Author Dorothy Parker is...

...best known for her wit, wisecracks, and eye for 20th century urban foibles.

With this in mind, we can expect that Parker will look at the world from a perspective different than many women of her time. She is not confused about what she sees: she is not one to hide from the truth. However, she is not completely helpless, as we see in the poem, through the persona of the poem's speaker.

The poem's speaker seems to be much more clever than the man she is speaking to—or perhaps he is so full of a sense of his own importance, that he does not care about the feelings of the speaker. She is a master of covering her feelings; she "plays" the eager listener:

Oh, I can smile for you, and tilt my head,
And drink your rushing words with eager lips...

However, as the poem continues, we realize there is physical contact between this woman and the man she is listening to:

...And trace your brows with tutored finger-tips.
When you rehearse your list of loves to me...

It is not just that she touches him, but the movement of her fingers is an intimate one, as she "traces his brows." The fact that her fingers are "tutored" means they have been "taught," we can infer through practice. She can deliver a delighted laugh and make her eyes glow as he laughs with her. However, we are given a hint of how the information he relays affects her within:

...nor can you ever see
The thousand little deaths my heart has died.

He has no idea how his behavior affects the speaker. She is very good at pretending and that he believes she is as...

...gay as morning, light as snow...

And he still knows nothing about what is in her heart—and she notes that he never will.

In the second stanza she continues to play her game, as she laughs at what he says and listens to his every word. And his words are all about his "adventurings" with other women...

...Of ladies delicately indiscreet,
Of lingering hands, and gently whispered things.

As she does all he expects of her, he is pleased. She repeats that she is all he wants of her. He sees what he wants to see in her, but nothing more. And from time to time, he leaves off of pursuing other women and comes to her ("strays") and when he goes, she kisses him goodbye.

Thus do you want me -- marveling, gay, and true,
Nor do you see my staring eyes of nights.
And when, in search of novelty, you stray,
Oh, I can kiss you blithely as you go ....

All of what the speaker has mentioned and described, of him and of herself, leads me to believe that she is his mistress or—more likely—a prostitute he visits. She is practiced, and her wishes and desires are meaningless—it's part of their "arrangement."

There are two important aspects of the relationship to consider. First, she is at least just a little in love with him. For as she listens to his tales, her heart dies a "thousand little deaths." Second, there is a twist at the end of the poem. And it is in this where we see Parker's wit. The lines read:

And what goes on, my love, while you're away,
You'll never know.

On one hand, it sounds as if this is an echo of the last two lines of the first stanza, where she notes "...all the straining things within my heart / You'll never know." However, I think we need to look deeper in our analysis of the closing: while the man takes her for granted and displays that she has no real value to him, when he is away, he also never knows what she is doing! And she won't tell.