This reminds me of an episode of that (now old) TV show Numbers (or, I suppose, NUMB3RS). A suspect was trying not to be found by hitting targets in seemingly r

This reminds me of an episode of that (now old) TV show Numbers (or, I suppose, NUMB3RS). A suspect was trying not to be found by hitting targets in seemingly random locations. The mathematician protagonist pointed out that whenever people think of "random" sequences -- like this guy's targets, or even just a shuffled playlist -- people don't expect duplicates, even though true randomness would have them. As a result, you can analyze the sequence under that artificial constraint and make predictions to the next element with more than random chance of being right. This isn't exactly the same, but it's another example of "trying to hide information is, in itself, giving away information". BTW, tangentially related: I remember reading that the original iPod shuffle function was truly uniformly shuffled, but people started thinking it wasn't and complaining because they'd notice when multiple songs by the same artist played in sequence. So Apple had to make the shuffling less random to avoid those strings so people would perceive it as being truly random.