"For all it's worth" or "for all its worth"?
Solution 1:
Apparently, the writer's intention was always to mean "it is," not "its." (A hasty conclusion and a sweeping statement, yes.)
Comparing "for all it's worth" and "for all its worth" with "for all it is worth," and considering that apostrophe use for the genitive was in fact an after thought.
nGram:
The arrival of the apostrophe as possessive indicator confused both the writer and the reader, so that today more often than not, authors do not know which is the "original idiom" and the reader is not sure what the author had meant to say.
The safest approach for writers would be to avoid the apostrophe altogether in this case and be specific, and for the reader to rely on context where needed and possible.
Solution 2:
"For all it's worth" wins in my opinion as it is more adaptable to other sentences also.
"For what it's worth" for example doesn't make sense if changed to "For what its worth". That might make one wonder "For what, its worth?"
It ultimately depends on what "it" is. Does it own the worth? Or is it simply worth the worth?