  Numerous pivotal concepts have been introduced to clarify the puzzle of
relaxation and/or equilibration in closed quantum systems. All of these
concepts rely in some way on specific conditions on Hamiltonians $H$,
observables $A$, and initial states $\rho$ or combinations thereof. We
numerically demonstrate and analytically argue that there is a multitude of
pairs $H,A$ that meet said conditions for equilibration and generate some
"typical" expectation value dynamics which means, $\langle A(t)\rangle \propto
f(t)$ approximately holds for the vast majority of all initial states.
Remarkably we find that, while restrictions on the $f(t)$ exist, they do not at
all exclude $f(t)$ that are rather adverse or "strange" regarding thermal
relaxation.
