[inimino]

The idea is that you bet before the sequence is known. Nowadays we would say it is the distribution (or the process producing the random sequences) that can be truly random or not, and we recognize that saying "sequence [...] is random" is incoherent, same as the joke of the random int set to 4 with a comment in the source code that it was chosen by fair dice roll.

If you know everything about the process and still can't beat chance at predicting it, that's the quality we are after. In this definition "random" just means unpredictable, which is another way to explain why it can only be a meaningful distinction when you don't yet know the result.