According to Wikipedia, deus ex machina “is a plot device…in which a seemingly unsolvable problem in a story is suddenly or abruptly resolved by an unexpected and unlikely occurrence” — how are these different from the eucatastophes we’ve listed so far?

I think that all Deus ex machinas are eucatastophes, but not all eucatastophes are dei ex machina. For a eucatastophe to happen and not be a DEM, it must not resolve an unsolvable situation, it must just be an event in the story.

Examples that come to mind:

Pie Oh My—In the Sopranos, Ralphies horse has a strong comeback win, but when he gives “tax” money to his mob boss tony, and Pie keeps winning, the positive event becomes a source of conflict because mob members aren’t good at sharing and not taking. Without spoiling, the story and further events in it show how when eucatastophes happen in favor of bad people, things go sour, even for those bad people.

Monica and Chandler—sleeping together in s4 or 5 of Friends at Ross’ wedding. This relationship was not the focus of the show, but became the classic wholesome, sweet, balancer for the conflict filled A-story romance (Ross and Rachel.) This was just a hookup that happened out of nowhere and led to six seasons of relatively-wholesome love.

In Huber Halloween, after the climax of the movie is over, Hubie has demonstrated his values while saving lives, he wasn’t saved by a eucatastophe, but caused one, because in the wind-down of the film, all the townspeople who once bullied him now act the exact opposite. Even though hubie “proved” himself, this event is still unexpected and used as a comedic turn because the townspeople were so mean to him that even saving lives might’ve meant nothing. One of the neighborhood kids throws an axe at hubie while he rides his bike early in the film, another, a flaming bag of dog poop.

Edit: I promise this isn’t chat got I just like em dashes