What is the thesis of "The Outcasts of Poker Flat"?

"The Outcasts of Poker Flat" could have more than a single thesis about it. A thesis is a statement that makes an argument about something. A thesis could make an argument about a writer's writing style or the effectiveness of a particular narrative point of view. It could make an argument about a theme or themes present in the story, and a thesis could make argument about one or more characters.
The thesis is entirely up to you, but it needs to make an argument that you intend to prove by using evidence from the story. It is not a statement of fact. For this reason, choose a thesis topic that is open to interpretation. I generally recommend writing a thesis that analyzes a particular theme or character(s). These two things generally overlap because often characters support a particular theme, or themes are illustrated by particular characters. For example, there is a strong theme present in this story that explores the difference between reality and appearance. When the story begins, the outcasts are described as "improper persons." They are being kicked out of town because they are supposedly the seedier and morally corrupt individuals of the town. Uncle Billy winds up typifying this description, as he leaves the other outcasts to fend for themselves. Readers have to wonder if they would have survived had Uncle Billy not taken everything with him. The rest of the characters, on the other hand, wind up being incredibly loving and caring for each other. They do not act like the gamblers and prostitutes that they are.
Once you have a general concept or argument in mind for the thesis, you have to word it. This can be a tricky thing because it needs to be detailed, but it also needs to be concise. In other words, it needs to make a clear argument without being overly wordy. Two formats tend to work well. The first format is a statement followed by a proof/examples statement. You make a statement and then tell your reader what you intend to use as evidence. Here is an example: "The theme of appearance versus reality is most clearly illustrated through the characters of Mother Shipton, Duchess, and Oakhurst." The other format that tends to work well is a point and counterpoint thesis format. Your main point is the second half of the statement. It would look something like the following statement: "Although the town of Poker Flat believes that the outcasts are the dregs of society, the outcasts more than prove their moral worth by the end of the story."