The infamous "with one bound, our hero was free" is deus ex machina; "our hero turned the corner and smashed into (anything)" might be random but it's also reasonable.
Can you show how it could matter that the event was "random" - wholly or partially?
Several answers have the same message: its the resolution of conflict that makes deus ex machina a problem. I would recommend using a phrasing from Brandon Sanderson: his First Law of Magic
Sanderson’s First Law of Magics: An author’s ability to solve conflict with magic is DIRECTLY PROPORTIONAL to how well the reader understands said magic.
The message ...
Author Shirley Hazzard:
I've thought that there may be more collisions ... in life than in
books. Maybe the element of coincidence is played down in literature
because it seems like cheating or can't be made believable. Whereas
life itself doesn't have to be fair, or convincing.
From The Transit of Venus, Viking Press, New York, 1980,
All literature relies on coincidence. That's because a narrative isn't a duplicate of life, it's a condensation of it, where things are brought into close proximity for maximum effect. So the audience is prepared to accept a certain amount of coincidence.
The general rule of thumb is this. Coincidence feels like a cheat when it makes things easier for the ...
When we talk about what is plausible or implausible in a story, we tend to approach causality front-to-back:
What are the chances you'd survive falling out of an airplane in flight?
Obviously, they are not good at all. If you're faced with the choice to jump from an airplane in flight, you expect it to be suicide - because the chances of survival are that ...
Does not look extremely unlikely. Of course it would depend on how large the area the tribe uses to move in is. They were nomadic but inside well defined and known areas.
Eventually he makes it out of the forest and nears Texas again, returning to the Great Plains. He does this because he figures it will be easier to spot people on the Plains than in the ...
I'd say this isn't a deus ex machina - those usually occur suddenly, resolve the story's conflict/dramatic tension, and in many cases occur from outside the narrative context.
Here you've essentially got a co-incidence (which aren't actually as unlikely as you'd might think) - two aggrieved parties with a common foe encounter each other and team up. This is ...