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Another Suit Combo
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I am amazed at how often I run into a simple card combination that I hadn't seen before.  Sure enough, in a recent Swiss Team, another new one arose.  Our opponents had taken a five club save against our game, and reached this ending, with the trumps gone, and the majors eliminated:

North
J863
Q108
South
Kxx
K976

We had scored two tricks, and the lead was in dummy.  At this point, declarer had a full count on the hand, and knew that diamonds were 3-3 and the ace had to be offside.  The queen could be in either hand.  The save is clearly down at least one trick, and the IMPs will depend on how many diamond tricks declarer can wrangle.

Let's analyze the play, and the defense, depending on what those x's are:

Two cases are pretty trivial.

Case 1:  South holds the ten and nine.

North
J863
Q108
South
K109
K976

Nothing to this, either the queen is on or not.

Case 2:  South holds the  nine but no ten.

North
J863
Q108
South
K95
K976

Again, nothing to this.  Lead low from the table and cover any card played by East.  South scores one diamond trick, and the save is two down.

Things get a bit more interesting when South holds the ten.

Case 3:  South holds the ten and seven.

 

North
J863
Q108
South
K107
K976

 

Obviously, there are two losers if West holds the diamond queen.  If East holds the diamond queen, it looks like declarer can take two tricks by guessing who has the diamond nine.  If East started with Q9x, take two finesses.  If West started with A9x, lead a diamond to the ten and the ace, endplaying West.

 

This superficial analysis is pretty clearly flawed.  If West started with A9x in diamonds, West won't win the diamond ten, and declarer loses two tricks.  So, here too, the play is clear.  Declarer must play East for the queen and nine.

Case 4:  South holds the ten but no seven.

 

North
J863
Q108
South
K102
K976

 

It is probably best to start with a diamond to the ten, hoping West, with A9x stupidly wins.  However, against competent defenders, there will always be two diamond losers.  Another obvious one, right?  Well ...  I'll return to this one later.

Case 5:  South holds the  seven.

North
J863
Q108
South
K72
K976

 

Now we get to some meat!  There are two certain losers, and we want to avoid losing three diamond tricks.  We will certainly start with a low diamond from the table, and insert the seven, if we can.  But East puts up the ten.  What should South play?

 

Ducking could be right, but only if East started with Q109:

West
A54
North
J863
East
Q109
South
K72
D

and ducking would be the only way to lose three tricks in this layout:

 

West
AQ9
North
J863
East
1054
South
K72
D

It must be percentage to cover.  Anyway, you cover, losing to the ace, and a low diamond comes back.  Do you play West for the nine or the queen?

The nine.  This is Restricted Choice, right?  East had no option holding Q10x, but could play either the ten or the nine holding 109x. 

 

Okay, one more scenario.  This time East puts up the nine.  You cover, and a low diamond comes back.   Do you play West for the ten or the queen?

 

The same argument seems to apply, but it doesn't!  No sane defender would ever put up the nine holding Q9x.  Go back to Case 4.  Playing the nine foolishly blows a certain trick when South holds the K10 with no seven.  

 

When the nine appears, declarer should always put up the jack on the next round.  Interesting.  What does this mean?  For starters, the 109 holding is not a Restricted Choice position - a sharp defender will always play the ten, not the nine.  

Next, suppose declarer reasons that way, and concludes, as I just did, that "No sane defender would ever put up the nine holding Q9x."  Then, some maniac defender who did recklessly play the nine from Q9x would lose a trick in two layouts - where South has K10 but no seven, and gain a trick in the three layouts where West held the ten!

This stuff makes my head hurt. 

 

Anyway, back to my Case 4.  Apparently, against some devious defenders, you might actually score two tricks.  Has this ever happened?

 

I hate to 'fess up, but in that match, I did put up the nine from Q94, and looked like a total idiot when declarer held K102.  I spent much of the long, long drive home kicking myself for that moronic play.  Why would I ever do such a thing?  Then I began to wonder - maybe my instincts weren't completely haywire.  

 

This stuff makes my head hurt.

What is the right play holding my Q94, when the diamond three is led from the table? 

 

In many contracts, that will depend on our trick target.  If we need two diamond tricks to set the hand, then it is mandatory to play the four.  If, however, we need three diamond tricks to set the hand, then East must play the nine.  It is the only hope.  The trick target, when they have saved, is not so easy to determine.  I remember thinking, at the time, that, if declarer held the diamond ten, we couldn't make our game, so the save was a phantom. So I was trying to maximize our tricks if we could make a game.  In retrospect, that wasn't very clear thinking - the save was normal, and the contract rated to be the same at the other table.  I had to gauge the percentages in this contract.  How do I do that?

 

Like I said, this stuff makes my head hurt.

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