Wikipedia
Bath coup is a coup in the game of contract bridge, where the declarer, holding AJx in a suit ducks the left-hand opponent's lead of a king (or a queen). The coup is presumed to be named after the city of Bath in England and dates from the game of Whist, the predecessor of bridge.
The purpose of the Bath coup is to either gain a trick by means of a free finesse if the suit is continued, or to gain a tempo, because the suit may not be continued by opponents without the loss of a trick. The basic position for the bath coup is like on the diagram: West leads the king at a notrump contract. If South takes the trick immediately, his jack can be subsequently finessed if East gains a later trick, providing four tricks in the suit for the defense. However, if South applies the Bath coup by ducking, he will either take two tricks with AJ, or the opponents would have to regain the lead twice to cash the suit—first, East must gain the lead in order to finesse through declarer's AJ, and later, West must regain the lead to cash the suit. If the suit is divided 5-2, as in the diagram, the declarer has in effect performed a hold up with an additional gain in tempo, as the opponents have to regain the lead once each. If the suit were divided 4-3, the last lead could be gained by any opponent to cash the suit, but the number of available tricks would be smaller. The coup also occurs when ace and jack are split, but the jack lies before KQ.