes CA and unblocks ST under it, and continues with CK. There is an another interesting technicality about guard squeezes: If the tenace in the middle suit is headed by a second winner, that winner must be played off prior to the squeeze card. A9x K Q - Tx Jxxx A - A K ? - KQ8x - - A If South cashes CA, West throws his idle card and North is squeezed out of a small spade, which is needed for a finesse. South must cash a high spade and must also, on this occasion, throw S9 under it. Another odd fact about guard squeezes is that declarer may decide in advance what he will do on the next trick, irrespective of what happens on the squeeze trick. In G1 and G3, he may cross to a spade; in G2 he will lead HA; in G4 or G5 he will cross to a heart winner. In the "trump guard squeeze", a ruffing finesse replaces the simple finesse. QJ AK K - K Ax Qxx Jxx A - - - - xxx - xx Clubs are trumps, and South leads a club. If West throws SK, DK is discarded and East's SA is destroyed with a ruffing finesse. If West throws a heart, DK is again discarded and East is in a trump squeeze. G2, in which the strong defender plays fourth hand to the squeeze card, admits a symmetric variation called the "hexagon squeeze", a 4- trick ending in which all 16 cards are busy: AJ x Q - Kx Q Q Kx K A - - x AJ - A On CA, if West throws DK, North throws Hx and the position is G2. (Or he can throw SJ and continue with a spade to the ace, for a simple squeeze.) Declarer requires both of his tenaces, with a small card opposite each. The hexagon squeeze was discovered in a post-mortem in 1935 and got wide publicity in _Bridge World_ and in Coffin's early classics on the endgame. But the hexagon squeeze has never been achieved at the table, as far as I know, probably because its diagnosis is very difficult. In practice declarer will have various other squeeze chances to steer for. Secondary and suicide guard squeezes are possible. Example: ATx - K x Qxxx Jx - KQ - A A - Kx Ax - x West ill-advisedly cashes CA, or declarer exits to West with a club. This position is derived from G2 by building up the spade menace to withstand a spade exit by West. With certain far-fetched exceptions, a single menace guarded by both defenders is of no use unless there is some sort of reinforced menace elsewhere which burdens them both. The double guard squeeze is the first illustration of such a reinforced menace. I have the feeling that the theory of guard squeezes is not yet fully worked out. They can do some interesting things. And, as Terence Reese said more than forty years ago, guard squeezes tend to get overlooked at the table, and should not be as rare as they are. ;;Compound squeezes A "compound squeeze" is a 1-loser position in which both defenders guard suits A and B, only one of them (say West) guards C, and declarer has two damaging winners in suit D. On the first of those tricks West may release A or B, but in either case a double squeeze remains in place. For this to be possible, the menace in suit C must be well-placed and declarer needs suitable communication to handle either of the double squeezes. - K Kxx Kx Kxx Kxx x x - A A - Qxx Jxx Jxx Qxx Qxx Jxx Jxx Qxx ? - - ? K - Ax Axx Ax Ax AK AK On the ace of clubs, the defender with SA must let go of a red suit, and we can assume he throws a heart. Declarer cashes HKA, and then the CK executes a double squeeze. - AKx x Kx - A Qxx Jxx Kx Qx ? - K x Ax Ax Declarer cashes both club tricks, ending in either hand. If East releases hearts and West a diamond, declarer cashes HAK for a simple squeeze against East. If East releases diamonds, the second club starts an automatic double squeeze. The compound squeeze, in effect two overlapping double squeezes, was studied by the late mathematician Clyde Love, who died in 1960. Overlapping reciprocal squeezes weren't discovered until much more recently. Here is one, from Reese & Bird, _Miracles of Card Play_. x Ax Ax Ax Kx Qx Kx - Jxx Qxx - ?? Ax - Kxx Kx South cashes both club tricks, ending in either hand. If West lets go diamonds, then DK followed by DA and HA executes a reciprocal squeeze. If West lets go spades, then SA, DA, HA does the same. The 4-item formula remains valid for compound squeezes. ;;No-loser double squeeze One might expect that in a no-loser position, if both opponents guard the blocked suit, declarer might get by with a menace against each. Apart from trivial variations of double squeezes (in which a high card is overtaken, just as if it were a loser), I know of only one such position: K K K - Qx Jx A - - A Ax - - A South leads CA, and must know how the single guards are divided. ;Triple squeezes and progressive squeezes In a "triple squeeze" one defender is burdened in three suits, and the other defender cannot help. Since two menaces against one opponent are enough to produce a trick, a "normal" triple squeeze operates while declarer still has two losers; more than two losers is possible if the squeezed defender is the only one who can cover them. If the defender cannot release a trick without leaving declarer with another (simple) squeeze, the ending gains two tricks and is called a progressive squeeze. But, aside from those normal cases, there is a dimly-understood class of 1-loser and even no-loser triple squeezes, in which the additional threat or two is needed to overcome some entry problem. The simple clash squeezes, which we treat separately, are in this group. ;;2-loser varieties This normal variety is just a congested simple squeeze. Almost any simple squeeze, plus a menace in a third suit, gives rise to a triple squeeze. It sometimes arises in play precisely because declarer cannot rectify the count, at least not without allowing the defence to expunge a needed entry or menace. Here are some examples of triple squeezes: T1 AJ T2 AJ T3 Ax - K K ? K x or K - - - KQ KQ Kx A A A A A A - - - x x Qx K - - K ?? K or x - A A Squeezed position South leads CA. South leads CA. by South. T4 Qx T5 Kx A AK K K - - Kx Ax Kx Qxx A A - - A - Qx Jxx x x - x (trumps) Squeezed position Squeezed position by by either hand. South. The automatic ending T1 still works and is still automatic if one of the single menaces is opposite the squeeze card. If both are (T2) or if the long menace is divided (T3) it is positional. In any of these three, the defender can hold declarer to one extra trick by unguarding the long menace. Any other defence might give two tricks, as in this case of T2: AJ K K - KQ A A - x Q x A On the club ace, if West throws a heart, dummy's HK is unblocked and declarer produces HQ. In T4 and T5, the defender should not unguard the single menace, in diamonds. It is better to concede a trick in such a way as to compel declarer to expend an entry to cash it. For a progressive squeeze, one of the menaces, once established, must serve as a second squeeze card. Relative to other triple squeezes, this necessitates an additional entry or an "extended menace" (an entry accompanied by two losers, both of which threaten to become tricks). The commoner cases are: P1: two single menaces with the squeeze card and an extended menace opposite (an automatic position) P2: an entry menace in each hand and a single menace over the defender. P1 AJT P2 AJ - K - x - x or A KQ KQ A A A KQ - - x x K x K AJ - A or x Squeezed position South cashes CA. by South. In P2, if the single menace in hearts were under the defender, he could defend in the usual way by unguarding the entry menace on his left. But that defect can be overcome by compensation in the form of an extended menace (P3 below) or a twin-entry menace (P4). P3 x P4 - AJT AJ - A9x - - KQ A KQ KQ A QJT - - AJ K x x K K8x - - Squeezed position Squeezed position by either hand. by either hand. In P4, note that the diamond spots must be such that declarer can win the third round in hand. If, say, South's diamonds were K32, West could hold declarer to one extra trick by discarding a diamond. ;;Defending 2-loser varieties To avoid giving away the second trick unnecessarily, a defender should cleave to these principles: -- If squeezed in three suits, unguard a long menace rather than a single menace. (Declarer would rather cash a single menace than a menace plus an entry.) -- It is better to unguard an entry menace on your left than an entry menace on your right. -- Rather than surrender two tricks by letting go a guard to an extended menace, unguard a single menace in the same hand as the extended menace. -- When (rarely) declarer has two long menaces in the same hand, unguard the single menace. A more wide-ranging principle addresses both defenders: If declarer has