Plot hole: After Margaret kills Mike at the end, she leaves through the door that is right next to his corpse, leaving her fingerprints on it, since she is not wearing any gloves. Under these circumstances, the police surely would have done some forensic investigation and dusted the doorknob for prints, which would lead back to her. Considering Margaret moved up from being a psychiatrist to a lively con criminal, you'd think it would occur to her to clean up a little bit, but she gets a happy ending.
House of Games (1987)
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Directed by: David Mamet
Starring: Joe Mantegna, Lindsay Crouse, Lilia Skala, Mike Nussbaum
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Suggested correction: Her touching the handle tells the police (assuming they check it) that someone they (presumably) don't have on record used that door handle at some time. And even if she was somehow connected to the murder, that sits outside the storyline, and therefore the plot, of the film. And things that might happen after the plot ends can't be considered a plot hole.
Suggested correction: As she tells Mike, she's out of control. I don't think she planned to kill him, but he goads her into it by telling her she really hadn't learned anything and he played her. THAT was the point she learned the lesson. She took the risk and killed him. The doorknob fingerprints were a risk, but not much of one since a lot of people probably used that door before the police got there.
As for many people using the door after the murder, probably only one person might have used it if they opened it from the hallway side, only touching the hall side knob. That person would have immediately seen the body and called the police. Anyone on the baggage handling side wouldn't have touched the doorknob. Still, Margaret is not in much peril from fingerprints, since we are led to believe she has always been a "good person" who would probably never have had her fingerprints taken.
Mike: What'd you do, win again?
George: That's right. If you wanna win the hand, you've gotta stay in 'til the end.