Sometimes, All Players Are Created Equal

In my study of Mirror Hands, thousands of deals were found on which any declarer could make 1-notrump against best defense; but the simulator also determined that no mirror-type matrix exists wherein all four players can fulfill the same contract in suit play.

Wondering whether such a contingency were possible on any hand at all, I set my computer to work.  After creating and analyzing a quarter-million hands per day for several weeks, my trusty PC finally answered the question.

On the following deal, every declarer can make 1-Diamond!

On the surface, North and South each have four cashable winners, and they can easily develop a second trick in clubs.  The diamond suit is frozen, however.  Having no natural trump trick, the other two winners will have to be developed somehow.  East and West declarers always can win three trump tricks, one spade, and a spade ruff.  The other tricks must come from somewhere else.  Let us see how the play might go.

— SOUTH DECLARES

Spade lead:  although declarer can win East's jack with the ace and still survive, taking the trick with the queen makes it easy.  He now can lead any card from his hand, having many options.

Heart lead:  this blows the heart suit.  Declarer now opts to control the hand by leading trumps and eventually running the hearts.  The defenders' tricks will be limited to not more than four diamonds, one spade, and one club; in fact, they must be careful in order to prevent an overtrick.

Diamond lead:  this sets up a natural trump trick for declarer, leaving the defenders no better off.  If two rounds of trump are led, then only a club switch from either side (not the king) will prevent an overtrick.

Club lead:  once again there are many options.  One is to play dummy's ten, winning the first two clubs.  Now declarer cashes the ace of spades and the two top hearts, then ruffs a club.  At this juncture, the only winning play is to lead the spade queen.  When east is forced to ruff a spade later, another trump winner will materialize for the offense.

— NORTH DECLARES

The only meaningful variation is a low spade lead from East, which must be ducked in dummy to force out West's king.

— EAST OR WEST DECLARES

Spade lead:  a critical difference here is that east can keep the jack this time, obviating the value of the defenders' spot-cards.  Now they have no suit with which to force East's trumps.

Heart lead:  this yields a heart trick for the offense, who now can set up a seventh trick in clubs.  There are other options as well.

Diamond lead:  this runs to the nine and ace.  Declarer plays back the diamond eight immediately.  After covering North's ten with the jack, he must himself be careful.  Playing a third trump now would be disastrous; for South could pitch any card in his hand and still defeat the contract by at least one trick.  Instead, declarer plays on clubs immediately, setting up tricks in that suit.

Club lead:  after winning the ace, South does best to shift to a trump, trying to prevent West from ruffing a heart.  The diamond lead runs to the jack and a spade is led.  If South ducks, the king scores and the heart queen is led, setting up an eventual heart ruff and a spade ruff for seven tricks.  Should south grab the first spade and return another diamond, West takes the ace and king of diamonds, then leads the spade jack; if that is covered, a spade is ruffed to set up the nine.  Now clubs are played, and the defenders cannot manage more than six winners.

Read more about this hand here:   [Dante's Infernal #47 – All Things Being Equal]