a threat in each hand, each guarded by both defenders, each should retain a guard to the menace on his right. ;;1-loser varieties At double dummy, a triple squeeze with one loser always reduces to a simple squeeze except in the presence of some entry problem. AJ - AJ AJ K AQ - x KQ A KQ KQ A Kx - - x Kx xx x - - AK AK In the first of these South is to lead. If the HA or SA had been played off earlier, declarer could cash CAK, throwing the J of that major, which is not needed. But as it is, South leads CA and West must give a trick to the North hand. In the second diagram, if the lead is with North, declarer cashes DA and throws his idle spade. He now takes the CA and leads CK, making the rest on a major-suit squeeze and also if West has both red suits. But if South is on lead that play is not available. Instead, South takes CA and leads CK, hoping that West has both red suits or East has all three suits. J4 A Kx A - QJ A K - KT - Q A South leads CA, and North discards from whichever suit West plays. If that is diamonds, DQ follows. If the diamonds are omitted from J4, it is just the jettison squeeze J3. - - K Ax A A A - K K - K South, on lead, has two winners, but cannot readily cash them owing to blockage. But on the lead of CK, West is squeezed and South gets two tricks. - - K Ax A K A - A - - xx Q K - K On CK West throws SA. But now declarer plays low in dummy and puts East in with SQ, throwing DK from the table. ;;Three menaces at the table At the table, declarer will try to retain threats in three suits in various cases. -- He has only one loser but doesn't know which simple squeeze to rely on. To construct examples, we can start with a simple squeeze and merely promote some idle card to a threat. AJ K - x x - K AK Clubs are trump, the defence has at most one left, and North is on lead. Rather than ruff the HK and play for a simple squeeze, declarer plays off CAK. A fourth trick materializes if (1) West has SKQ and _either_ red ace, (2) East has SKQ and DA, or (3) West has HA and East has DA. Double squeezes can likewise reduce the ambiguity when declarer has three menaces and only one loser; see "Either-Or squeezes". -- No simple squeeze can be done Typically declarer has a running suit but cannot run it without damaging the opposite hand; perhaps that hand has two menaces, both of which are under the guards. Here is an example from Clyde Love in which there is no running suit: K743 AQ962 AJ 73 AQ5 KJ Q52 AKQJ9 Against 7NT West leads DT to dummy's ace, East playing the 7. You try HKJ but West throws D3 on the second round. On SA West plays the 6 and East the 2. On CAK, East discards D4 on the second round. If anyone has 4 spades it is likely East, in which case he is squeezed in three suits when you now play CQ, throwing DJ. As is normal in a one-loser triple squeeze, the _second-last_ of the club winners is the squeeze card, for otherwise North would be squeezed before East. -- He can't rectify the count We saw such endings in the section "2-loser varieties". -- He can develop enough tricks, but the opponents would then have too many winners. We will look at this case in the section "Control pressure". It is an interesting fact that pressure of a triple or progressive nature can have a showup effect, squeezing a defender out of a tell- tale _loser_ in a 1-loser position: AQx AQx - - Kx Kx KQ - x x AJ AK On CA East throws a spade or a heart rather than the more revealing DQ. At double dummy declarer now has the rest. But at the table he should continue with CK, throwing North's remaining idle card. He cannot now go wrong. To play DA instead would consume the tables's last idle card, without getting information from East. ;Clash squeezes This interesting little group was studied by Chien-Hwa Wang in the 1950's. The basic position is a one-loser triple squeeze, in which a third menace overcomes a shortage of entries to one hand. If the other hand's entries are built up, however, the squeeze still works when one menace is guarded by both opponents ("double clash squeeze"). All the clash variations are positional, because there is no idle card opposite the squeeze card. In all the diagrams the squeeze card is CA. 1) Ax 2) Ax 3) Kx AJ KT AJ - - - - - - K Jx K Jx Q AT KQ ?? QJ Ax KQ x A - A - A - - - - - - x Q Q J x x x K K K A A A All the clash squeezes derive from (1), with its characteristic "clash menace" in spades. East's hand does not participate except to prevent declarer from overtaking SQ. If East guards either of the red suits, the squeeze fails. If SA had been played off earlier, CA would execute a simple squeeze. The two secondary forms, derived from (1) by demoting one of North's menaces, still work with only four cards, provided that East has nothing in a third suit, as shown. 