In The Big Sleep, While I find cigars in ashtray.
What is the significance of cigarettes in ashtray at opening & closing credits?
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The simple answer would be "because it's noir and it looks good". (And I think it's the right answer).
The more complex would be something like waves and smoke in the beginning and end in the "Death in Venice" so it's a sign of mortality and fragile of human life that can be easily put out like a cigarette. Two cigarettes are a sign of the human relations where two individuals can burn next o each other started with the same match (passion) which end in demise of them both.