Simple answer there.... just have the system automatically lock the account if you statistically miss the password, just at it statistacally allows you in if you play properly.
Or maybe it's only accessible from secure locations - you don't go this much trouble to secure day to day stuff.
It's not unbreakable, but the idea that you're letting someone in by statistical analysis of their conditioned response to a game, including their mistakes is clever - no reason you couldn't lock them out or use other security measures by failure to meet that response.
My first thought was "how would locking the account if you miss it help, if you don't know how to miss it?"
However, if you're in a situation where someone is trying to forcibly extract access from you, there's s good chance that a stressed state of mind would be reflected in variations in how you play, which could be noticed by the system.
Even if it's limited to a specific secured location, though, you still have to worry about the possibility of keyloggers, which could be used to mount a reply attack without you ever having to know.
Or maybe it's only accessible from secure locations - you don't go this much trouble to secure day to day stuff.
It's not unbreakable, but the idea that you're letting someone in by statistical analysis of their conditioned response to a game, including their mistakes is clever - no reason you couldn't lock them out or use other security measures by failure to meet that response.