To be "hoist by [or with] your own petard" is to be blown up by your own bomb. ... A petar or petard is a small explosive device, so to be "hoist with his own petar" is to be blown up by your own bomb (as in Hamlet, Act 3, Scene 4, where Hamlet refers to Polonius being destroyed by his own plotting).
Sorry - couldn't resist. Enjoyed your post and sometimes it's fun to be picky. Trust me I make lots of 'mistakes'...
I regard 'word play' as a mark of education, for the knowledge, and intelligence, for using said knowledge appropriately! I did have a good family environment as another advantage, we even played SCRABBLE as a family! Does anyone do that anymore?