A Declarer Play Problem

I was playing with a client in the senior pairs at the NYC regional on May 25, 2006, and I after the auction listed below I faced the following declarer play problem. 

I was lucky to get a trump lead.  That gives me time to try to set up a trick in diamonds so I can discard one of my black losers.  How would you play the hand?

This auction would not occur with my top partners.  With them I play 2§ as Drury over a 1ª overcall.  I would rebid 2© and stop one level lower.  But here I was playing with a client, and we were not playing 2§ as Reverse Drury over the spade overcall.  If you have seen some of my other hands of the month, you would have seen that I like to open the bidding with very weak hands in 3rd seat, so Drury is vital with my style.  This hand is much stronger than my minimum, but even here we are overbid at the 3-level.

So it was my job to find 9 tricks, and there is only one suit where I can produce my 9th trick.  I can either play for: 1) a 3-3 diamond break, 2) a 4-2 diamond break with a doubleton honor, guessing who has the doubleton honor, or 3) for both the King-Queen of diamonds onside.

A 3-3 diamond break is 36%, and that seems to be much more likely than a 4-2 break with a doubleton King or Queen.  More specifically, one honor doubleton is around 26% and two honors doubleton is an additional 7%.  So, for RHO to have that holding would be half of that time, with LHO having the key holding the other half of the time.  So without other considerations, to play for LHO to have ¨Kx or ¨Qx is around 13%, and to play RHO for either ¨Kx or ¨Qx or ¨KQ is around 17%.  But there is a clue from the bidding that makes it less likely that RHO has only 2 diamonds.  Since LHO apparently has 5 spades and RHO has only 2 spades, that means that LHO has only 8 non-spade cards, and RHO has 11 non-spade cards.  Furthermore, it would not be surprising to find LHO having a diamond honor as part of her values for overcalling, while RHO never bid is less likely to hold both the King-Queen of diamonds.

But, in all cases, a 36% diamond break is much more likely than some percentage action less than 20%.  So, a 3-3 diamond break is the most likely play.

But there was something else very interesting.  My LHO had led a trump on opening lead, so apparently was nervous about leading from her black suit holdings.  I could imagine that my LHO held something like the King-Jacks in the black suits, and was afraid that an attacking opening lead would give me a free trick.

I wanted to find a way to give myself additional chances to pick up 2 diamond tricks, while keeping the 3-3 diamond break as my main chance.

Can you imagine how I played the hand?

I wanted to keep my LHO on lead, so she might keep from attacking in spades.  While I can use the heart as an entry to the last diamond if diamonds break 3-3, I might be able to handle a 4-1 heart break if the spade entry remains in dummy.

So, to give myself additional chances beyond the 3-3 diamond break, I won the first trick in dummy and led dummy's ¨8.  My RHO covered very quickly with the 9 (implying holding the 7), and I finessed with the 10, losing to the King.  Back came another heart.  So I won that in dummy (RHO following suit), and I led the ¨J from dummy.  My RHO covered with the Queen, and I won the ace.  I now drew the last trump, and led the ¨4 to dummy's 5, losing to the 7.  But now dummy's ¨6 was higher than RHO's 3, so I made the contract.

This was the entire hand:

 It turns out, that as the cards lie, that my LHO could have beaten the contract with my line of play, by attacking in spades at trick 3.  But upon seeing dummy, she had no reason to find the spade play at trick 3 that was unappealing at trick 1.  So, by playing as I did, I ended up making the contract with a 3-3 diamond break, and also with many of the 4-2 breaks. 

I was going to duck the diamond 9, if my RHO had played small.  I was aware, that if diamonds were going to break 4-2, that it was much more likely that my RHO would have 4 and my LHO would have 2.  Therefore, if diamonds were 2-4, it was twice as likely that my RHO held the 9 than my LHO.  Finally, I had to choose on the second round of diamonds to either finesse for the ¨7, or to lead the ¨J.  Leading the ¨J is best if my LHO has the ¨K7, while leading small is best if my LHO began with the ¨KQ.  It is not clear to me which of these two finesses is the best percentage.  Without table presence, I like the odds of playing for split honors, but since RHO had covered dummy's ¨8 without any hesitation, it certainly seemed likely that he held the ¨7.  With the actual layout, it was not surprising that both lines of play worked.

I could easily have chosen to win the second round of hearts in my hand, and then entering dummy drawing the last trump.

I wanted to present this hand, as a cute example of how you can make use of small cards to give yourself extra chances to make your contract.  I hope you enjoyed the analysis.  If anyone wants to learn how I calculated the odds of the 4-2 diamond breaks, I will be happy to respond to an email.  My email is hand_jeff@hotmail.com.