Unlucky private eye Herbie Stolz (Allen Garfield) narrates about an exceptional client, Harry Adams (David Janssen), who had caught Herbie spying on him, and turns the tables around using him to spy on his wife, later confirmed to be having an affair.
With the background of President Kennedy's assassination, Harry has decided to totally replace his unhappy life with a more successful one, by using a method he devised for winning money at blackjack. He grows a beard, learns of an identity which he can adopt without harming anyone, and slowly builds up his escape which will be under the false identity, and will include a false suicide, ridding him of his real identity, and leaving no one in pursuit of him, with all his potential adversaries including his wife, receiving ample compensation and no hard feelings against him.
Harry's plot is accomplished with the paid assistance of Herbie who slowly discovers and comprehends what his employer's plans are, while confronting his own unlucky life, bad divorce and bad job, which he seems to be stuck in.
Amy, a beautiful woman (Linda Evans) falls in love with Harry, and towards the end of the movie, as he is completing his escape, he decides to change his flight destination to Israel coinciding with Amy's. The money from the blackjack winnings is in his suitcase taken as personal luggage. A woman with an identical suitcase boards the plane.
At a stop in Greece, terrorists who have robbed a bank board the plane. All passengers are now being checked while the authorities are hoping to find the stolen money. Harry exchanges his suitcase with the lady's, and she is arrested but then released. The terrorists then open their suitcase and discover the lady's underwear inside.
At the hotel room in Israel Harry and Amy open his suitcase and discover that the terrorist bank-robbers mistakenly had exchanged their suitcase with the lady's first, and so they have even more money than he had originally accumulated from the blackjack winnings.
Back at his office Herbie tells the viewers that somehow, although Harry had showed him how to work the blackjack-winning method, he never won, and he is stuck with his continued "bad luck".