Summary: In spite of its undeniable success, there are still open questions regarding C. Tsallis’s non-extensive statistical formalism, whose founding stone was laid in 1988 in [J. Stat. Phys. 52, No. 1-2, 479-487 (1988; Zbl 1082.82501)]. Some of them are concerned with the so-called normalization problem of just how to evaluate expectation values. The Jaynes’ MaxEnt approach for deriving statistical mechanics is based on the adoption of (1) a specific entropic functional form \(S\) and (2) physically appropriate constraints. The literature on non-extensive thermostatistics has considered, in its historical evolution, four possible choices for the evaluation of expectation values: (i) the 1988 Tsallis original, (ii) the Curado-Tsallis version, (iii) the Tsallis-Mendes-Plastino version, and (iv) the Tsallis-Mendes-Plastino version, but using centred operators as constraints. The 1988 version was promptly abandoned and replaced, mostly with versions (ii) and (iii). We will here (a) show that the 1988 version is as good as any of the others, (b) demonstrate that the four cases can be easily derived from just one (any) of them, i.e., the probability distribution function in each of these four instances may be evaluated with a unique formula, and (c) numerically analyse some consequences that emerge from these four choices.