July 29, 2013

Let’s continue with our suit combination theme:  Try both of these club suits.

and

In both cases, find the best line to win four tricks, and the best line to win all five tricks.

There were lots of swings Sunday night, including some spectacular swings, but these were created almost entirely in the bidding, leaving me with little to discuss.  Even some of the quiet hands involved big bidding decisions, such as Board 3, where both tables played in 2NT, with 26 combined high card points and a nine card heart fit (six hearts was around a 50% contract, and would make as the cards lay).

The only big play swing came on Board 7, but that was worth 17 IMPs.  I’ll focus on that hand. 

First, my suit combination problems.  On the first,

 
four tricks are trivial if the suit splits 3-2, and there is no chance to win four tricks if the suit splits 5-0, so we can simply focus on the ten 4-1 splits.  Only a singleton king will help, and to cater to that, we start with the club ace.

To win all five tricks, we need West to hold a doubleton king.  Nothing else will help.  So, lead the club two or five to the jack and cash the ace next.

The second holding is more complicated:

Again, if we need only four tricks, we can look at the various 4-1 club splits.  Cashing the ace first works if either player has a singleton king or singleton ten – 4 of the 10 splits.  We do better by leading the queen first, and, assuming West covers, winning the ace and leading back towards our nine.  This gains a fourth trick when West holds the singleton ten or king, and when East holds the singleton ten, eight, or seven.  Notice, in this layout,

after the club queen is covered and won, and a club is played back to our nine and West’s ten, we have a marked finesse against the eight. 

Leading the queen first, and then back towards the nine, gains in 5 of the ten key splits, which is one case better than cashing the ace.  That’s the best line.

By the way, some of these probability calculations are easy, and others require some memorization, but you should become familiar with common odds.  For instance, a 3-2 split in a suit will happen around 68% of the time, and the suit will go 4-1 around 28% of the time. 

How did I come up with ten four-one splits?  Easy.  Either player could be dealt one of the five singletons.  Likewise, if the suit splits 3-2, there are 5*4/2 ways to be dealt two specific cards, so there are 20 three-two splits.  This means that a specific singleton holding will appear 2.8% of the time, and a specific doubleton holding will appear 3.4% of the time.  I’ll use these numbers in a moment.

Continuing on, what is the best play to win all five tricks with the second holding:

As in the first layout, we can run the suit if West started with a doubleton king, by leading to the jack, and cashing the ace next.  We could also run the suit if East was dealt a doubleton ten by leading the queen on the first or second round of the suit:

 

There are two other obscure holdings where we could, theoretically, run the suit.  Name those!

Obscure Position #1:

 

We start with the two from hand, and when the king pops up, finesse for the ten coming back.

Obscure Position #2:

 

Here, we start with the queen, king, and ace, and spot the seven or eight from East.  Then we could return to hand, and lead the nine next, running it if West plays the five. 

Obscure Position #2 is not one that I would ever play for.  If I go for that when I see the eight or seven fall, then I lose if East had either 108 or 107 doubleton.  It’s a fancy play that gains in one case, and loses in two.

Obscure Position #1 may not be so obscure – after all, if you lead the two and the king pops up, isn’t the ten marked?  Maybe …  Or maybe these are the cards,

 

Recall my arithmetic above – West will be dealt the singleton king 2.8% of the time, and the doubleton king-ten 3.4% of the time.  If we lead the two to the king and ace, and finesse coming back, we risk losing to the layout above, which is more likely than the singleton king.  That assumes, however, that West would always find the king play in this diagram.  Even the world’s best don’t always find that play. 

The king-ten doubleton of clubs has a special place in our sport’s history.  In the 1975 World Championships, Italy beat the US in the finals, in a close match.  Five boards from the end, came this hand:

 

  
   
The Italians had a huge bidding mix-up and wound up in seven clubs, needing a miracle in the trump suit, a miracle that was amazingly present, and the match went to Italy.  Had seven clubs failed, the US would have won.  Eddie Kantar, sitting West, wrote a great piece about this hand, which ran in Sports Illustrated,

http://sportsillustrated.cnn.com/vault/article/magazine/MAG1089534/index.htm

Read it – it’s a nice article.

