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The terms threat and menace have been used interchangeably by most writers on squeeze play. At the same time, at least since the writings of Geza Ottlik in the late 60's and early 70's, a distinction has been drawn between material and non-material threats.(A suit contains a material threat if a particular choice of discards by your opponents will allow you to win an extra trick in that suit; a suit contains a non-material threat if you have no chance of developing an extra trick in the suit, but the overall strategy of the deal forces your opponents to retain certain cards in that suit anyway.)
To avoid the clumsy phrases "material threat" and "non-material threat", I intend, on this website, to use the term "menace" for material threats only, to introduce the term "constraint" for non-material threats, and to retain the general term "threat" to cover both cases. Similarly, when describing a position from the point of view of the victim of a squeeze, I will use the corresponding terms "stopper" (for the card(s) threatened by a menace), "option" (for the card(s) threatened by a constraint), and "asset" (for the general term). Feel free to ignore all this as a harmless bit of pedantry on my part; you don't need to remember my whims as you explore the site.
The first step to a deeper understanding of squeeze play is to gain an appreciation for the great variety of holdings which can exert pressure on the opponents when they are forced to discard.
We will distinguish five classes of menace:
Single Menaces
A single menace is a losing card which can only be beaten by one opponent. It may be a single menace by virtue of strength (for instance, the king of a suit can only be defeated by the ace), or by virtue of length (for instance, the fourth round of a suit such as A2 opposite KQ43 can be controlled by only one opponent).[In the two instances cited, the suit automatically contains a single threat, but in practice, it may require a favourable division of the opponents' cards to make a given holding into a single threat: for instance, the Q of a suit which has not yet been played will be a single threat only if one opponent holds both the A and K, while the third round of a suit such as A32 opposite K54 will be a single threat only if one opponent holds 5 or more cards in the suit.]
A single menace which requires an opponent to retain exactly n cards to stop the suit is called an n-card single menace. For instance, the K alone is a 1-card menace against an opponent's A, while the AJ is a 2-card menace against an opponent who holds both K and Q.
It is useful to distinguish several special types of single menace, since different configurations permit different types of squeeze.
It should be noted that the identical holding may serve as an ordinary, recessed, or extended menace, according to the context of the entire hand. Consider the spade suit in the following three endings:
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In 1), South crosses to the spade A, discards a heart on the diamond A, then cashes two clubs, discarding a spade from the North hand, to squeeze East in hearts and spades - here the spade threat, initially an extended recessed menace, has been converted to an ordinary 2-card menace.
In 2), North cashes the club A while South discards a spade, converting the spade threat into a recessed menace. West is compelled to discard a heart, and now the spade winners squeeze East in the red suits.
In 3), South cashes the club A, and West is squeezed. If West chooses to discard a spade, then North discards a heart, and South concedes a spade to West, making the rest of the tricks.
Double Menaces
A double menace is a suit which is stopped by both opponents independently. This means that even if one opponent discards all cards held in the suit, the other opponent will still retain a stopper, so that both opponents must abandon the suit in order for it to produce an extra trick. A single menace can be a menace either by virtue of strength or by virtue of length, but a double menace is always a length menace (when the specific ranks of the threat card(s) in the suit are important, the menace is a dual rather than a double menace). This distinction is important, because double and dual menaces are governed by quite different principles.
Normally, a double threat is only useful if it is accompanied by an entry in its own suit (Ax opposite x or the like), but there are a number of positions in which a single card which can be beaten by either opponent is nonetheless an effective menace. Recessed and twin-entry double menaces are frequently useful in complex squeeze positions, but extended double menaces play a much more limited role.
Dual and Discovered Menaces
For certain menaces, the combined holdings of both opponents are required to prevent the development of an extra trick; neither opponent can discard from the suit without the loss of a trick. By their nature, such menaces can exert pressure on either opponent alone in a unilateral squeeze, or on both opponents together in a bilateral squeeze. If only one opponent is under pressure, we will call the resulting position a discovered squeeze, and the menace itself will be called a discovered menace; if both opponents are squeezed, it is a dual squeeze based on a dual menace.
The principal types of dual/discovered menace are:
Vice menaces
In a vice menace, the squeezer holds (between the two hands) two cards which surround one or more high cards in one of the opponent's hand, and which are in turn surrounded by two cards in the other opponent's hand. The two key cards in squeezer's hands constitute the vice, and either may be established as a result of the opponent's discards. The vice menaces are balanced, in the sense that both defenders need to retain the same length in the suit. Some examples are shown below:
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Guard menaces
In a guard menace, one opponent must protect the other opponent against a potential finesse. The standard positions are:
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There are many other positions in which one player's cards are needed to prevent a finesse, an intra-finesse, a ruffing finesse, an endplay, or a simple development play against the other defender. For convenience, we will list examples of such menaces here under the general heading of guard menaces.
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Clash Menaces
The clash menace bears a close relationship to the standard guard menace, and gives rise to very similar positions.
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Frozen-Suit Menaces
A suit is said to be frozen when none of the four players can lead it without loss. There are five frozen suits which occur with some frequency in squeeze positions:
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A K 3 2
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A
2