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I got a nail right in the middle of a brand new tire a few years ago. I ran that tire almost to no tread over the patched part and it never lost a bit of air once.
It wasn't even one of those fancy mushroom plugs either, it was just your regular tar string ones and I used rubber cement when i installed it.
plug it and forget it. just keep track of your tire pressures which I do once a week on my bike anyways