Let's say that your guaranteed that the stream will be sparse — that no more than 10%, for example, of the bits will be 1s (or, conversely that more than 90% will be).
But if such drastically opposing conclusions can be drawn simply by shuffling the figures a different way, it is surely best to believe the outcome that most accords with common sense.
Opposing this is information in your head, which refers to knowledge that you have learned or memorized, like the back-alley shortcut that isn't printed on any map.
In contrast, it's quite common for personal computers to be booted or re-booted (re-started) and it's rather rare for them not to be stopped and re-started at least once a day.