4) Axx 5) Ax 6) Ax K AJ Kxx A x - - - - QJ xxx K Jx K Jx A - KQ ? Qxx ?? Kx Qx Kx Qx A K - - - - - - KT Q Q - x Ax xx Ax Q A A A Adding an entry to the South hand makes it allowable for East to guard the menace on his left, diamonds. If West throws a diamond, North's heart menace is discarded. East is squeezed already in (4), or on a heart to the ace in (5), or on HKA in (6). 7) Ax 8) Ax Axx Kx - A - - K Jx K Jx Qxx ?? Ax ? A K Kx Qx - - - - Q Q x - K Jx AK (trumps) AK (trumps) A ruffing entry to the South hand, like a side entry, allows East to guard South's menace (i.e. not the ruffing menace). (7) and (8) are alike except for the location of the second entry opposite the trumps. 9) Q 10) Q Jx Qx Ax Ax - - K Jx K Jx Kx Qx Kx ? KQ ? Kx Qx - - - - Ax Ax A A x x A A In the inverted case, East may guard either of the red menaces. In (9), if West throws a heart, Dx is discarded, HA cashed, and DA squeezes East. In (9), if West throws a diamond, Hx is discarded, and again HA followed by DA squeezes East, although one trick sooner. The 4-item formula holds for clash squeezes if we regard the clash suit as a menace in the _longer_ hand, i.e. North in the diagrams (1) through (8), and South in the inverted case. ;Squeeze throw-ins The squeeze throw-in is one of the commoner special endgames. It resembles a squeeze which prepares for a throw-in by extracting the defender's exit cards and winners. It is classed as a secondary squeeze, and has often been confused with other types, but it is not a full-fledged squeeze, and we shall be at pains to explain its real nature. All "real" secondary squeezes are based on simpler positions in which the count has been rectified; a squeeze throw-in has no such underlying squeeze position. It is just a throw-in that is assisted, in a way, by what we will call a "pseudomenace". ;;Throw-ins Here is a pair of positions to start bringing out the notions: 1) xx 2) xx K or x x x x Kx Kx Ax AK - - AQ AQ x or K x A A South cashes DA. In (1), West has three unsatifactory options in only two suits. A spade discard, or HA, costs a trick, and to throw his small heart sets up a throw-in. Is this a squeeze? If HK is with South, there is no entry nor anything else of value opposite the "squeeze card". In (2), moreover, the ending still works even though HK has been given away to West. No one would regard (2) as a squeeze, since West cannot expect to make all three of his winners when South has two of the last four on top. So (1), which is an example of a squeeze throw-in, is just a throw-in assisted by a pseudomenace, the HK: Since declarer has HK, the ending works whenever West has the ace. If declarer had only the jack, for example, West could defend by unblocking unless he is saddled with the singleton A, doubleton AK, or AKQ any length. In (2) there is no pseudomenace, but South must cash DA first. That brings us to the next notion: control pressure. The preparation for a throw-in is not about pressure at all. But communication, control, and card-reading are all involved. To illustrate: 3) Jxx 4) Jxx x x x x KQx KQx x xx x - Axx Axx A A A A In (3), declarer must cash both red aces first, to remove West's exit cards, and then lead a low spade. In (4), oddly, only DA works. He cannot afford to give away control of hearts by cashing HA first. DA seems to put a sort of pressure on West: if he throws a spade, it costs a tempo (i.e. a unit of control), for then one spade lead is enough for South. Suppose he throws a heart -- a winner, mark you. Then declarer has succeeded in transferring his control from diamonds, where it isn't needed, to hearts. The position now converges with (3). But there is nothing special about being "squeezed" out of established winners; it occurs on every hand. (It can be proved mathematically that in any deal, no matter how it is