  We consider the one-parameter family of interval maps arising from
generalized continued fraction expansions known as alpha-continued fractions.
For such maps, we perform a numerical study of the behaviour of metric entropy
as a function of the parameter. The behaviour of entropy is known to be quite
regular for parameters for which a matching condition on the orbits of the
endpoints holds. We give a detailed description of the set M where this
condition is met: it consists of a countable union of open intervals,
corresponding to different combinatorial data, which appear to be arranged in a
hierarchical structure. Our experimental data suggest that the complement of M
is a proper subset of the set of bounded-type numbers, hence it has measure
zero. Furthermore, we give evidence that the entropy on matching intervals is
smooth; on the other hand, we can construct points outside of M on which it is
not even locally monotone.
