Dormer on Deduction

More inferences from the opponent’s actions

Remember the fable of the donkey and the two bundles of hay? The bundles were equally lucious and the donley couldn’t make up his mind which to eat first. EVentually he starved to death.

Declarer often finds himself in a rather similar delimma when there are two or more ways to play a hand. Slight differences in percentage chances are difficult to calculate — and may mean little when you have calculated them. In actual practice, it is far better to solve close problems by good old deduction — that is, by drawing inferences from what the opponents have or have not bid. For example, let’s say you are declarer on this hand:

North
♠ 6 5
9 8 5 3
A K Q 6 3
♣ 7 4
South
♠ K J 4
Q 10 2
5 4
♣ A K 8 6 5
South North
1♣ 1
1NT Pass

West leads the ♠2 and East wins the ace. East returns the ♠3, your jack loses to the queen, and a third spade is played to your king. How do you continue.

It is evident that East started life with the ♠A-x-x-x and West with the ♠Q-x-x-x, so the opponents have only one more spade trick to cash. You therefore have quite a wide freedom of action, and in fact there are three reasonable things you could do.

  1. You could duck a round of diamonds in anticipation of a 4-2 division. If such division does exist, the duck is quite essential, both to establish the long diamond and to maintain communication with dummy. As long as you duck a diamond, you are likely to make the contract with four diamond tricks, two clubs and a spade, unless the opponents switch to hearts and you are able to cash three tricks in that suit.
  2. Alternatively, you could cross to dummy with a diamond and lead a heart towards the Q-10-x, inserting the 10. If West is forced to win the ace or king, you should have a very good chance of gaining a seventh trick by later leading the 9 toward your queen for a second finesse against East’s jack. This line gives you an additional chance, for after entering dummy with a second diamond, you can try to split the diamonds 3-3 before leading the heart. If the diamonds do divide you will make eight tricks for +120.
  3. Finally, you could simply try to split the diamonds 3-3 immediately — admittedly only a 36% chance — but if this works, you come home with an extra overtrick. Of course if diamonds are 4-2, your contract almost certainly goes the way of all flesh.

Before making a decision, another consideration enters the picture. As you know, it is sometimes — but not often — permissible to risk your contract for an overtrick. On this deal East-West have almost half the deck — and eight spades — between them, and there is thus a strong possibility that they may enter the suction at some tables. If so, some of the North-South pairs may wind up collecting a penalty of 100 points. This means that you stand to gain more matchpoints by going for a risky 120 than you stand to lose by going down one at your contract.

Taking everything into account, the three lines of play are very close together, and if you try to solve the problem by mathematical methods you could wind up suffering a fate similar to the poor old donkey’s. Do not attempt such a calculation: It is more sensible to flip a coin, or say eeny-meeny-miny-mo. But best of all is to see what you can deduce from the opponent’s bidding — or rather, in this instance, their lack of bidding.

Either opponent could have entered the auction at a low level, but didn’t. If the diamonds had been breaking badly, it is just a little more likely that one opponent or the other would have a hand that merited some form of competitive action. On this reasoning declarer would be justified in going for the big score by adopting line 3.

Remember the reasoning, for it can simplify many decisions that would otherwise be very difficult. If the opponents don’t bid when you expect them to bid, your suits are likely to break favorably. If the opponents do bid when you didn’t expect them to, your suits are likely to break badly. Naturally, you have to take the vulnerability and other factors into account.

The same type of reasoning applies even more strongly when the opponents enter the bidding, find a fit and then drop out below the three-level. This suggests that your trump suit is likely to break well: if either defender had been short in the suit, the opponents would have been that much more likely to contest to the all important three-level.

Conversely, if the opponents do contest to the three-level, you can often draw a similar inference. For example:

Dlr: South North
Vul: All ♠ J 10 7
K J 6
J 10 4
♣ A 6 4 3
South
♠ A 8 6 5 3 2
A Q 4
♣ J 8 52
South West North East
1♠ 2 2♠ 3
3♠ All Pass

West leads the K which you ruff. You lay down the ace of trumps and both opponents play low. What now?

If the trumps are evenly divided you can probably make an overtrick by simply playing another trump and then conceding two club tricks , establishing a long club whenever the suit breaks normally.

If the trumps are 3-1, however, and you play another one at this point, you will end up with a minus score. The opponents will draw a third round of trumps and force you in again in diamonds, reducing you to one trump with the clubs still untouched. You will never be able to establish the long club you need to make the contract.

The vital club trick could be established, of course, if you tackled the club suit immediately after laying down the ace of trumps. You would then be a step ahead of the game and could expect to set up the long club in time. The disadvantage of this plan is that the opponents would be able to make their trumps separately, even if they are 2-2, and this may give away a valuable overtrick.

The answer to this problem lies in the fact that the opponents have competed to the three-level, vulnerable, even though they hold the minority of points. It is therefore likely that one or the other of them has a singleton in your trump suit. Accordingly, you should play safe for nine tricks by shifting to clubs after taking the ace of trumps.

It’s a very moot point whether sleuthlike deductions about your opponents’ distribution, as in the two previous examples, are not more reliable than deductions about their high cards. However, there is no doubt that at all that if you have a choice, you should bank on an opponent who has overcalled to hold a missing ace rather than a missing queen, which is a card of dubious value. This deal shows a skillful play based on just such a deduction:

Dlr: South North
Vul: N-S ♠ A K 5
Q 2
K 8 7 3 2
♣ K J 10
South
♠ —
K 8 4
A Q J  9 6
♣ A 7 5 4 3
South West North East
1 1♠ 2♠ Pass
3♣ Pass 4 Pass
6 All Pass

West, who has overcalled in spades, leads the ♠Q against 6. Rather than win the trick with the ace and thus give yourself an immediate problem about what to discard, we’ll say that you ruff the queen and draw the opponents’ trumps in two rounds (West showing out on the second round).

Since you hold no less than three quarters of the high cards, it is tempting to assume that West is bound to hold the missing 10 points, including the ♣Q. However, it would be rash indeed to go overboard on this theory. It makes little difference to the soundness of West’s overcall whether his hand is:

♠Q J 10 9 x x A x x x &clubs: Q x x

or whether it is:

♠Q J 10 9 x x A x x x &clubs: x x x

If you take a finesse in clubs and it loses, you will go down, for the opponents will immediately cash a heart trick.

It would certainly be far more satisfactory if you could find a way of making the contract on the assumption that West holds the A, for the probability of West holding that card is infinitely stronger than any deduction you could make about the ♣Q

Once you begin to think along these lines you are halfway to the winning play. After drawing trumps, you lead a low heart from the closed hand. If West plays low, you put up the queen and speedily discard the K-8 on the ♠A-K, so ensuring at least 12 tricks.

If West instead elects to play the A when you lead one, then in the fullness of time you will discard a club from dummy on the K and thereby obviate the necessity to guess the ♣Q.

Whatever he does, poor old West comes off second best — provided you make the right deduction from the bidding and act accordingly.