played, at least three established cards get discarded on someone else's tricks.) In (4), declarer can take three tricks off the top, so West cannot expect to make a heart and two spades. Thus (4) should not be regarded as a squeeze. But it does illustrate what we call "control pressure", about which we will have more to say later. ;;Simple squeeze throw-ins A squeeze throw-in is less trivial. Declarer's basic assets are simply a tenace and a pseudomenace, in different suits, both guarded the same defender, plus a modicum of communication and control. If he has a major tenace (the "major" squeeze throw-in, let's call it), he normally has all the remaining tricks but two, and if a minor tenace, all but three. We will refer to those two main suits as the tenace suit and the exit suit. The squeeze card is in a third suit, where the defender is void. E1 illustrates the major case and E2 the minor. In each, the tenace suit is spades and the exit suit hearts. E1 Qx E2 xx K Jx x x Kx Ax A? KQ? - - Ax Kx x Ax A A South cashes DA. South cashes DA. The query may be a "winner" for which declarer has no corresponding loser, as here: Qx xx Qx Q Tx K x x x - - - Kx Ax Kx AK KQJ A - - - - - A Ax Kx Ax x Ax x A A A - - - Any squeeze throw-in is intrinsically automatic, for this reason: The pseudomenace can throw in either opponent; and it doesn't matter whether the opponent then leads through or leads up to declarer's tenace, since by hypothesis he himself has the missing high card. AJx x x Kxx xx Ax Qxx - - Qxx K A Declarer cashes DA and loses only one trick. But if we swap the East and West hands, he loses three. Positional? No, because in the latter case declarer cannot run all but two of the tricks. The all-but-two and all-but-three rules are easy to understand: If declarer has the major tenace, the defender has one trick in that suit and one winner for the exit card; declarer needs the rest, for otherwise the defender will have an exit card or something to cash when thrown in. If declarer has the minor tenace, the defence is waiting for two tricks in the tenace suit rather than one, so declarer needs all but three rather than two. But more than two or three losers makes no difference if the same defender has to cover them all: Qx xx K Txx K - x x Kx Ax Ax KQJx A - - - Ax Kx x Axx x - A A If any heart or diamond tricks could be won by East, West could defend by unblocking. Even if declarer's tenace is well-placed (behind the enemy), he may require a throw-in or a squeeze throw-in to overcome a shortage of communication: Qxx AQJ x K - x Kx Jx Kxx - Ax Qx Ax xx - - - KQx Ax x K x A Axx At left, South can establish SQ by leading toward it, but will never cash it. Leading DA solves the problem. At right, declarer cashes DA and then finesses in spades. He cannot afford to finesse first. At the table, the tough thing about squeeze throw-ins is reading the defender's hand. A defender may well come down to a bare king or bare winner in such positions. Therefore declarer, even if he can place the high cards, may need to take a view on the distribution, and must count all the defender's relevant small cards as they are played. This ambiguity about small cards is common in third-kind secondary squeezes as well. ;Stepping-stone and winkle squeezes. These are 1-loser secondary squeezes in which pressure overcomes an entry problem. Their names and most of their theory are due to Terence Reese. The automatic stepping-stone positions: B1 AJ B2 K ? x? Qx Qx Ax Ax K AJ Kx K Squeezed positions by either hand. B1 still works if the Q and K of spades are swapped between South and the defender, provided that North has a small heart or the lead is with South. For automatic stepping-stones, the doubleton in the blocked suit (spades) must contain the master card. But there is also this positional variety, akin to the jettison squeeze: B3 A xxx - QJ Ax - KT K A South leads DA. The double stepping-stone squeeze, derived from the no-loser double squeeze, involves menaces in three suits: B4 Ax x or K - Qx Jx A x x A K K or x K Squeezed position by either hand. Clearly neither opponent can throw his ace. If both throw spades, dummy takes two spade tricks. Otherwise, one opponent must throw his exit card, and declarer cashes SK and exits to that opponent. There is one more, quite