I live in New York and I did not notice people around to use only "American grammar". Personally I prefer the "British" one as it helps to express nuances
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March 30, 2019
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Corrected
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January 14, 2019
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Answered
I think, they are not. "By chance" and "by accident" means randomly, without intent but action "by accident" usually causes some undesirable consequences. By mistake - as a result of some not intentional but wrong actions