It is the Mertzes' 18th wedding anniversary, and they and the Ricardos want to do something to celebrate. However, the gentlemen and the ladies have different ideas about what to do. Ricky and Fred want to go to a boxing match, but Lucy and Ethel want to go to a nightclub. They argue and are unable to come to an accord. Finally, Lucy announces that she and Ethel will find dates to take them out. The men go downstairs to Fred's apartment where Ricky expresses concern about "what might happen" when the girls go out with other men. Fred agrees it would be a good idea to get dates themselves and go to the nightclub to keep an eye on their wives.
Lucy tries calling up old boyfriends, but most of them are busy, married or, in one case, babysitting a grandson (Lucy explains that when she had dated this fellow, he was an "interesting older man"). Meanwhile, Ricky is in a similar situation, having burned his "little black book" upon marrying Lucy (she had told him that doing this was an American marriage tradition). Finally, Ricky decides to phone a friend, Ginny Jones, who has connections to all the women in town. She agrees to set them up. Lucy also remembers Ginny's connections and phones her for the same reason. Ginny lets Lucy in on the husbands' scheme, and Lucy has an idea. She tells Ginny to arrange dates for Ricky and Fred—but with Ethel and herself. The evening comes around, and Ricky and Fred are anxiously waiting for their dates. The doorbell rings, and it's Lucy and Ethel, dressed in stereotypical hillbilly attire, and calling themselves "Eunice" and "Ma," respectively. Ricky and Fred are shocked and don't realize it is their wives behind the costumes. Ricky is eventually tipped off when Lucy gives herself away by knowing exactly where the cigarettes and matches are. Ricky takes Fred aside, fills him in, and they turn the tables on the women by being overly amorous. Lucy realizes that Ricky knows what's up, and the charade is over.
Later that evening finds the couples out celebrating the Mertzes' anniversary—at the fights. "Happy anniversary, Ethel", Lucy sighs. "Thank you, Lucy", Ethel sighs back.