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Mystery Menaces
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It is not uncommon to play a simple squeeze "as a double".  Many of you will be familiar with layouts such as:

North
AKQ2
2
South
43
K
K
A

If the red aces are split, you have the rest by cashing A and, if no red king is established, running spades.  This looks exactly like a [B2] double squeeze, but technically only one opponent can guard spades.  It plays the same as a double, and has the same power, it's just that the deck only has 13 spades.  If somehow it had 14, and the opponents' spades were 4-4, then this would be a double squeeze.  

Let's call spades a mystery menace: only one opponent guards it, but it's a mystery who that is.  In the example above, this has no technical benefit, but in other situations it might.  This article explores some of those.

This layout (slightly modified) appeared in another thread recently:

North
AK9x
A107x
Kxx
xx
South
Qx
K9x
AQJ10x
Axx

The 6 was led and the 7 held.  That gets you up to 12 tricks, and you have a "basic" menace in hearts.  This could be played "as a compound", where you cash some winners and come down to:

North
AK9
A10x
x
South
x
K9
A
Axx

In this 7-card ending, West must retain 3 hearts and thus at most 4 black cards.  If West guards clubs, AK, K, A effects an RFL squeeze.  If West guards spades (so not clubs), then many lines work, but the "normal compound" approach would be to cash round winners and then A for an "as a" double squeeze around spades.  Really, this is just a major-suit squeeze. 

This is not the best line, though. Spades is a mystery menace, which here has a technical advantage.  Suppose you cash spades and diamonds to come down to:

North
9
A10
x
South
9
A
Ax

Again, only West stops hearts.  Either player might stop spades, but not both.  If it's RHO, you have the same RFL squeeze as before (A, to extract a club from West, then A to extract a club from East, and run clubs).  If it's West, you don't need a double, you have a single major-suit squeeze.  In a compound, where spades is a doubly-stopped menace, you need a spade entry to hold the position.  When either *might* stop it, but only one does, the entry need goes away.  This has a lot in common with a compound squeeze, but is meaningfully different.  

What you have gained is additional count information.  Most obviously: if spades were 5-2, you don't need to guess in this position and are 100% cold. Less obviously: if spades are 4-3 you've seen one spade honor drop in a restricted choice situation, and are about 2:1 to guess the position correctly. In the "as a compound" variant, you'd be much closer to 50-50.

Now, let's try to generalize...

A mystery menace with entries might play "as a" squeeze where you treat it as a doubly-stopped menace.  However, the extra tidbit that it can't be doubly stopped may allow you to gain useful information--or apply extra pressure--by cashing those entries without "breaking" the position.  For this to matter, *both* other menace suits will need entries.  Except for a curiosity position, one of those will need to be "basic" (over its sole guard), but the other can normally survive being doubly-stopped. 

I think there are 4 main endings:

Type-R:  a basic menace alone opposite a double and a mystery:

North
A2
2
AK
South
3
A3
2
2

Here, West guards spades, both guard hearts, and only one guards diamonds, but it's a mystery.

On the last club (after seeing East discard), you have to commit to who you think guards diamonds.  If it's West, pitch a heart (unless it's good) and play A.  If it's East, pitch a spade and play A.

Type-L, mystery-adjacent:  a double menace alone, with a basic and a "mystery" in the same hand.

North
A2
2
2
2
South
3
A3
AK

Here, West guards spades, both guard diamonds, and hearts is the mystery menace.

Again you have to commit on the last club after one discard.  If West guards hearts, pitch a diamond and play A.  If East guards hearts, pitch a spade (unless good), then play A.  This is the same ending as the full deal from page 1 (with suits changed).

Type-L, mystery-opposite:  

North
A2
A32
2
South
3
K4
2
AK

As usual, West guards spades, but this time both stop hearts, and diamonds is the mystery.

The cross-roads comes after one club.  If West stops diamonds, AK, A.  If East stops diamonds, A, K, A.

There's at least one additional variant where the basic menace has an alternate threat with an entry in the other hand:

North
32
A2
2
AK
South
A4
AK3
32

West has the only spade guard, hearts is the mystery, and both stop diamonds.  After one club, if West stops hearts AK, A works.  If it's East, A, A, A works.

The last variant is the curiosity I mentioned earlier:

North
2
Q
AK3
South
AK3
K
2

You can succeed in this position against any initial layout by picking the right pointed suit winners to cash.

I don't pretend this is overwhelmingly useful, but I believe it actually comes up in real play.  While most squeeze situations are studied as-if they were double dummy, I think that overlooks technical issues relevant at single dummy, and the mystery menace demonstrates that this can matter.

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