In House of Games, the Lindsay Crouse character (psychiatrist Margaret Ford) seems to be unaware of her being the mark until the red convertible shows up unexpectantly. She then performs a rudimentary investigation by visiting the tavern and overhears the recap of the con by Mike (Joe Mantegna) and this co-conspirators that solidifies her suspicions.
I suspect she knew she was the mark much earlier than that, since it would be much too difficult to devise a counter-con (the elements in parens below) that quickly. It was already night when she heard the conversation, had to develop a plan before 10 PM, and execute it at the airport:
A bank story and a bag with ($250,000 cash),
A convincing story of being followed ("I'm frightened all the time"),
The gun had to have bullets (Did her suicidal "patient" really give her a loaded gun?),
The accusation and (her confidence in Mike's bravado - false or otherwise),
Mike turns against her because of her ("crap out of turn"),
"You're all bluff" - ("It's not my pistol, I was never here")
So, how early in this counter-con did Margaret know she would kill Mike?