This is a harder version of the fixed wall variation.
Every day you walk across a flat plane from a point $A$ to a point $B$. The points are $3$ miles apart. However, every day there is a 50% chance that there is an invisible force field between the two points. The force field extends $1$ mile in each direction perpendicular to the line between $A$ and $B$, and its position is uniformly distributed between the two points. You don't know if the force field is present or where it is until you run into it.
What path should you take to minimize the distance you must travel to reach point $B$ from point $A$ on average? This a mathematical problem, so your solution shouldn't involve "lateral thinking," like climbing over the wall. You can assume that you can follow your planned path exactly, the wall has negligible thickness, etc.
Computer simulation might be a good way to try to solve this but mathematical solutions are encouraged as well.
I am not good at drawing out diagrams here to show the possible paths so I hope someone can add it to their answer.
The answer could be expressed as an angle to leave starting point $A$; I am not sure how else the answer can be expressed other than maybe total distance traveled on average.
How the hell can this be off topic when the previous simpler version of this was not? Whoever stated it is off topic is very inconsistent and also this question received 2 upvotes and 3 favorite votes so it would make sense to keep it open and active, not on hold. Please "fix" this ASAP.
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