Random Is Not Fair
Randomness is really not compatible with the human mind. We see order in everything. Only homogeneous distributions feel random to humans. If you role a dice three times and it comes up sixes, you (and me) either suspect the dice is weighted or the next throw, for sure, is going to be not-six. Don’t deny it, random must be “fair.” Look at the dots in the scatter plots above, which is schemed and which is random? Sometimes a whole paper is needed to convince scientist that distributions are just random and that there is no underlaying scheme. Look for example at [Clustering of the Cosmic Ray Ages of Stone Meteorites] (Andrew S. Tanenbaum).
To accommodate human feelings some form of control over the randomness is needed. “The way to handle controlled randomness is actually pretty simple. It’s commonly called a shuffle bag.” (Sean McArthur) [A Less-Random Generator] Almost all successful games use random control like that.