Though I have to say that kicking over the board isn't winning but more scorched earth.

Sometimes it is, sometimes it isn't. An example of where it wasn't was the episode where the Eleventh Doctor had been taken over by Cybermen, and he outwitted the possession by pretending he'd outwitted it, and the cyber-brain spent more and more of its processing power trying to figure out how. I'd call that a kicking-over-the-board solution.