How Deeply Can You Think Ahead?

In this column I’ll ask a question whose answer I don’t know. During Silver Linings Week, I encountered the hand described below, fortunately as declarer, not as defender. I hope the readers will answer in the Replies. You’ll be East facing the defender’s problem. 

Here’s enough to get started. 


Click NEXT to see the play

Opening Lead:  ♣6.

West led the  ♣6. North played the ♣Q, East the ♣K, and South, the ♣A. South then led the 2 to A.  On the third trick, he led the 6 to East’s J, South’s Q, which West won with the  K.  West continued with the  ♣3, which South won with the ♣10. South plays a third round of diamonds on which all show out and a third round of clubs on which West shows out.  You can play along by clicking the NEXT button in the hand diagram above.

After six tricks, you now have a full count of all four hands in the minor suits.  South had seven diamonds and four clubs.  His major suit holdings could be:  2=0 or 1=1 or 0=2.  You can foresee that at trick 11, dummy will lead one of the major suits and you will have to decide what to do to be ready for that blind choice.  Declarer might at that time hold one of the following layouts, where we have less notion of his heart than his spade holding.  Let’s guess he has the heart Ace and if a second heart, one lower than West’s second highest card.  That is, declarer might hold the heart Ace, but if so, he doesn’t hold the Queen.  He might not hold the Ace.  Here are declarer’s possible layouts, not all equally likely:

You will hold three cards.  Start with the notion that you should hold ♠A K8. 

If declarer holds: 

  • Case A, you can win only one trick; or
  • Case B you can win one trick, or
  • Case C, you can win one trick; or
  • Case D, you can win one trick; or
  • Case E, you can win one trick.

From East’s perspective if he holds ♠A K8, no matter the layout of the cards in Cases A – E, East will win one trick. 

Now, consider the five cases if you as East hold  ♠AQ  K.   

If declarer holds:

  • Case A, you can win only one trick; or
  • Case B you win no tricks; or
  • Case C, you win one trick; or 
  • Case D, you win two tricks; or
  • Case E, you win one trick.

Here, you win an average of one trick in each of the five cases—one each in three, two in one, and zero in the fifth. 

What do we think? Winning one trick in all cases is likely better than winning two sometimes and zero others. So, I think I would prefer to plan to hold  ♠A  K8. This is preference, not analysis.

Now, what about West?  Suppose West holds the A.  His top spade might be the King or it might be the ten.  He faces the same problem as you, with spades and hearts reversed.   Symmetric reasoning suggests he should hold  ♠ K10  A. 

How hard is this thought process at the table?  Nearly impossible I’d say—and maybe, not necessary. At my table, East played as though he thought Case D was likely; he held two spades, Ace and Queen, and the singleton heart King.   Meanwhile, West played as though he carried out the analysis of the five cases above and held:  ♠ K10  A. 

I, as South, held Case E:   Q 5.  When I lead the 9 from North at trick ten, I saw East play the K; I played my 5 and with a twitch watched as West played … the A.   Perforce, West lead a spade, which I trumped and won the 13th trick with the Q.   I got more pleasure from this triumphant pseudo-squeeze than I had from any real squeeze in memory.  I planned it and it worked as planned. 

Experts can handle the defense on this deal.  BBO'er Strategyst showed me one way.  West is to discard from his short suit, spades.   If he discards only once, then South must have a doubleton, cases A and D, but the discarded singleton will tell East which.  If West discards two spades, then East will know which singleton South holds.  If West discards three spades, then East knows South holds only hearts.  Easy when you think of it, which I didn’t.  Wouldn’t work in all cases, but would with these hands.

Another expert, BBO’er MiamiJD, suggested signaling length will solve the problem, as it would here.  I learn from the quick sure responses from two experts that there likely is no general answer, but that partnerships should spend the time to have understanding for these matters. 

Not that this could affect the analysis I sought, but perhaps you get closure from seeing the actual deal.

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4 comments on “How Deeply Can You Think Ahead?”

  1. Silly problem. W must have all of the missing major honors, except possibly the heart Q or J . So, you don't need to worry about S's distribution. The only issue, which the discussion takes forever to reach, is how to communicate with partner about what to keep. In the absence of agreement, it seems very clear to discard hearts before spades, lowest first up to K. That will tell partner he must keep hearts and will give him a count of the heart suit.

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