It is actually the FRIEND who turns the tables on the NARRATOR in Mark Twain's short story, "The Celebrated Jumping Frog of Calaveras County." In the opening paragraph, the narrator tells the reader that his friend has asked him "to call on garrulous old Simon Wheeler and inquire(d) after my friend's friend, Leonidas W. Smiley, as requested to do..." The narrator speculates that his friend knew that by asking about the aforementioned Leonidas Smiley, 

it would remind him of his infamous Jim Smiley, and he would go to work and bore me nearly to death with some infernal reminiscence of him as long and tedious as it should be useless to me. If that was the design, it certainly succeeded.

So, apparently there was no Leonidas W. Smiley--only a Jim Smiley. The narrator's friend turned the tables on the narrator by setting into motion the process by which the narrator would learn of the extremely long-winded tale that climaxed with the humorous story about the jumping frog.

In my opinion, and from what I have read of others' opinions, the narrator does not turn the tables.

I think he could have turned the tables in a couple of ways.  If this story had been a letter written to the friend, he could have bored the friend by subjecting him to the same stories the narrator just heard.

Of if the narrator had actually enjoyed the stories, that would have been a good way to turn the tables too. But neither of these things happened.  The narrator ends up being annoyed by the stories and can't wait to escape from Smiley.