A coincidence is defined as "a remarkable concurrence of events without apparent causal connection." When I lead writing workshops, I warn writers to avoid coincidences that work to the main character's advantage. A malign coincidence that makes things worse for the main character can sometimes be okay, as readers are prone to believe coincidences for the worst much more than coincidences for the better.
But recently I've been thinking about books that rely on coincidence and still work. I reread one of my favorites books, I Am David by Anne Holm (much, much better than the movie!) and it occurred to me in this rereading just how many coincidences there were in it. David's final scene could never have happened without several critical coincidences working to help him. His meeting the artist in order to acquire a vital piece of information always struck me, from my very first reading, as way too convenient. Yet the book works for me.
Right after that (a coincidence?) I read The Line by Teri Hall, and was again struck by the remarkable coincidence that, of all the "Others" Rachel might conceivably meet, she meets a boy who knows someone she has always wanted to learn more about. What are the odds? Yet, again, the book works for me.
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Even though fact is always stranger than fiction, and all writers know we shouldn't write anything that really happened in our lives exactly the way it happened as part of our fiction, maybe coincidences aren't all that unbelievable after all. But they certainly are remarkable.