I think we're saying the same thing, yeah. I was remarking that any clever strategy doesn't confer any advantage to the attacker because there is no advantage to confer. They have perfect knowledge of your strategy just by knowing one previous move, and perfect knowledge is the most you can get.

Unless I'm confused again, it seems to me that there's just no advantage to them remembering more moves, since they know everything you're going to do from that last one. It's not that your strategy being stupid actively forces them to be stupid, they're not losing anything by being cleverer, they just don't gain anything because they already have it all.