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A deus ex machina actually does solve the problem. I can't tell, from what you have written in your question, if winning the lottery eventually does solve all her problems. If it does not immediat...
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Source: https://writers.stackexchange.com/a/43599 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/43599 License name: CC BY-SA 3.0 License URL: https://creativecommons.org/licenses/by-sa/3.0/
#2: Initial revision
A deus ex machina **actually does solve the problem.** I can't tell, from what you have written in your question, if winning the lottery eventually **does** solve all her problems. If it does not _immediately_ but does _eventually_ there is no escaping that fact that you used a deus ex machina, and this is not a good story. Her problems were not solved by her own efforts, or her own sacrifice, or her own imaginative solution, so she doesn't **deserve** the solution. No matter what "character growth" you have given her. If the lottery win is not real, but the idea of it spurs her to solve her problems, then that is okay. If the lottery win is real but the only way to solve her problems is to donate all the money to charity or use it all to help somebody else, that is probably okay too. The miracle of the lottery win cannot solve her problem in any way. But once it is "undone" (she will not benefit personally from any of the money), it can be used for her to learn a lesson, change her life goals, or accept a situation and then _this personal change in her_ may provide the solution to her problem. Like Dorothy in the Wizard of Oz, the way home was always with her, she was wearing the ruby slippers the whole time. But the WoZ is a kid-to-adult story; so Dorothy had to become a hero first, and save her friends, and be betrayed by the Wizard (he left without her) before she got her heart's desire. You can't use a true deus ex machina "safely", you cannot solve the character's problem with any kind of million-to-one payoff. A satisfying ending must be a result of character, of bravery, of sacrifice, of risk-taking, of resolve, of selflessness, of one or more of the aspects of personality we find admirable, perhaps enough to bring us to tears. Being lucky isn't one of those. In fact being lucky is one of the things many of us can resent! We use dismissive terms for it, like being born on third base, or being born with a silver spoon in her mouth, or being a trust-fund baby. It doesn't inspire admiration or sympathy; it generally inspires jealousy and resentment.