From                   1st October, 2008

                                          Difficulty            * * * *

East’s 2♠ is alerted as showing 4-card support, and West leads the K♠ against your 4♥ contract.  Next, West cashes the Q♠ and shifts to the T♦.

How do you propose to make 10 tricks?

SOLUTION

The bidding and the play so far tell us that East has all of the missing HCP’s, with the possible exception of the J♥.  Declarer’s trumps are not good enough to make 10 tricks on a cross-ruff so the Clubs will need to be established.  That being so, the two obvious lines of play are:

-         Line A: Play A♣ and take a ruffing finesse against East’s K♣, hoping that the suit is 3-3.  Once the K♣ is flushed out, Declarer draws trumps ending in Dummy.  If trumps are 3-2 it’s 11 tricks, otherwise it’s curtains.

-         Line B: Play A♣ and ruff a low Club, hoping that East started with two Clubs.  As before, if trumps are 3-2 it’s 11 tricks, otherwise it’s down.

What are East’s possible distributions?  It seems like the only relevant ones are:

            4=1=5=3         4=2=5=2         4=2=4=3         4=3=4=2

We’ve eliminated 4=3=3=3 (most players open 1♣ with that), and 4=1=4=4 (contract cannot be made if East has 4 Clubs), and more extreme distributions where the contract has no play.

Let’s assume that each of the 4 relevant distributions have an approximately equal probability.  If so, in the universe of makeable distributions, Line A works 25% of the time, and Line B works 50% of the time (4=2=4=3 works, but not 4=1=5=3 which fails because of the 4-1 trumps).  Well, 50% is better than 25%, so you go for Line B, eh?

Not so fast!  There’s a Line C which wipes the floor with both A and B!  If Declarer finesses the T♥ on the second round of trumps he can greatly improve his chances.  Yes, really!  The suggested line is: Lose the 2 Spades, win the A♦, cash K♥, over to the A♣, Q♣ covered by the King and Ace, finesse the T♥!  This line gives Declarer an extra entry whenever the Jack is with East, and that extra entry makes it possible for Dummy to ruff two of Declarer’s Clubs, catering for East having 2 or 3 Clubs, not just one or the other.  Here is the full deal:

What are the probabilities of success for Line C?

-         4=1=5=3:  Score up all 25% for this one (when East shows out on the second round of trumps, Declarer runs the Clubs, pitching Diamonds  … West can ruff, but he has no Diamonds left and Declarer still has a Heart entry for the rest of the Clubs).

-         4=2=5=2:  Makes when the Heart finesse works, which it should do 60% of the time (because West started with 60% of the Hearts).  60% of 25% gives a 15% score.

-         4=2=4=3:  Similarly, this line also provides a 15% score.

-         4=3=4=2:  Similar logic, but the finesse will only work 40% of the time in this case, so score up just 10% more.

Add it all up and you’ll get a whopping 65%!  Line C is the winner by a handy margin!
 

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