How do you handle the trump suit?

Rex Stout, the creator of Nero Wolfe, said,“To read of a detective’s daring finesse or ingenious stratagem is a rare joy.” A bridge player should not be taking daring finesses. However, to watch an expert’s ingenious stratagem is a rare joy. Before we get to the play of today’s deal, though, what should South bid after West opens one diamond, North makes a takeout double, and East passes? Next, plan South’s stratagem in four spades after West cashes his two top diamonds and shifts to a heart. In the auction, if South bids one spade, it shows 0-8 points; if he jumps to two spades, it indicates 9-11 points. With more than that, he starts with a two-diamond cue-bid. The auction continues two hearts - two spades - four spades - pass. South can afford one trump loser, but not two. Strangely, the best play is the same even if East and West have passed throughout. Here, West is marked with the spade king from his opening bid. So first playing low to the queen cannot be right. The second-best play is low to the 10, planning, if it loses to the jack, to cash the ace next. But even better is immediately to cash the ace. When the king comes down, South can gain an overtrick by finessing East out of his spade jack. In isolation against passing opponents, if the ace dropped the jack, South would continue with the queen to drive out the king. Or, if the ace collected only the four and nine, declarer would cross to the dummy with a club and lead a spade toward his queen-10. He would have no guesswork.