I've watched House of Games about 3 or 4 times in my life. I never understood what Mike meant that Margaret gave herself away, when she told him she took his knife. Wasn't it Mike's knife? Or was it the Black man's knife? Please help me out, what's the key element of how Margaret "gave herself away"? I don't get it.
Earlier in the film, Mike and Margaret "steal into someone's hotel room". In fact, this is part of the con being played on Margaret, and the room is simply made up to look like someone is staying there.
This fact is revealed in the conversation between Mike and Dean, that Margaret overhears.
We're spreading personal junk on the bureau. We put some personal stuff on the bureau. So it'll look like somebody's in the room.
Get this. Listen to this.
The broad steals my pocket knife.
If the con is going correctly, then Margaret should not be aware of this conversation, and she should believe that the knife belonged the person who rented the hotel room. By saying "your knife", Margaret reveals that she was aware of the con.
The knife was supposed to be the black man's knife (the man who had the room). However, she overhears Mike saying it was his knife that she stole.
When she sees him, she slips and says "I took your knife". Mike does not know how she knows that, but he knows she is not supposed to know that fact. Therefore he understands she has figured them out.