June 3, 2013

Lots of interesting hands last night, and lots to discuss.  Let me start you off with two new suit combination problems.  You are playing in four hearts, and will make the contract if you can hold your trump losers to one.  Here is your trump suit:
(1)

You lead the two from the table, and East plays a low card.  What do you play from hand?

I’ll get you started on this.  There are two real choices,
Line A:  Play the suit from the top, A, K, ten,
Line B:  Finesse, sticking in the nine or the ten.  Then play the suit from the top as soon as you can.

You will always succeed in four hearts if trumps break 3-3, and you are always going down if trumps break 5-1 (or 6-0).  Nor will your play matter if East has a doubleton heart.  So you can ignore all of those cases, and focus on the key splits – where East started with four trumps, and West a doubleton.  Take it from there.
(2) Again, hearts are trumps, and you can afford one loser.  This time, trumps are

  
Line A is the same, but line B now has two subcases.
B1:  Finesse, and if the finesse loses, play the suit from the top.
B2:  Finesse, and if the finesse loses, go back to dummy and finesse again.

Choose your line.

I’ll come back to these, but first, I want to look at Board 2, a defensive problem, where the key was, come on, say it, COUNTING. 

             

With East-West vulnerable, South dealt, and opened a weak notrump (11-13), and everyone passed.  You start with your fourth best heart, won in dummy with the queen, as partner plays the nine, standard carding, probably showing an even number.  Dummy plays a diamond to declarer’s jack, and you give count with the ten.  Declarer continues with the diamond queen, won by partner with the ace.  Partner returns a heart, and you start running your hearts, as declarer also shows out on the third round.

Time for the usual questions:

1. How many tricks do you have coming so far?
2.  You need more to set one notrump.  How many?
3.  How are the diamonds split?
4.   How many tricks can you count for declarer?
5.  How many points has South shown so far?
6.  How many more points will South hold?

And, of course, how should you defend?

Answering these:

 

1.     Five.  Four hearts and partner’s ace, so
2.    You need two more.
3. Partner would not win the second diamond, letting the suit run, if partner held three diamonds.  So partner started with either two or four diamonds.  Given that South had only two hearts, odds are that partner, not South, had the doubleton diamond.
4.  So South has a heart trick in, and, apparently, four diamond winners to come.
5.  South has shown up with six points, the heart king, and the diamond queen and jack.
6. Since the opening showed 11-13, South will produce 5-7 more points.

Partner will need another ace to set the contract, but, since South has at most seven more points, partner must hold an ace.  If partner holds the spade ace, we can simply take two spade winners.  If partner holds the club ace, we can hope to get that trick and a spade. 

It feels like we should run our hearts, and then play the spade king.  That sets the hand if partner has the spade ace, or if partner has the club ace and the spade queen.  Could this play cost?

Yes, but only if South has both the spade ace and queen.  That’s twelve points, and so partner will have almost everything else, including the ace, king, and queen of clubs.  Surely partner would have played a big club with such good clubs, so this defense should always work.

 
Here is the full hand:

Warning:  It’s going to get pretty advanced now!

During practice a couple of weeks ago, Stan discussed giving suit preference signals in the way you play your cards on defense.  Here, East played the heart nine at trick one, to give count, but could play the remaining hearts in any order, and those orders can be used to give various messages.  Likewise, the order that you, as West, cash out your hearts has a meaning.  Let’s really make this tricky, and have South opening a strong notrump.  Again, you, as West, will place partner with a black ace, as the only hope.  The cards might look like this, where you need to cash two spades:

 

Or maybe they look like this:

 

To set the hand here, you need to get partner to play a spade through.  Can you do that?  Maybe.  You can force partner to win the fourth heart by playing your deuce on the fourth round!  Then, if partner knows enough to play a spade through, you will set the hand, on either layout.  How could partner know to play a spade, and not a club?  By the way you cash your hearts!

If you wanted a spade, as here, you win the heart king with the ace, leaving you with J102 in hearts.  Now you play the heart jack, then the two to partner.  If, instead, you had the club king, you would play heart ten, heart two. 

Bridge is an amazing game. 

