A person who knows only one thing and repeats it over and over; limited-minded repetition.
彼は意見がいつも同じで、馬鹿の一つ覚えのようだ。
His opinion is always the same; he's like someone with only one trick.
新しい方法を試さず、昔のやり方を繰り返すのは馬鹿の一つ覚えだ。
Not trying new methods and repeating old ones is the behavior of someone with only one trick.
そのジョークばかり言う彼にみんなが飽きている。まさに馬鹿の一つ覚えだ。
Everyone is tired of his repeating the same joke. It's exactly that 'one-trick' behavior.