In 1976, Rauzy studied two complexity functions, $\underlineβ$ and $\overlineβ$, for infinite sequences over a finite alphabet. The function $\underlineβ$ achieves its maximum precisely for Borel normal sequences, while $\overlineβ$ reaches its minimum for sequences that, when added to any Borel normal sequence, result in another Borel normal sequence. We establish a connection between Rauzy's complexity functions, $\underlineβ$ and $\overlineβ$, and the notions of non-aligned block entropy, $\underline{h}$ and $\overline{h}$, by providing sharp upper and lower bounds for $\underline{h}$ in terms of $\underlineβ$, and sharp upper and lower bounds for $\overline{h}$ in terms of $\overlineβ$. We adopt a probabilistic approach by considering an infinite sequence of random variables over a finite alphabet. The proof relies on a new characterization of non-aligned block entropies, $\overline{h}$ and $\underline{h}$, in terms of Shannon's conditional entropy. The bounds imply that sequences with $\overline{h} = 0$ coincide with those for which $\overlineβ = 0$. We also show that the non-aligned block entropies, $\underline{h}$ and $\overline{h}$, are essentially subadditive.