Deductions by the Defenders

Deductions by the defenders

When you defend a hand you can either stick quite closely to the rules (or adages) you learned in your student days — such as “second hand low” and so forth — or you can occasionally attempt to improve your lot by breaking the “rules” whenever logic and deductive reasoning so indicate.

The first type of approach does not strain the mental faculties and, moreover, it assures you of a certain minimum standard of accuracy. But, in the competitive world of duplicate bridge, it does not guarantee super-duper results.

The second type of approach — drawing sleuthlike deductions from your opponents’ or partner’s bids and plays, using them to improve your estimate of the lie of the cards — is certainly the thing to aim at. But even this isn’t a bowl of cherries, for some of the deductions you make are bound to be wrong. (Your opponent or, heaven forbid, your partner, may have made an illogical bid or play, causing you to go astray when you attempted to base your deduction on it.)

For example, suppose you are West and lead the ♣3 against South’s contract of 2♠:
1.

Dummy
West ♣ A J 4
 ♣ 10 8 5 3

Dummy plays the jack, East covers with the queen and declarer wins with the king. Several tricks later you find yourself on lead once more and we’ll say that, based on developments to this point, you have formed the view that the correct play is to continue to attack clubs in hopes of setting up a trick in the suit.

It may now occur to you that there’s an element of risk in leading away from the ♣10: after all, declarer could have the nine-spot, in which case your lead would allow him to win a trick with it. Perhaps, you say to yourself, you should shift to another suit in the hope that East can win and return a club through declarer’s nine (if he has it).

To solve the problem, think back to the first round of the suit. Declarer would surely not have played the jack from dummy if the full layout happened to be something like this:
2.

 Dummy
 West ♣  A J 4  East
 ♣ 10 8 5 3  ♣ Q 7 2
 Declarer
♣  K 9 6

To put up the jack in this situation would be poor play, for the presence of the nine in declarer’s hand gives him an extra chance to win three tricks by playing low from dummy. Provided East hasn’t got the 10, declarer is then assured of three tricks no matter what; and even if East does have the 10, nothing is lost, because South can win the 10 with the king and finesse the jack on the next round.

Returning to Diagram 1, therefore, West should certainly proceed on the assumption that South hasn’t got the nine and that a second round of clubs may be safely led. At the same time, however, it has to be admitted that this deduction is something less than cast-iron. South may have goofed when he put in the jack — or he may have had some kind of mysterious motive which you couldn’t possibly be expected to figure out. When you act on this type of deduction, therefore, you do so in the full knowledge that you may occasionally end up with egg on your face. Unfortunately, you just have to live with this, especially when playing against inexperienced performers.

However, there is one class of deduction that does not depend on the motives or relative skills of your opponents. This type of deduction is based on the actions of none other than your illustrious partner. The idea is to concentrate on the plays your partner has made in order to understand what he’s trying to do. (After all, someone should.)

Coming down to cases, you start by asking why your partner has led a certain suit. What does it tell you about his holdings in other suits? How many cards is your partner likely to hold in the suit he has led, and what is the full layout of the suit likely to be? Suppose you are East in this situation:

 Dummy
 West   10 5  East
  3 led   A 9 4
 Declarer

West leads the 3 against South’s notrump partial. Nine times out of 10, of course, it will be correct to win the ace and return the suit — partner just might have been endowed by Nature with the K-Q-x-x-x or K-J-x-x-x. Before doing anything, however, you should review the bidding , study the dummy, and see what you can deduce about the hand. It may become clear that it is impossible for partner to have five hearts, in which case you would have to consider playing the nine rather than the ace. The layout could be something like this:

 Dummy
 West   10 5  East
  K 8 6 3   A 9 4
 Declarer
 ♥ Q J 7 2

If you play the ace at trick one, declarer automatically gets two tricks in the suit, but if you insert the nine instead, he can be held to one trick.

Some inferences from the opening lead are very obvious, others are less so. If your partner leads an eight or nine it is likely that he holds no high honors in the suit. If he leads a low card against a notrump contract, you can usually assume that he is leading fourth best from his longest suit. This much is routine. From there you can go on to consider other possibilities: the very fact that your partner has led a particular suit almost always tells you something, however slight, about his holdings in other suits. For example, suppose you are East in this situation:

Dummy
♠ A 10 9 3
8 7
J 6
♣ A Q J 10 2  East
 ♠ K 7
  Q J 9 6
  10 8 7 4 2
 ♣ 6 3
West North East South
1♣ Pass 1♠
Pass 2♠ Pass 3NT
Pass 4♠ All Pass

Your partner leads a low heart and declarer takes your jack with the ace. Declarer returns the queen of trumps and plays low from dummy, losing to your king.

It is just within the realm of possibility that you can beat this contract: after all, your partner could have the K and the A-Q. It is much more likely, however, that you cannot smite the declarer low, and that the best you can do is to avoid yielding unnecessary overtricks. In this connection, the question of whether to return a heart or a diamond is of some importance.

If your partner has the K, you can simply cash the jack of the suit and them lead a diamond. By this sequence of play you ensure getting all the tricks that belong to you.

But if declarer has the K, returning the jack would hardly be a great ply. Declarer would win and eventually divest himself of some number of diamonds on dummy’s clubs. To make matters worse, your partner would probably exchange one of those maddeningly significant glances with you as he stuffed the A-Q back in the board.

There is no completely reliable way of selecting the best return, but you can draw a deduction of sorts from the opening lead. The bidding has marked South with considerable strength in the red suits and therefore it is not likely that your partner would lead away from an unsupported K if he had any choice in the matter. Lacking a sequence of honors in either of the red suits, he would be more likely to lead away from 10xxx than from Kxxx. Therefore it is probably best to return a diamond, even though on a purely mathematical basis your partner would seem more likely to have the K than the AK.

(continued next week)