different, position that uses the stepping- stone mechanism: B5 AQ AQ - - Ax Ax Kx Kx - Ax Ax Kx - - Qx - - Kxx QJx K K South leads DK. South leads DK. The variation at right shows that the pseudomenace may be guarded by both defenders if fourth hand has no good exit. This time declarer would have a finesse for all four tricks if he had a small spade. There are three rather different winkle squeezes, but they all feature a third-ranked pseudomenace. B6 Ax Q Qx Jx Kx Ax K Jx Squeezed position by either hand. B6 is sometimes designated the "double" winkle, referring to the fact that both defenders guard the blocked suit. But it plays the same way and is still needed if only one does. If both opponents throw spades, dummy takes two spade tricks. If either throws a heart, declarer cashes SK and exits with Hx. In practice, East or West may have one fewer card in the two suits, having followed suit to the squeeze card. B7 - - Jxx Jxx x Kx xx Kx Kxx Ax Kx Ax AQ AQ Q Q Squeezed position by South. B7 is derived from the major squeeze throw-in in which both defenders guard the pseudomenace. Like the latter, it requires that the weaker defender have no exit cards. B8 Ax QJ - Kx JT Ax Kx - - Qx x A South leads DA. B8 is also derived from the major squeeze throw-in, but is positional. Note that the squeeze fails if the HK and HA are swapped between East and West: West throws his small heart and East discards from whichever suit North tosses. Another technicality is that the exit suit (hearts) must not contain a winner: Ax JTx - Kx JT Kxx Qxx - - Qx Ax A South must cash HA first, then DA. ;Specialized menaces ;;Pinning menaces 1a) AT 1b) Ax Kx Jx Kx Jx Qx QT 2a) A9 2b) Ax Kx JT Kx JT Qx Q9 The above are called pinning menaces. As is evident, they burden both defenders. If one defender weakens his holding, his high card will be dropped; if the other, it will be destroyed by a pinning finesse. An ending which uses this type of menace is called a pinning squeeze or a squeeze finesse. Pinning squeezes are intrinsically positional, but some of them resemble automatic squeezes of other kinds. A pinning menace resembles a guard menace, with the possibility of a pinning finesse instead of an ordinary finesse. In practice, declarer may have a second entry in the suit. Adding the ace to the South or North hand and demoting all the other cards gives variations like these: K9x Kxx AKx Qxx Txx Qxx T9x Qxx Txx AJx AJ8 J9x In these 3-3-3-3 cases, declarer can transfer the guard to the East hand, but we will see that that may not be the best play. In practice, declarer may have only a doubleton facing three, or a singleton facing two, but then the longer hand (which contains the menace) needs an extra entry somewhere else. In a 2-loser position, a pinning menace has extra value: an opponent cannot lead the suit without losing a trick in it. In 1a and 1b this is true of either opponent; in 2a and 2b, only of West. This property is retained in the 3-card "twin-entry" variants. One more remark, before we look at some endings: If declarer's intermediates are slightly weaker, he might get by with some luck in the distribution: K87 Kxx Qxx T9x Qxx T98 AJx AJ7 Here are two applications of pinning menaces: Kx Jx Qxx T9x Qx Kx AJ8 A Squeezed position by South. This one, called the "double two-suit squeeze" is a sort of crisscross ending in which both defenders may guard the blocked menace in hearts, since both are burdened in spades. North's shortage in the pinning suit is overcome by an extra entry to the other hand: if West throws a heart and East a spade, SJ is run (West ducking, let's suppose), then SK is taken, and then HA allows South to make his isolated SA. X1 KT X2 AQ9 X3 KT AK A A ? ? A QJ Ax JTx Kxx QJ Ax Qxx Jxx Qx Kx Kx Qx - - - - - - - x - xxx xx xx Ax Ax xx Diamonds are trumps, and South cashes DA. This is known as the "squeeze finesse at trumps" or the "double trump squeeze". If West sheds a spade, a ruffing finesse replaces the usual pinning lead toward a winner. If East lets a spade go, his stopper can be ruffed down. The diagrams are alike except for the location of the second entry opposite the last trump. X4) KT Diamonds are trumps, and declarer cashes A DA. This is the same as X3 except for a Ax ruffing menace rather than a normal menace QJ Ax