Of all the gin joints in all the towns in all the world, the line goes, and the joint in question is a white-walled café in a Moroccan port crowded with refugees, black-market visas and a piano nobody will let rest. A cynical American in a white dinner jacket runs the place and swears he sticks his neck out for nobody. Then a woman he used to love walks back in on the arm of another man, and the careful armour of his indifference begins to come apart. That is the engine of Casablanca, and it has been running without a stall for the better part of a century.

The film’s origin is the kind of story the studios usually invent after the fact, except this one is true: the screenplay was being written more or less as it was shot. The Epstein brothers, Julius and Philip, traded pages with Howard Koch, and for a long stretch nobody on set was sure whether Ilsa would leave with Rick or with her husband. Ingrid Bergman asked which man she was supposed to be in love with and was told to play it down the middle until someone decided. Out of that committee-built improvisation came a script so tight it won the Academy Award for writing and supplied more lasting lines than any other movie ever made.

Michael Curtiz directed it the way a great studio craftsman did everything in 1942 — invisibly, and at speed. There is no shot in Casablanca that asks to be admired on its own, and yet Arthur Edeson’s photography turns cigarette smoke, venetian-blind shadow and a fog-bound airfield into a whole moral weather. Max Steiner’s score keeps folding “As Time Goes By” back into the action until the melody itself starts to ache, and the scene where the refugees drown out the German officers with “La Marseillaise” is still one of the most stirring things the studio system ever produced.

Humphrey Bogart had spent a decade playing gangsters and heavies; here, as Rick Blaine, he became a romantic lead without softening a single edge, and the screen persona that carried the rest of his career was essentially born in this one part. Ingrid Bergman gives Ilsa a luminous indecision the camera cannot stop watching. Around them sits one of the deepest benches in any American film: Claude Rains as the deliciously corrupt Captain Renault, Paul Henreid’s upright Laszlo, Conrad Veidt’s Nazi major, Sydney Greenstreet and Peter Lorre trading in human lives, and Dooley Wilson’s Sam at the piano, gently refusing to play the song everyone remembers him for.

The plot turns on a pair of letters of transit — papers that cannot be questioned, that will carry their bearer out of occupied Europe — and Hitchcock would have called them a perfect MacGuffin, an object whose only real job is to make these people choose. The choosing is what lasts. Rick’s decision on the tarmac, to do the decent thing at the cost of the one thing he wants, is the rare piece of wartime propaganda that plays as pure feeling rather than message. The film tells you the problems of three little people don’t amount to a hill of beans, then spends its final minutes proving the exact opposite.

Almost no film has been absorbed so completely into the language. “Here’s looking at you, kid,” “We’ll always have Paris,” “Round up the usual suspects,” “I think this is the beginning of a beautiful friendship” — the American Film Institute counted more memorable lines here than in any other movie, and the one everybody quotes, “Play it again, Sam,” is never actually spoken. The picture has been referenced, parodied and borrowed from so often that newcomers sometimes arrive convinced they have already seen it. They haven’t.

What keeps Casablanca from being merely a well-loved antique is that the romance underneath the legend is genuinely good — adult, unsentimental, alert to the cost of doing right. It was a hit on release, took the Oscars for Best Picture, Best Director and Best Screenplay, and has sat near the top of every serious list of the greatest films ever made for decades. Watch it cold, without the weight of its reputation, and the surprise is how light on its feet it still is. They were making it up as they went along. They got it perfect anyway.