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I wonder how much truth there actually is to this? While it is difficult to imagine during a war threatening a nations existence, if it was a minor quarrel over land or extradition it might well be useful to settle it this way in some cultures. Both parties assert their willingness to fight but spare casualties not to mention time better suited for plowing or herding. And if the two parties were small enough that one Badass can affect the course of a war by his personal skill(as with a small band), there is an innate guarentee against treachery. If Mighty Bob has slain Mighty Andy, then Andy's tribe has lost an important asset if it chooses to resume hostilities.
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How well does it match the trope?