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Set in Hamburg, West Germany, several criminals take advantage of the German bank privacy laws to use safe deposit boxes in a German bank to store large amounts of illicit cash. These include a Las Vegas mobster as well as a ruthless drug smuggler known as the Candy Man and a crooked overbearing U.S. Army sergeant and his meek-mannered partner the Major, who conspire on a big heroin and LSD smuggling score. Joe Collins (Warren Beatty), an American bank security consultant, has been spying on them and makes mysterious and elaborate preparations to steal their money (totaling more than $1.5 million) with the help of Dawn Divine (Goldie Hawn), a hooker with a heart of gold.
Joe has Dawn phone in a bomb threat to the bank president, Mr. Kessel (Gert Fröbe), to create a diversion. Joe locks himself inside the bank vault with a gold bar normally displayed in the lobby to supposedly save it. The bank is closed and evacuated while Joe uses duplicate keys to empty the criminals' three safe deposit boxes into Dawn's large-size deposit box. (It is implied that Joe had obtained the necessary bank information and secretly copied the criminals' keys while they were engaged in sexual trysts with Dawn.) Despite the fact that Kessel insists on burning through the wall to rescue Joe instead of waiting for the time lock to open, Joe succeeds in the heist and is hailed as a hero for "preventing" the robbery of the gold bar.
The next day, the three criminals, one by one, discover that their boxes are empty and they cannot complete their schemes or go to the police to report the thief. The Las Vegas mobster flees the country while the others (Sarge, his partner the Major, and the Candy Man) search Dawn Divine's apartment — as she was their common link — and find clues that connect her to Joe. Sarge calls Kessel to get Joe's home address, but Joe is quickly tipped off by Kessel and he hurriedly sends Dawn to the train station with a suitcase packed with her tak — $765,000 — promising to meet her later someplace out of the country.
A long climactic chase begins as Dawn gives the Major the slip at the train station while the Candy Man and the Sarge chase Joe across a rail yard and through the Elbe Tunnel. Joe escapes on a car carrier truck, lugging his suitcase, but the Candy Man and the Sarge follow and catch up in the morning at a frozen lake in the countryside, where the Candy Man crashes a car through the ice and drowns.
Joe escapes again by hopping a train, but during the night the Sarge catches up to him, only to find that Joe's suitcase contains nothing but a bottle of champagne and wads of newspaper. They conclude that Dawn double-crossed Joe by repacking the suitcases while he was getting the car, and the Sarge proposes a plan to Joe to go after Dawn together. But, upon drinking a swallow of the champagne, the Sarge instantly goes into violent convulsions and falls down dead. The bottle was one of three that the Candy Man had filled with a solution of concentrated LSD to sneak them through customs earlier in the film.
An epilog shows Dawn in a sunny climate in the USA, joyfully driving a gleaming new yellow Corvette, and then later cuddling in bed with an unseen someone. The other suitcase is sitting near the bed, and Joe's bomber jacket hangs on the coat rack. Dawn smugly explains to Joe that she was certain the criminals wouldn't kill him and leave themselves with no way to get the money.