opposite the pinning menace. Kxx Qxx - - - Jxx xx The trump guard squeeze (above, under "Guard squeezes") is a close relative of the squeeze finesse at trumps. Since a pinning menace ties up two cards in the hand of each defender, it makes possible a squeeze against both defenders with two losers. (We won't call this phenomenon "fourth kind", because _both_ defenders are involved, and I don't know of any uniform way to extend such positions to 2-loser cases.) Two examples follow. A9 Declarer has 2 of the last 4 tricks, but K comes to 3 on the lead of CA. If East - discards DA, West is thrown in with DK. x Notice that one of the single menaces is Kx JT guarded by both defenders, and the other - A is unfavorably placed. K A ? - Qx - Q A KT Declarer cashes DA. Like the squeeze Ax finesse at trumps, this looks like a x double squeeze in which a pinning menace QJ Ax replaces the two single menaces. But in Qxx Jxx this 2-loser case, no ruffing is needed; - - instead, declarer has a small card x opposite the KT. Kxx A ;;Vice menace Another of Terence Reese's patents is the "vice squeeze", or just "the vice". It is a secondary squeeze characterized by the "vice menace": KT Tx QJ Axx QJ Axx x K The first form is the commoner of the two. The 3-card vice squeezes are: V1) KT V2) Tx - - x x QJ Axx QJ Axx A - A - - - - - x K K K A A One trick turns into two on the lead of DA. V1 is just a demoted variant of Z2; like Z2 it is automatic, but if the East and West hands are swapped, no squeeze is needed to develop a trick from SK. V2 is automatic as well. In these simple cases, East must hold three cards of the vice suit, or a card with which he can follow to the squeeze card, so that the ten will win the last trick if West gives up his stopper. In place of a single menace with the squeeze card, an entry menace opposite will do, and will also serve to control a side suit: V3) KT AJ - QJ Ax KQ xx - - x xx A Like V1, V3 is a demoted simple squeeze. If both opponents guard the entry menace, there is still the positional "double vice squeeze": V4) xx Ax - Ax QJ Kx Qx - - KT x A Note that two small cards are needed opposite the vice menace. ;;Two-trick menaces A two-trick menace is a holding in which one enemy discard may set up two tricks at once. The extended menace used in the automatic progressive squeeze is the only common case. But here are a couple more illustrations: AJT KQ - - KQ A KQ - x - AJT A South leads CA and, thanks to three two-trick menaces, West must surrender two tricks on a single squeeze card. K98x A QJT QJT A K98x Squeezed position by either hand. The "exaggerated crisscross squeeze". South can only run four tricks (counting the squeeze card), but if the squeeze is on, he rakes in all six. The 4-card suits may be stronger, in which case declarer need not find so many important cards in the hand of one defender, and the chance of five tricks is increased. A two-trick menace can overcome blockage in one of the menace suits. An illustration, also of a crisscross character: K QJx x Qxx Kx - AJT A A South cashes DA. If West let's go a heart, South can take the balance without using the SA, since he has two new heart tricks. Various progressive squeezes have been constructed which generate two tricks, relying on a two-trick menace. A two-trick ruffing menace is possible. There even exist three-trick menaces, and endings that gain three tricks. ;;Unblockable menaces If an ending is defective in that one of declarer's hands will come under pressure as well as an opponent's, compensation may exist in the form of an overbuilt menace which allows some unblocking. The three examples below are all 1-loser triple squeezes. AJ K x x KQ A KQ - x Q AJ A South cashes CA, and gets two more tricks from the progressive squeeze P2 if West, rather than East, has all three guards. However, DQ falls from East. Declarer now cashes DAJ and discards HK, "turning the tables". AT AJ K - KQ KQ A - J xx or x - or x AK If clubs are trump, South can take HA, ruff a heart or a diamond, and lead his last trump for a simple squeeze. But at NT, South to lead, he has no entry to hand and must cash CAK. If West throws a spade on the first club, declarer need not place him with the other spade. He may throw ST; if West throws a second spade on the second club, declarer