[RESOLVED] Help with math algorithm

[nuzzle]

why can't you go a step further and prove your claims quantitatively according to modern probability theory ?

Because my interest in this is to use plain reasoning only.

BTW, yes, the argcos(1/8) angle is always in the "window of opportunity" but it's not the middle point of the "window of opportunity".

Our models define the window of opportunity slightly different. In my model it's a section on shore and the optimal escape angle is the direction to its exact middle.

This is also the reason why an unbiased symmetric compass response can slightly shift the optimal angle as read by the runner and it's the core of the simple proof in post #31.

Well, okay but it doesn't change the optimal escape angle as you claimed it would. And the compass definately is a modification of the original problem.

Still it's clear to me now where the constant in #31 comes from. I have no immediate reason to believe #31 wouldn't hold so assuming it does then: When the compass is set to the optimal escape angle it will deviate according to some probability distribution due to errors. This distribution of deviation will be symmetric in compass angles but when angles are translated to positions on shore the distribution is skewed and becomes asymmetrical. To still get as much as possible of the skewed probability mass inside any window of opportunity (making escape maximally probable) the whole distribution needs to be shifted. To do that the compass is set to the optimal escape angle adjusted by a constant.

With that I feel ready to drop this thread. Hopefully I get asked this question at a job interview sometime.