2-Trick Triple Squeezes

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Structure

The 2-trick triple squeeze (often called a repeating or progressive squeeze) is characterized by three conditions:

This type of triple squeeze occurs when the last free winner is cashed; then either (i) the opponent's discard establishes one extra winner for the squeezer, and cashing the new winner subsequently enforces a simple squeeze, or (ii) the opponent's discard establishes two extra winners immediately.

[Aside for the mathematically minded: To see why this is so, suppose a player comes under pressure when forced to discard from holdings of p, q, and r cards in three suits, and is forced to concede the remaining tricks no matter which choice of discard is made. Suppose the victim discards from the p-card suit. Then the squeezer must be able to win the first p-1, q-1, and r-1 rounds respectively of the three threat suits, so if f is the number of free winners held by the squeezer immediately before the squeeze, the squeezer will hold a total of (p-1) + (q-1) + (r-1) + f winners before the squeeze takes place. Since the squeezer has two losers, this total must be 2 less than the number of cards held by the victim, which is p + q + r; so p+q+r+f-3 must equal p+q+r-2, i.e., f must be 1.]

Classification

The classification of 2-trick triples is rather difficult, since the possibility of extended menaces worth two tricks leads to an amazing proliferation of possible endings. One way to simplify the classification is to systematically group adjoint positions together, and this will be done here. (Recall that two squeeze endings are said to be adjoint when the arrangement of menaces is the same in both positions, but the first squeeze card lies in opposite hands.)

The main family of 2-trick triples consists of the progressive 2-trick triple squeezes, in which at least one choice of discard forces the squeezer to execute a second squeeze, which will be a simple squeeze. These can be subdivided according to the nature of the most complex simple squeeze involved:

  1. the positional progressive squeeze, in which the first discard either concedes two tricks, or else sets up a positional simple squeeze
  2. the automatic progressive squeeze, in which the first discard either concedes two tricks, or else sets up an automatic simple squeeze
  3. the twin-entry progressive squeeze, in which the first discard either concedes two tricks, or sets up a positional simple squeeze, or sets up a twin-entry simple squeeze
  4. the split positional progressive squeeze, in which the first discard either concedes two tricks, or sets up a twin-entry simple squeeze, or sets up a split-positional simple squeeze
  5. the criss-cross progressive squeeze, in which the first discard either concedes two tricks, or sets up a positional or a twin-entry simple squeeze, or sets up a criss-cross simple squeeze
  6. the ruffing progressive squeeze, in which the first discard either concedes two tricks, or sets up a positional, twin-entry, or criss-cross simple squeeze, or sets up a ruffing simple squeeze
  7. the cross-ruffing progressive squeeze

The second family is the instant 2-trick triple squeeze, in which any discard sets up two tricks immediately..

The third family is the alternating 2-trick triple squeeze, in which at least one of the threat suits contains a viable threat in each hand (for instance, if the squeezer holds A93 opposite K83 in a suit in which an opponent holds QJ10, then either the 9 or the 8 could serve as a threat). Endings are included in this family only when both menaces are necessary for the squeeze. The alternating squeezes can be divided in the same way as the progressive squeezes, although there are far fewer possibilities:

  1. the twin-entry alternating squeeze
  2. the split positional alternating squeeze
  3. the criss-cross alternating squeeze
  4. the ruffing alternating squeeze