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The issue with Deus Ex Machina (DEM), regardless of when it occurs, is when you have led the reader (by whatever means) to expect your character to solve her own problem, and she gets a win by the ...
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#4: Attribution notice removed
Source: https://writers.stackexchange.com/a/39239 License name: CC BY-SA 3.0 License URL: https://creativecommons.org/licenses/by-sa/3.0/
#3: Attribution notice added
Source: https://writers.stackexchange.com/a/39239 License name: CC BY-SA 3.0 License URL: https://creativecommons.org/licenses/by-sa/3.0/
#2: Initial revision
The issue with Deus Ex Machina (DEM), regardless of when it occurs, is when you have led the reader (by whatever means) to expect your character to solve her own problem, and she gets a win by the gods doing her a favor out of nowhere. Readers will accept undeserved **bad** luck, but they expect the hero to be an agent of good luck, not the _recipient_ of it, or at least _overcoming_ bad luck. If she gets herself in trouble through recklessness or stupidity, we don't expect her to be saved by a stranger. Your story would be better if she struggled out of her trouble on her own, taking risks that paid off, and frees herself from danger but ends up muddied, in torn clothing -- THEN the guy she's looking for shows up, just MISSING the nick of time. Now she has another obstacle to overcome, meeting the one she needs looking like a filthy stinking vagabond. Your hero can BE the DEM showing up just in the nick of time to save somebody in distress, or can BE the DEM as the "chosen one". But your hero should always be an active agent (and proactive agent) in their OWN fate, don't ever give them an obvious break (I mean a break the reader will _know_ is a break). Stories are very much about heroes _overcoming_ obstacles by dint of their own will, skill, determination, action and risk taking. That is why they are inspiring or entertaining. We like to see people win when they **_aren't_** lucky and have to struggle every step up the mountain. So no free rides for the heroes, not directly or indirectly. That's what the modern meaning of DEM is; a gimme or free ride or lucky break the hero did not earn.