No problem. This is the place to ask the questions…
I see what you were trying to do, but nope, the GREP query shortcode refers only to what’s in the Find part of the query. It finds what’s in the query, and then sticks that into the file name, omitting, as usual, all illegal characters, so the slashes disappear.
I can’t think of a simple workaround here, I’m afraid. If you included some hidden text on your pages with the word “half” or “third”, you could pick that up in the file name, I suppose.