Mirror Hands (2)

—  ANY DECLARER CAN MAKE 1-NOTRUMP  —

There are many thousands of mirror configurations in which the opening leader pays a penalty for being the first to play.  Sometimes the two sides have one or more suit fits, whereas  sometimes there is no fit at all.  Overall, more than half of all hand-patterns have no solution.

Here are a few that do work:

Exchange the five-spots and the six-spots, and the contract fails.

Some deals are so complicated that they make my brain hurt:

The wilder the distribution, the fewer the solutions.  There are just 145 distinct workable matrices for 7-6-0-0.  All involve adjusting the strengths of the two suits so as to maintain a delicate balance of power between declarer and defender.

The workable 6-card suits range from AKQJ92 down to AQJ984.

The distribution can be even wilder; but 9-4-0-0 is the limit:

Observe that if the east and west hands were to be exchanged, the play would be effectively the same!  Even if the rotation of play were changed to counter-clockwise, the result would not change!

Although there are 126 qualifying 9-4 layouts, no other 9-card pattern works.  There also are many workable 8-5-0-0 hands.

Tenaces and smother plays are key factors here:

The 5-4-4-0 hands appear to be more complicated than most other patterns.  This particular one crashed DeepFinesse on my computer, because the program exhausted its available memory in the effort.  With subsequent tweaking of the conditions, I was able to verify that 1-notrump is indeed makable.

This 6-5-2-0 deal is somewhat special for a fascinating reason to be explained later: