On a 32 or 36 spoke wheel a broken spoke is no big deal. People have ridden with broken spokes for god know how long. When I used to lead tours, my bike was fine but some riders were forced to ride over 100 miles on a broken spoke until we could find a replacement (back in the sixties and seventies).
I only broke one spoke in my riding career. It had been sawn part way through by an overshifted chain, and let go. I trued the wheel around the break and rode it another few hundred miles to finish the trip. I later replaced it and the wheel lasted until retired for other reasons.
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