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Let us say that in the infamous duel of 1804, Burr and Hamilton both miss. In OTL, only Hamilton missed, and in some ATLs (not remembering the titles or authors, sorry), Hamilton hit and Burr missed, but I don't think I've seen one where the duel still happened, but both missed (not sure I've seen one where they both died, either).
Would they have the sense to not have a second go at it?
How might their careers progress from that point?
As an alternate, much less probable scenario, each hits the other in the gun arm, and they suspect divine providence is trying to tell them something.