Does this actually work for any proportions of A and B? Is there a simple proof?
Yes, but I'm not sure it's worth proving? I'd say that the "Factoring" section explains how this works, though there are no proofs. Will add pointers at the beginning.
Could we have arranged the rectangle so that B and -B were divided by a straight line w/o changing any of the probabilities?
And is there any significance to the fact that A and -A are divided by a straight line, but B and -B are divided by a jagged line? Could we have arranged the rectangle so that B and -B were divided by a straight line w/o changing any of the probabilities?
Does this actually work for any proportions of A and B? Is there a simple proof?
Yes, but I'm not sure it's worth proving? I'd say that the "Factoring" section explains how this works, though there are no proofs. Will add pointers at the beginning.
This is addressed in the factoring section.
And is there any significance to the fact that A and -A are divided by a straight line, but B and -B are divided by a jagged line? Could we have arranged the rectangle so that B and -B were divided by a straight line w/o changing any of the probabilities?