Dormer on Deduction

Deductions from the Defender’s Plays

Robert Burns, Scotland’s national poet — he was the chappie, you remember, who so aptly remarked that the best laid schemes of mice and men often get all fouled up — made a very good point when he said:
Oh wad some pow’r the giftie gie us
To see ourselves as others see us!
It wad frae mony a blunder free us.

There is little doubt that what Burns meant was that the declarer, when faced with a tough hand, should try the effect of studying it from the angle of his opponents, remembering that what is obvious to him may be far from obvious to them. Declarer may then be able to draw some highly valuable deductions from the way his opponents have elected to defend.

Consider these two very common situations:

1.

North
A K J
South
10 4 2
2.

North
A K 2
South
J 10 4

Looking at either one of these combinations you would have no difficulty in coming to the conclusion that you have a 50% chance of winning three tricks in the suit, no more, no less.

Now let’s suppose that, along about the middle of the hand, West, with several options open to him, elects to lead a low card of the suit. How would you say the fact that West has led the suit has affected your chances of making three tricks in it?

In (1) there are no real grounds for changing your diagnosis. West can see the A-K-J in dummy and he knows you can take a finesse in the suit any time you like, whether he leads it or not. So the fact that he has led it makes little difference to your chances.

In (2), however, West would take quite a different view of the situation if he held the queen, since he has no way of knowing that you have the J-10 of the suit and are in the position to take a finesse under your own steam. Accordingly, West would have to allow for the possibility that you hold the jack without the 10, in which case leading away from the queen could prove a grave indiscretion on his part. For that reason alone, West would be less inclined to lead away from the queen than he would in the previous example. Consequently in (2) — once West has led the suit — there is less than a 50% chance of the finesse succeeding.

This is simple enough, no doubt, but nevertheless you can easily miss the opportunity for this type of deduction unless you cultivate the practice of trying to look at matters through your opponents’ eyes. Here’s another example, equally simple at first sight, but in reality more subtle:

1.

North
A Q J
South
7 6 3
2.

North
A J 7
South
Q 6 3

Let’s say that in the first example, West, during the middle of the game, leads the two and dummy’s queen holds the trick. This is most delightful, you may say to yourself, but when you stop to think about it you realize that although the finesse has apparently succeeded, you really know very little about the position of the king. West may well have led away from it because he can see to do so gives nothing away, or he may have led away from it because in the fullness of time he hopes to win the fourth round of the suit. At the same time, it is almost equally possible that East is holding up the king, expecting you to repeat the finesse later on.

In the second example, you have the same high cards in the two hands, but because one is not visible to West, the situation is radically different. Let’s say that West again leads a low card of the suit, dummy plays low, East puts up the 10 and you win with the queen. Who would you say has the king?

This time it is highly likely that East has it, for if West had it, he would be very disinclined to lead away from it. It would be obvious to him that leading away from the king would give away a trick whenever you held the queen or 10 in the closed hand. In this case, therefore, you should assume that East, in playing the 10, has made a normal finesse against the dummy holding K-10-x of the suit.

Before going further, it may be well to remind ourselves that the trust to be placed in this type of deduction depends to some extent won the standard of the opposition. The more competent they are, the safer the deduction. More often than not it will pay to assume that your opponents are playing intelligently. But by the same token you should not assume that they can see through the back of the cards.

Frequently declarer has to try to figure out whether an opponent has underled an ace. It is very well known that against a suit contract, defenders seldom underplay an ace on opening lead. But they frequently do resort to the maneuver later during the play and therefore — on the surface — it may seem that you have to spin a coin in such situations as the following:

1.

North
5 2
South
K J 3
2.

North
J 4
South
K 5 3

Let’s say you are at a trump contract and this is a side suit. Your only object is to avoid losing two tricks straight off when the opponent on your right leads a low card in the suit.

It may appear that you have exactly the same chances in (1) as you have in (2), but this fact is not the case.

In the first example it is true that you have very little to go on: the chances are that even Sherlock Holmes himself would end up studying the ceiling or employing one or another of the time honored methods of gaining inspiration. East didn’t have to lead the suit, but from his angle there can be no harm in leading it, no matter what his holding may be. The fact that he has led it makes you none the wiser about the location of either the ace or the queen.

IN the second example, however, assuming East has one of the missing honors, there is a very strong inference that he has led away from the ace, rather than from the queen. The reason is that in this case East can see the jack in dummy. This means that if he leads away from the queen and you then guess correctly and play low, he has given you a trick you could neber have made if left to your own devices. Of course, if you guess wrong and put up the king from K-x-(x), you will lose two tricks in the suit — but the point is that you would have lost them anyway.

Conversely, if East happens to have the ace rather than the queen, he would reason that leading away from it may provide the only hope of obtaining two defensive tricks in the suit if you have K-x-(x). He knows that if this is indeed your holding, when the time comes for you to tackle the suit yourself, you will have no choice but to lead from the dummy toward your king. East would therefore certainly be very strongly motivated to underlead the ace if he had it, and even if his plan fails, he will still get the trick he was entitled to later on.

The foregoing examples prove the point that if declarer takes time out to consider how matters may appear to his opponents, he may be able to improve on the normal percentage chances. The same idea cuts both ways, and in the following example it is East who should ask himself how the situation may look to declarer.

6 3
10 8 7 5 K J 2
A Q 9 4

Let’s say South is at a trump contract and this is a side suit in which declarer can afford no losers. Before drawing trumps, he leads the suit from dummy, finesses the queen, cashes the ace, and then leads a low card with the intention of ruffing.

If East has played his deuce and jack on the first two rounds of the suit, declarer will know for sure that he can ruff the third round low with safety. This knowledge will certainly make him a happier man than if he had to contend with the possibility of an overruff.

To deny declarer this comfort, the king should be played under the ace on the second round. East’s jack of the suit is just as good as the king once the queen has gone. This play is made not so much with the idea of fooling declarer as to prevent him from drawing a cast-iron inference about the card or cards remaining in East’s hand.

This same principle is of very widespread application and may be stated thus: “Whenever he can do so without loss of a trick, a defender should play a card that he is known (by the declarer) to hold, rather than another card which the declarer does not know him to hold.” You can see the value of applying this principle in a situation like the following:

A 9 7 4
8 6 2 Q 10 3
K J 5

Declarer (South) leads the four from dummy, finesses the jack and then cashes the king. If East mechanically follows with the 10 when the king is led, he is simply making a bed of roses for the declarer who will continue with a third round of the suit and will know — when West produces the eight — that the queen is absolutely bound to fall under the ace.

East should therefore play the queen when the king is led. East is already known — by declarer — to hold the queen, but declarer cannot know who holds the 10. Now, when declarer plays the third round of the suit, he will not know whether to go up with the dummy’s ace or finesse the nine.