I too am impatient to learn the logical conclusion of “eternal struggle.”

An edge point's probability of being hit should be proportional to the length of every path leading to that edge point. An area closer to many short black paths and many long white paths will show black expansion (and vice-versa). So I suspect that any variation of the central line from a straight bisection of the circle should get hammered out over time.

you can run frameRate(x) in your browser's console to speed it up a bit - might be limited by your monitor's refresh rate though

you can keep tab open and check in few weeks.