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).
- You can't see the 2 in dummy, so West probably has it for a fifth card.
- 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.
- 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).
- 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?