Finding missing queens is a big part of declarer play. It’s simple when there is a finessing position. When there is no finesse available, things can be more difficult for both declarer and the defenders. Let us look at a few positions and we assume the long holding is hidden in declarer’s hand.
Firstly, J53 opposite AK642: if declarer needs five tricks from this suit then it is necessary to play off the ace and king and find someone with the queen doubleton. If declarer only needs four tricks then the safety play is the ace and then small to the jack. This succeeds in all 3-2 breaks, any 4-1 split with singleton queen and any 4-1 split where South has the length. That’s all simple, or is it? Let’s try J53 opposite K7642: the only time declarer can make 4 tricks is if AQ doubleton is onside so it is clear to play small to the king. If the king wins without the queen appearing, duck in both hands next. If the king loses, lead up to the jack next. Let’s look at it from the defenders’ point of view now.
With three suits having been bid, South decides to lead the 4H from the unbid suit. Declarer plays a spade to the ace and a diamond to the king. Now a small diamond towards the jack, leaves South with a dilemma: which of the holdings does East have? If it’s the AK, then South must rise or lose the queen. If it is just the king then South must duck to let partner win the ace. Are there any clues? Yes, Declarer has shown the KD, the QH and surely the KS when playing small to the ace. If he also had the AD, he would bid 2NT (or 3NT) and not 1NT. Hence, it is correct for South to duck here. When North wins and plays a heart, the contract is easily beaten. Note also that with AK of diamonds, declarer might just cash the ace and lead small to the jack leading to another problem since this is how to play Jxx opposite Axxxx and in that case South needs to duck to North’s king to get the next heart led through. Since only three diamond tricks are needed, East might start with small to the jack at trick 2.