Most bicycle/automobile accidents happen at some kind of intersection. When you bicycle facing traffic, you approach every single intersection, driveway, and parking lot entrance from a direction other users aren't expecting.
Back in my running days I took to running against traffic in the daylight and running in the same direction as traffic after dark. Otherwise the car headlights would blind me and I couldn't see where I was stepping off the road.
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My greatest fear is all of my kids standing around my coffin and talking about "how sensible" dad was.