The great Belladonna, declarer, trumped the heart lead, and led a trump to the ten and queen.  At that point, his face lit up, he looked to the heavens, called for the ace of trumps, and …
At the victory banquet, he was asked, “What would have happened had West played the club king on the first round of trumps?”  He answered, “the Americans would be World Champions today!”  Why?  See this link:

http://www.nytimes.com/2006/09/18/crosswords/bridge/18card.html 

So, to conclude:  In suit combination 2, our best play is to start with the two from hand, planning on playing the jack from dummy.  If West plays the king on the first round, we should probably believe it, and finesse the nine coming back, but an expert defender might have bamboozled us.  If the jack wins, we can either continue with the ace next, or cross to hand and lead the queen.  At this stage, the odds that West’s other card is the king or that East’s other card is the ten are the same.  There is no advantage to either play.  As usual, the bidding and play gives us distributional clues.  If West has more known cards than East, then West rates to be short in clubs, and we should play the ace next. 

The fall of the other club spot cards shouldn’t matter, but they do, and I tend to pay close attention to these. 

                          Look for the Middle Card

In this case, the three low, irrelevant cards were the 8,7, and 5.  If the eight or five are missing, we haven’t learned much, but if the middle card, the seven, is still out, then we know something.  We assume, as usual, that the cards lie in a way where our play will matter, so we assume that West started with the Kx or Kxx of clubs, and that East started with the 10x or 10xx in clubs.  When the seven is still out, after a club to the jack, then we know that one player has played the eight from honor-8-7, or the other player has played the five from honor-7-5.  Which is more likely?

Let’s assume, for starters, that you are playing against stodgy old folks like me, people who consider it immoral to give partner false count.  Then, all you need know is our carding methods.  If we use standard signals, the seven is with the five.  If we use upside down, the seven is with the eight.  If I am up against hot-shot juniors, I figure that they never give accurate count in these positions, so, as declarer, I reverse all of this.  True experts, in a case like this, vary their choice of card, and the spots won’t help you at all.

This suit combination arose in this play problem:

 
Looking at these cards, both six clubs and six spades are excellent slams.  At both tables, North opened one spade and South responded with a game-forcing two clubs.  At one table, North rebid three spades, which propelled them to the good spade slam.  At the other table, North raised clubs, which should have steered them to six clubs, but South, at the end, decided to play in six notrump. 
West found the best lead, the diamond seven, to the jack, king, and your ace.  You start on spades, but East discards the diamond four on the second round.  Unlucky.  Where do you go now?

Counting our winners, we have three spades, three hearts, and the diamond ace.  We can’t give up a spade, or we lose diamond tricks, so we have to score all five club tricks – suit combination two from above. 

All we know is that West has the spade length, so, given the choice between playing East for Kx in clubs, or West for 10x, the latter is more likely.  Best play is this:  Play the club two to the jack next.  If East plays the king, I’d trust it, and play a club back to the nine.  If the jack holds, I’d play heart ace, heart to the queen, throw a diamond on the good spade, and make my club guess.  A six-one heart split might change my mind, and I might rely on information gained from the club seven, but, most of the time, I’d play West for the short clubs, and continue with the club queen.

 
How would the play go in six spades, from North, on a diamond lead?

Similarly.  After the bad trump split, you need to guess clubs, but, playing in spades, you would have time to get a better count on the hand.  Here is one reasonable approach:  Continue trumps, discarding two clubs from dummy.  Trump the diamond return, lead a club to the jack, trump another diamond, and play three rounds of hearts, ending in hand. Follow the play using the next button below, and assuming fourth best leads and standard carding (I’ve rotated the hand to make South the declarer):

All that would be left is:

 There are only four cards out, the club king, ten, and eight, and one other card.  What is that other card?

If you don’t remember, go back over the play until you know.

The last card out is the diamond seven.  Who has it?

West, originally, held either

or

The fourth best lead of the diamond five is consistent with the first hand, so you should lead the club queen in the ending. 

 

Here was the full hand:

  

At the table, one of our newest, and youngest members, Cooper, played in six notrump.  After two rounds of spades, I think he decided to play West for the doubleton ten of clubs, and led the club queen next.  It was covered, and he noted West’s club seven.  He crossed to the heart queen, cashed the third spade, and now had to make his club play.  The odds favored leading the two to the jack, but he may have been considering Obscure Position #2, and leading the club nine, hoping for 87 doubleton on his left.  We’ll never know, because East discarded the club five on the third spade, resolving any guess. 

What happened in six spades?  Did declarer guess the clubs?  No – Ellie, East, led the club five.  Declarer, afraid that this was a singleton, and in a contract that was cold if trumps split, put up the club ace and could no longer make the slam.  Nice lead!  This was a well-earned 17 IMP swing.