What's the difference between "any way" and "any which way"?

Why should I use "any which way" (like in "any which way you can") instead of simply "any way"?

I've been studying English as a foreign language for some time, and never came across this particular construct before.

"Any which way" adds a random or haphazard flavour that plain old "any way" doesn't have.

"Any way" would work for "go this way or that way, it won't make any difference you'll get where you're going". "Any which way" would work for "go whichever way you want for all the good it will do".

The same applies when "way" means manner as well as direction.

"in any which way" adds a rough, rude and indifferent tone to your statement (usually used by superiors to talk to their subordinates or used by angry parents). E.g. Reach the reporting station by 9 a.m. in any which way you can. (It almost implies - I don't really care which mode of transport you use. Just reach by 9 a.m.)

"Any which way" is an informal manner of speech. It implies an arbitrary choice of direction, to be determined by the person being addressed.