May 6, 2013

I didn’t find a lot to discuss in the play of the hands from Sunday.  Only one hand really caught my attention, board 11, where the contract depended on finding the best way to tackle a side suit.

 
We will get back to that hand in a bit.  But that concept, the best way to tackle various holdings, seems like a good topic for this week.  We call these suit combinations, and learning the best way to tackle various suits is integral to developing your declarer play skills.  Many books discuss suit combinations, and there is an excellent software program out that finds the best way to deal with any suit combination.  The program is called Suit Play, available as freeware at http://home.planet.nl/~narcis45/SuitPlay/

Let me start with a very simple suit combination:  Suppose you face

and need to win five tricks in the suit.  How should you play?

We can win all the tricks here if the suit splits out two-two.  We could also win all the tricks if West holds a singleton honor, say:

                      
by leading the five to the king, and finessing the ten coming back.  Of course, if we try that, we may end up losing a trick if West has both the queen and the jack, doubleton –

 

It is still best to finesse here.  Why?

The phenomenal author Terrence Reese came up with the term restricted choice for these positions.  If West held the lone queen, then West had no choice but to play that card.  If West held both the queen and the jack, West could play either card first.  As declarer, you would see the queen every time it was singleton, but only around half the time when West held both Q and J.  That makes the odds roughly 2-1 in favor of finessing. 

Okay, now let me make the suit a bit stronger:

                                                          
Again, you need to take five tricks in this suit.  What is the best way to play?

 
Here, again, we will cash a high honor.  If nothing interesting happens, we will cash the other biggie and hope for a 2-2 split.  If our honor fetches the queen or jack offside, then we will finesse next.  What makes this a bit tricky is that we could cash the ace or king first, to cater to a singleton honor in either hand, but, once we choose, we can no longer pick up the other hand’s singleton honor. 

As usual, we have clues from the rest of the play and the bidding as guides.  If East has shown a very long suit in the auction, then East is much more likely to be short in this suit, and so we would begin with the ace first.

New question:  Suppose you need only four tricks in this suit.  How do you play?

Is there any danger of taking only three tricks?  Yes!  Say we lay down the ace, and West shows out.  Suddenly East, holding QJ65 will take two tricks –

 

Likewise, if we start with the king, we could pay out if East has a void. 

In fact, we can guarantee four winners here, with a technique known in the jargon as a safety play.  Lead the seven from hand, and, if West follows low, play low from the table.  Think this one through, and convince yourself that you can always assure winning four tricks in the suit this way.
Here is the suit in a full hand:
 

 

You open 1NT, and partner raises to 4NT.  Since you only have fifteen points, maybe you should quit, but you bid 6NT anyway, because you like your five card club suit, and because you feel young, and lucky. 

West leads the ten of spades.  Plan out your play!

Counting up winners, we have three spades, two diamonds, and two or three hearts.  So five clubs will see us home, and four club winners might, if the hearts are friendly.  So, how do you tackle clubs?

You don’t, not yet.  You need to know more about the hand first.  Win the spade and try the heart finesse.  If it wins, play another spade and take the heart finesse again (just to be sure – sometimes tricky opponents let us win a losing finesse the first time).  If that wins, we can guarantee the contract by leading a low club and running it.  Maybe this is the full hand: 

 

Now, let’s suppose our heart finesse loses.  Then we need five club tricks.  We can start by laying down the ace or king.  Which is best?  

We don’t know yet.  Instead, delay the clubs for as long as possible, and play out the other suits, trying to learn more about the hand.  You can follow the play below to see how an expert declarer might handle this hand. 

Notice how declarer delayed playing clubs.  First declarer cashed out both major suits, finding that West started with five of each.  So, if anyone was short in clubs, it rated to be West, although, it is barely possible that West was originally 5-5-0-3.  Just to be certain, declarer cashed the diamond king.  When West followed, declarer now played a club to the king, and the queen appeared.  That meant twelve of West’s cards were known – five spades, five hearts, the club queen and one diamond.  The remaining card was either another diamond or the club jack.  So declarer cashed the diamond ace to find out, making the club play an absolute lock either way. 

It is quite amazing to watch a great declarer guess out every card, and it seemed like magic to me when I started.  Turns out, it is not magic, just careful counting. 

 

Moving on, let’s now imagine that we hold this club suit in a spade contract, and need two club tricks to see us home:

This is another suit combination.  What is your best play for two club winners?

We will need the suit to split 3-2,  and then the long card will set up.  There are two ways to generate one more winner.  We could try a finesse, and lead to the king, or we could duck two rounds and hope the ace comes down.  Which is better?

Many hands come down to these type of probability calculations.  The best line won’t always work, but, following the percentages will do you quite well in the long haul.  Here, leading to the king will work exactly half the time (assuming a 3-2 split).  How often will ducking two clubs work?  That is surprisingly easy to work out.  Which player is more likely to hold the ace – the one dealt two clubs or the one dealt three?  The three carder, by odds of exactly 3-2. 
The finesse will work 50% of the time, while the double-duck will win 40% of the time.  Take the finesse. 

Once again, let’s look at this suit when it is a bit stronger:

                                                         
Not much has changed.  We still will basically hope for a 3-2 club split with the ace onside.  However, it costs us nothing to lead a club to the ten on the first round.  We can still lead up to the club king later, and perhaps, we’ll get lucky and find this layout:

Here is another twist, making the suit a little stronger still:

As we have seen, there is no hurry in playing a club to the king.  It is better to try a club to the ten first, which will gain an extra trick on either of these layouts:   

                                                                                                   
or

There is another possible play – we could play a club to the seven or eight.  That would gain a trick on this layout:

 

and also work out when East has the singleton jack, or singleton queen, or AQ tight.  That works twice as often as playing to the ten, and so is a much better play.

Finally, consider this sequence: 

 

You correctly start by leading the club two to the six, eight, and jack.  When you get back in, you play another club from hand and West plays the nine.  Is it right to play the king or the ten?

Playing the ten will lose if East produces the queen – essentially if East had QJ alone.  Covering with the ten gains whenever West holds the queen.  Guess what!  We are back to restricted choice.  With both the queen and jack, East might have played either card.  Since you saw the jack, the odds are 2-1 that West has the other one, the queen.  So, cover the nine with the ten.

Here was the club suit from Sunday’s board eleven:

 

The best play for two club tricks was, as we have seen, to finesse West for the nine on the first round.  In practice, on the first club, the nine popped up, and it was right now to cover with the ten.  On the next round the queen would appear, and though the king would lose to the ace, declarer would win two club tricks, and the contract.  Unfortunately, declarer put up the king on the first club play, and finished one down. 

Here is the BBO movie of board 11:

 

One last point – if you choose to lead a diamond from a suit like AQJ942, the correct card to lead is the queen defending a notrump contract, but the ace against a suit contract.  Too often, in suit play, someone will have a singleton diamond, and underleading your ace will work out poorly.  Here, it didn’t matter, but swap partner’s diamonds with dummy’s, and the queen lead lost our diamond trick.  Likewise, if partner holds the singleton, we are much better off starting with the ace, and giving partner a ruff.