throws SA, then leads SJ, and the squeeze is still there. This is another illustration of how pressure in three suits can bring forth information and thus reduce the ambiguity from declarer's angle. A related phenomenon is the "Vienna gambit": AJT Lead with South. If HA had been played off Ax earlier, this would be an automatic squeeze in - only two suits, spades and diamonds. As it is, - South plays off CAK and discards HAx. This costs KQ one winner but causes the ending to converge Kx with the automatic progressive squeeze, which A gains two tricks. - x Q K AK ;Control pressure, or mock-squeezes 1) Jxx 2) Axx x Jxx x - - x KQx QJx xx KQ - AK - - Axx KTxx A ATx A - - A We saw (1) in connection with throw-ins. South cashes DA. If West throws a heart, it does not set up a winner for declarer; instead, it strengthens declarer's _control_. He can now pull the remaining heart and establish a trick in spades, aided in this case by a lead from West. In (2), declarer can develop a fifth trick in spades or hearts, but then East gets two diamonds, leaving declarer only four tricks anyway. But South starts by playing off CA. If East throws one of his established diamonds, that does not give declarer a trick in diamonds. Instead, it gives him _time_ to drive out one of East's stoppers (or guards) and make five tricks. Both positions are mock-squeezes, in that the defender need not give declarer a trick, but may concede a _tempo_ instead. (2), with no involvement of a throw-in, is the sort of mock-squeeze that sometimes arises in the middle game, without planning. The contract is usually at notrumps, because declarer does not generally play out his long trumps while he still has several losers. The defender is apt to be burdened in two enemy suits, as here, but possibly in only one. xx Kxx Kxxx AQxx QTxxx Axx QJx xxxx QJx xx xx JTxx KJx ATx Axxx Kxx Against 3NT the defence starts with a spade to the ace, a spade back to the Q, and a third spade, dummy shedding a heart. Declarer runs 3 clubs and, if West parts with an established spade, gets time to develop a ninth trick in diamonds. ;Unclassified endings ;;See-saw squeeze ATx x Kx KQJ KQJ - x ATx AQ The see-saw is a secondary squeeze characterized by colliding winners in the suit of the squeeze card. South leads DA (DQ won't do.) If West throws a spade, North follows with Dx and declarer gives up a spade to establish the North hand. If West lets go a heart instead, DK is unblocked and declarer gives up a heart, establishing the South hand. North's small heart is not needed (since there are two entries to the South hand) but South's small spade is. If East has the defensive strength, North must be on lead, and must start with Dx, not DK. ;;Overtaking trump squeeze This one bears a resemblance to the see-saw squeeze. 1) Qx 2) Jxx - ? Ax Ax AK - AKQ - AK ??? AQJ ????? - Q - Q - - Qx Kxx Kx Kxx Diamonds are trump, and South leads DK. In the secondary variety at right, which is from Kelsey's _Strip- squeezes_, declarer needs a third trump and a minor tenace with the squeeze card, as shown. If West throws a spade, declarer overtakes DK, ruffs a spade, and concedes a heart. If West throws a heart on DK, declarer can follow suit low and concede a heart next. ;;Backwash (trump) squeeze K K K K - - A A x A xx A x A x A A - - - - Q - Q - - - - xx AK K K Clubs are trump, and South ruffs a diamond. At left, this establishes the little diamond, making it a sort of menace (although a winner) against East's trump loser. At right, the diamond ruff is still necessary even though the diamonds are already good. Geza Ottlik has described (_Bridge World_ Feb. 1974) some fancier backwash varieties, including a two-loser form. ;;One-suit squeeze We have seen cases in which a defender with only two suits may have three unsatisfactory options, one of them being to leave himself with a stiff winner with which he can be thrown in. In the same way, he may have two options with only one suit. AQx K9x x x 9x KJT7 Tx AQJ8 xx - xx - 8xx xxx A A South cashes HA, and East is squeezed, in the sense that he can't unblock (to avoid a throw-in) except at the cost of a trick in the suit. As usual in a squeeze throw-in, declarer has three losers with the minor tenace or two with the major. His tenace may be divided between his two hands.