  We analyze several natural Goodstein principles which themselves are defined
with respect to the Ackermann function and the extended Ackermann function.
These Ackermann functions are well established canonical fast growing functions
labeled by ordinals not exceeding $\varepsilon_0$. Among the
Goodsteinprinciples under consideration, the giant ones, will be
proof-theoretically strong (being unprovable in $\mathrm{PA}$ in the
Ackermannian case and being unprovable in $\mathrm{ID}_1$ in the extended
Ackermannian case) whereas others, the illusionary giant ones, will turn out to
be comparatively much much weaker although they look strong at first sight.
