On the other hand, this stream isn't random. If it were truly random, the player would just move pointlessly in a horrible Brownian motion. It's nonsensical, to be sure, but in some weird way it encapsulates knowledge about the game, and as a result the game makes progress.
It sort of enlightens other places where true randomness is required, and the presence of any information or understanding radically changes the behavior of a system. In cryptography, even the slightest weakness in the probabilistic underpinnings of a cryptosystem can render it useless. In finance, even the slightest edge over the market can be leveraged to produce gains.