What is the significance of the two poker games in A Streetcar Named Desire?
Two aspects come to mind:
1) The aspect of luck, fortune and destiny: One underlying theme of "A Streetcar Named Desire" is that people are sometimes arbitrarily subjected to hardship, such as when Blanche and Stella's family lose their home "Belle Reve." Hand-in-hand with this idea, though, is counter statement that people can take charge of their lives and are not necessarily at the mercy of fate (as Blanche often supposes).
2)The leit motif of deception and appearance versus reality: Blanche puts a lot of emphasis on putting forth a good image and making things seem better than they really are. This is certainly a mechanism of defence, but it keeps her from dealing with her problems. Instead she puts on "a poker face" until she talks more honestly with Mitch in the end.