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I'm not too stressed about it (unless I'm catching trains) but at the same time watches are for timekeeping so it's nice when you get one that does it very well. I think I got a good Pelagos- I set it at Christmas, and by the time the clocks went back end of March it had lost 5 seconds.Not sure why people are bothered by accuracy that much to be honest. As long as it doesn't lose or gain more than 5 seconds or so a day.
I did have a citizen radio controlled watch years back and the tech was kinda cool though
I have three Citizen Atomic Eco Drives. It still makes me giggle to see three second hands ticking in absolute sync!