Deductions from the defender’s discards

The theme throughout this series has been that a fine declarer constantly seeks to develop a picture of the unseen hands by drawing deductions from what the defenders have — or haven’t — bid, led or played. Next on the agenda is the highly important matter of discards.

A defender will often be unable to discard on a suit led by one of the other players without providing the declarer with quite reliable clues to his holdings. Consider this very common situation:
A K 7 4

Q 3

This is a side suit at a trump contract, and while trumps are being drawn an opponent lets go a card in the suit. Straight away you can assume, with no other information to guide you, that the defender most probably started with five or more cards in the suit.

You can be quite sure that he has not made the discard from four cards, as he can see the length in dummy. And while in theory he might have begun with only two or three cards in the suit, the chances are that in case he would have preferred to make his first discard in some longer suit.

The declarer who is capable of drawing such inferences will clearly fare better in the long run than one who is oblivious to them. The full deal might be something like this:
♠ A K 7 4
K 6
10 6 3
♣ 10 4 3 2

♠ Q 3
A J 10 9 5 4
A 7 4
♣ A Q

A low diamond is led and you commence operations in the normal fashion by taking the ace and leading a trump to the king. However, East shows out when the next trump is led, discarding a spade. You go up with the ace and are then faced with a decision of sorts.

The cast-iron method of play is to lead the jack of trumps, forcing out the queen. The defenders could then cash a couple of diamond tricks, but after that you would be able to win any continuation, draw the outstanding trump, discard the ♣Q on a spade, and make four hearts on the nose.

The more speculative line is to try to cash the Q-K-A of spades before playing any more trumps, planning to discard a diamond on the third round and then to take the club finesse in the hope of notching up a precious overtrick. Of course, you would never dream of playing the hand this way at IMPs or rubber bridge. At duplicate, however, the chance to make an overtrick is undeniably attractive, and in certain circumstances would not be unreasonable to take the risk.

Nevertheless you should dismiss all idea of playing this particular hand for an overtrick in view of East’s discard of a spade on the second round of trumps. The spade discard almost certainly means that East started with five of them, in which case if you try to cash the Q-K-A you will speedily be laid low. (West ruffs the third one with his small trump and you eventually have to play clubs from your own hand to go down a trick.)

The significance of East’s spade discard in the above hand is obvious once you think about it, but the hard fact is that very few players would think about it. Fewer still would draw the appropriate inference if East happened to discard a club or a diamond instead of a spade. In this case declarer could assume that East held fewer than five spades — with five of them his first discard would be a spade, as he would quite certainly have holdings in the minor suits from which it would appear safe to discard. Playing for an overtrick in this instance, therefore, would involve taking virtually no risk at all.

Of course, drawing inferences from the defenders’ discards is not always as easy as falling off a log. For a start, you need a memory, some discards don’t convey very much at the time they are made, and not until later does their real significance dawn. Consider this example:

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

West leads the ♠6 to his partner’s king and South ducks the trick. When East returns the trey, declarer realizes from the play of spot cards that West has led from a five-card suit and that there is no point in holding up further. In any case, South wants to retain an exit card in spades, and accordingly he wins the second trick with the ace.

Declarer has eight winners and the ninth will obviously have to come, by some manner or means, from the diamond suit. For the moment, declarer plays off four rounds of clubs, on which West throws a diamond and East discards first a heart then a diamond. The following cards are left:

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

At this point declarer is still undecided as to whether to take the straight diamond finesse for his contract or to try to endplay West by throwing him in with a spade. He cashes the K-A and then has to finally take a position.

Declarer knows that if West began with only two hearts, he is now out of them and the contract can be assured by exiting with a spade. West will be able to cash his three spade, but then will have to lead a diamond into declarer’s A-Q.

But if West began with three hearts, the throw in will fail, for West will cash three spades and a heart, to defeat the contract. In this case declarer would be far better advised to take the straight diamond finesse instead of attempting an endplay.

On the surface it would appear that South has to guess, but East’s discards have been revealing. On the clubs, remember, East discarded first a heart and then a diamond. This surely suggests that he had a 2-5-4-2 pattern originally: if he had a five-card diamond suit and only four hearts, he would not have discarded a heart on the third club, since he would have given South the opportunity to score an extra trick with dummy’s fourth heart.

So declarer exits with a spade after cashing the K-A and duly makes the contract.

As he approaches the end game, a good declarer becomes especially aware of whether a defender has been late, or reluctant, to discard from a particular suit. Such considerations may prove important when at the end of a hand you have to tackle a combination such as this:
7 4 2


You may have begun with more cards in the suit, but now you are down to this holding. You lead low from dummy and East follows low. If East has discarded once or twice from this suit he is more likely to hold the ace than the queen. Alternatively, if West is the player who has been discarding from the suit while East has been clinging grimly to all of his spot cards until late in the hand, the chances are that East has been keeping a guard to the queen.

The same sort of inference may arise with a combination like this:
A 7 5 2

Q 10 4

You are playing at notrump and East, quite early in the play, divests himself of a card in this suit. You require two tricks from this holding, and later in the hand you play the ace and return the two. East follows low and the problem now is whether to play him for the king or for the jack.

East has already produced three small cards in the suit and therefore you have to decide, in effect, whether to play him for an original holding of K-x-x-x or J-x-x-x. It is surely much more likely that he started out with K-x-x-x, for with that holding he would be willing to discard, whereas with J-x-x-x he would be reluctant to. It is because they take note of such matters that good players get the reputation of being good guessers.

One final pointer: in general, do not assume the opponents have discarded in such a way as to present you with tricks. Take this very common holding:
K J 10 3

A 7 4

While you are playing off another suit at notrump, both defenders discard once in this suit. You should not assume that one player, out of a spirit of bonhomie, has discarded from Q-x-x and the other from x-x-x. It is far more likely that the queen is still guarded. You may be able to judge which defender is more likely to have begun life with the Q-x-x-x, but if you cannot, you should still be inclined to take a finesse against someone rather than playing for a drop of the queen.