Popping or Dropping

Len Aberbach played a grand slam contract on Friday morning in a way that he could take full advantage of some non-optimal discarding by the opponents.

 

North ♠   AKJ64 ♥   J742 ♦   72 ♣   82

South ♠   5 ♥   A6 ♦   AT ♣   AKT97654

 

West	North	East	South
—	P	P	2♣
P	2♠ (controls: one ace and one king)	P	3♣
P	3♠	P	4♣
P	6♣	P	7♣
All pass

The 7♣ call strikes me as an overbid, particularly in a club game where even reaching a possibly low-range high card small slam is quite likely to score well.

West opened the ♦K and Len won the ace in hand.  He then proceeded to play all eight rounds of clubs.  West followed suit twice and discarded two hearts (the 8 and 3), two diamonds (the J and 4) and two small spades.  East followed suit once.  East’s first discard was the ♥K, and his remaining six discards were two more hearts (5 and 9) and four small diamonds.

Len reached this four card end position:

 

North ♠   AKJ ♥   J ♦   ♣

South ♠   5 ♥   A6 ♦   T ♣

When Len played the ♥A, West discarded a small spade, dummy followed suit with the ♥J, and East discarded ♥T.

“Known” from the discards was that West retained the ♦Q (to which Len’s ♦T was a threat card) and East retained the ♥Q (the only remaining heart of the opponents that can top Len’s ♥6).  Accordingly, each defender had retained two spades.  Len played spades from the top and found that East had been dealt the ♠QT doubleton.  Making seven for a top board.

The opponents had discarded less than optimally.  East should retain a heart that could be played on the Trick ♥A, so that the distribution of hearts is not fully disclosed.  East might also consider earlier discarding the ♦Q, a “known” card, rather than the ♦J, a “not quite known” card.  And on the ♥A West should play the “known” ♥Q rather than the not known ♥T. 

Let’s say that the opponents had discarded as I suggest.

At the four card end position shown above, West would follow suit on the lead of the ♥A, dummy would follow suit with the ♥J and East, who at this stage would hold ♥QT, should play the ♥Q, the card he is known to hold.

At this point, Len would realize that the six cards retained by the opponents were the ♦Q (or ♦J), ♥T, and four spades to the queen.  Of these six cards, only West’s ownership of the ♦ honor can be inferred.  West’s other two cards might be two spades or could be the ♥T and only one spade.  And East’s remaining three cards might be three spades or could be two spades and the ♥T.  Since only the latter of each of those two possibilities would land the slam (assuming any singleton spade held by West was not the singleton ♠Q), Len would have played for spades to drop and landed the slam.

Essentially, once declarer infers that West has retained a diamond honor (necessary because Len’s ♦T is a threat card), the hand can play as a pop-up squeeze.  If West were dealt the ♠Q, no finesse is necessary because the ♠Q must fall (“pop”) from West on the two top spades in dummy.  Meanwhile, the vigorish in playing for the pop-up squeeze is that the slam is also landed in the event that East were dealt ♠Q or ♠Qx, in which case the ♠Q would “drop” from East.

 

Dealer: N, #13 Vul: Both	North ♠   AKJ64 ♥   J742 ♦   72 ♣   82
West ♠   98732 ♥   83 ♦   KQJ4 ♣   Q3		East ♠   QT ♥   KQT95 ♦   98653 ♣   J
	South ♠   5 ♥   A6 ♦   AT ♣   AKT97654