In bridge, what are exceptions to "third hand high?"

Question

You are sitting "East" (with dummy to your right), and your partner West leads a low (presumably fourth best) card in a suit against a 3 no trump contract. When dummy plays low from "nothing," and you hold KT6 of the suit, you are usually expected to play "third hand high," i.e. the king, either forcing out, or trapping South's supposedly lone honor. When the suit is established, you can usually defeat the contract. (According to Kantar.)

But in a problem in another bridge book, declarer held QJ74 in the suit, and the correct play was the T, not the K. Since this is a problem, focus only on the following (unless you are constructing a counterexample).

1. You can't see the 2 in dummy, so West probably has it for a fifth card.
2. The 5 played by dummy is singleton, so given this fact, 1) above, and your KT6, declarer has four, not the usual three cards in the suit.
3. West has either A of his led suit and no side entry, (as was the case in the problem), or the Q or J and a side entry. In either case, declarer has two honors (and two small cards).
4. You have ONE side entry, a Kxxx offsuit dummy's AQJx in another suit. This is enough to defeat the 3NT contract if you get four tricks in West's led suit by leading through declarer.

The solution to the problem was to play the T and try to induce declarer to cover with the Q or J. If declarer failed to "split honors" (and playing the king would discourage this), declarer would make his contract. But most declarers WOULD split honors.

How do you tell that you should play the T and not the K. Is it the four cards in declarer? Is it the double honor with declarer? Are there other considerations that I haven't addressed?

Are there other examples where playing "third hand high" would be wrong?

Answer 1

It usually depends on the whole hand, but the typical cases where you don't play third hand high relate to communication/entry issues like keeping the communication between the two hands, creating/denying entries, messing up the entry timing etc.

Here is a classic example where the purpose is to deny an entry:

QJx
KQJTxx
xx
xx
          KT9xx
          Axx
          xxx
          xx
Axx
xx
AKxx
AKxx

Declarer (South) is in 3NT and partner leads a high spade and declarer plays the Q.

It would be a mistake to cover with the K. Declarer can then win the A, knock out the heart A, and enjoy overtricks.

If you duck, you are giving declarer the spade trick early, and forcing him to use the entry to dummy, before hearts are established.

Now when declarer plays hearts, you can duck once and cut him off from dummy.

Of course, declarer made a mistake by playing the Q! He should play low, and win the A. Now he has a sure entry in the form of QJ of spades, which he can use, after he knocks out the heart A.

Here is an example of maintaining communication between the two hands.

QJx
KQJTxx
xx
Qx
          AKTxx
          xxx
          xxx
          xx
xxx
xx
AKxx
AKJx

Declarer (south) is in 3NT, and partner leads the spade 9 (probably from 9x). Declarer plays the Q from dummy and you must let it win. The purpose here is to ensure that partner has a spade (i.e. maintaining communication) when he gets in with the heart A. When he wins the heart A, he can lead a spade and you can cash your four spade tricks, setting the contract. Notice that this is quite similar to ducking plays by declarer where he needs to duck early in order to establish suit and maintain communication with the dummy.