When do you know its time to replace your strop?

Reason I'm asking is a guy I work with collects straight and he brought me one of his strops he has for me to use with my straight... It looks pretty rough really and I didn't know if I should use it or save my money to buy a new one. This is my first strop BTW. It has 2 strips of leather, one dark brown side and a black side. Which is what? There appears to be a "Keen Kutter" stamped very faintly on the end of the brown side... May be also on the other? Is there any way to bring it back into shape? Sorry, in a hurry leaving work and have to get ready for the XMAS parade...