They do not need to know that you could be playing a different game than they are. Some ideas and alternatives...

Yeah, quoted for truth. In my experience, most people do not believe that rational arguments have any kind of a practical applicability. Even if you get them to agree on common premises, then build a logical chain of reasoning leading to the undeniable conclusion that their beliefs are wrong, you won't win the argument in any meaningful sense. Instead, your audience will feel that you'd beaten them at some sort of a clever word-game. Sure, the loss will sting a bit, but in the end it's all just a game, so who cares, right ?