In Handbook of applied cryptography, Golomb's randomness postulates are given: Let $s$ be a periodic sequence of period $N$. Golomb’s randomness postulates are the following.
R1: In the cycle $s_N$ of $s$, the number of $1$s differs from the number of $0$s by at most $1$.
R2: In the cycle $s_N$, at least half the runs have length $1$, at least one-fourth have length $2$, at least one-eighth have length $3$, etc., as long as the number of runs so indicated exceeds $1$. Moreover, for each of these lengths, there are (almost) equally many gaps and blocks.6
R3: The autocorrelation function $C(t)$ is two-valued. That is for some integer $K$, $C(t)=K$ for $t\neq 0 \pmod N$ while $C(0)=N.$
But why do those postulates make sense?