Back to the actual hand.  At the table, East returned the heart eight, then followed with the seven, finally the three, and discarded the spade seven on the fifth heart.  If the heart plays really were intended as suit preference, then East screamed for a spade three times!  Good defense?  I’m not so sure.  What if this were the full hand:

 

This time, West needs to find a club shift after running the hearts.  How can East tell?  East can’t.  East needs partner to lead from strength.  A club shift is fine if West has a club honor, and a spade shift is great if West has a spade honor.  So East, with goodies in both suits, should really try to signal complete neutrality.  I think East should return the seven of hearts, then play the eight, and then the three, trying to suggest stuff in both suits, with better spades. 

Bridge is an amazing game. 

Onward, hopefully to easier stuff.  Let’s look at the two suit combination problems. 

For (1)

 

I suggested you consider only various doubletons with West.  Line A, banging out the ace and king loses when West holds two small cards.  We can list all of these cases:

                                                      87, 86, 85, 76, 75, 65

Six cases in total.  You may recall from math classes – C(n,r), the number of ways to choose r things from a set of n.  There are four spot cards out, and West can be dealt two of them in C(4,2) ways, or 6 ways.

Line B handles these doubletons, but loses if West has a doubleton queen or jack, any of

                            Q8, Q7, Q6, Q5, J8, J7, J6, J5.

Eight losing cases, so line A is better by two full cases.  According to the software I recommended, SuitPlay, line A will succeed 64.6% of the time versus 61.4% for line B.  A is more than three percentage points better.

For (2),

we have a third option, B2, finessing twice.  This picks up all of the doubletons with West listed above, but loses when West has QJ tight, or QJx.  It loses in five cases, and so is now the best of the lot.  According to SuitPlay, line B2 will work around 65.6% of the time. 

If you worked these out, bravo.  That brings me to the declarer play problem faced on board five:

South was in four hearts on the simple auction, with N-S vulnerable:

West led the spade queen, overtaken by East with the king, and a trump came back.  We can get rid of a spade quickly on the clubs, but that still leaves us with two spade losers.  To make four hearts, we need to hold our heart losers to one.  Which of my two suit combinations is this?  (Careful, the answer is not as obvious as it seems.)  How should you play the hand?

This appears like combination (2), but that is deceptive.  If you opt for B2, and finesse, planning to finesse again, the defense can continue spades, and force dummy to trump, depriving you of the trump needed to finesse twice.  So, in essence, you won’t have the luxury of taking two finesses, which makes this combination (1), and line A is best.

 
Still, there is more to the hand than tackling trumps.  Suppose you opt for line A, and play ace, king, ten of trumps.  Will anything bad happen? 

Of course, the defenders will win and cash two more spades!  So, at the table, declarer cashed both high trumps, then played three rounds of clubs, discarding a spade.  Here was the full hand:

After discarding the spade, there were still two trumps out, so South came to hand with the diamond king, and played another trump.  That left this ending:

East played ace of spades, and a spade.  South trumped, and claimed.  Instead, East should have played the spade nine over to partner’s jack, to get a diamond ruff.  That would be a neat defense.

South should have anticipated this pitfall.  There were two reasonable solutions.  After the heart ace, take the clubs immediately, then continue trumps.  That would work here, but risks problems if clubs were 6-2.  Alternatively, declarer could finesse immediately in trumps, choosing the slightly inferior line B.  That avoids any dangers of diamond or club ruffs, but would fail on this layout, if the defense wins the trump and continues spades.

Let’s back this up even further.  At trick one, East could see this:

 

Setting four hearts looks pretty hard facing such a good dummy, but East could hope to win two spades and a trump.  Where would a fourth trick come from?  How about a diamond ruff?  The best defense is to overtake the queen of spades with the king, and shift to the singleton diamond.  On this layout, this defense kills the contract.  The best declarer can do is discard a spade, and play hearts from the top, but East wins the third heart, underleads the spade ace, and gets a ruff. 

Opportunities to underlead the top two spades to get a diamond ruff must be pretty rare.  When was the last time you saw such a play?  Turns out, the previous board!  Here was board 4, from West’s perspective:

The lively auction, with both sides vulnerable, was

West started with the spade ace, which won the trick.  That is quite a good dummy, and it feels like declarer will win seven heart tricks, and the four in dummy, for eleven.  Prospects look poor, but West could see one big defensive plus – the diamond void.  So West underled the spades, hoping partner could win the queen and play back a diamond.  Great defense!

The good news – partner produced the spade queen.  The bad news – declarer trumped it.  Oh well.  Nice try.