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I find it odd that this hasn't come up yet, so here's another alternative to the dilemma, that provides a purely technical solution: A has access to overpowered magic, right? He doesn't have to k...
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#3: Attribution notice added
Source: https://writers.stackexchange.com/a/48055 License name: CC BY-SA 4.0 License URL: https://creativecommons.org/licenses/by-sa/4.0/
#2: Initial revision
I find it odd that this hasn't come up yet, so here's another alternative to the dilemma, that provides a purely technical solution: A has access to overpowered magic, right? He doesn't have to kill to win. All that he has to do is prove that B will never defeat him - either by nonlethally subduing B several times, _permanently_ nonlethally subduing B (say by putting some form of long-term curse on him), or by escaping to a place where B has no realistic chance of being able to follow. Depending on the particulars of the nonlethal solution used, A could come off as a superior person patiently putting up with B's idiocy, a villain who only technically upholds his vow while still being generally nasty, or a frightened innocent successfully escaping from the real villain.