  Ram pressure stripping of the hot gas that surrounds normal galaxies as they
fall into groups and clusters (also referred to as `strangulation' or
`starvation') is generally thought to shut down star formation on a time scale
of a few Gyr. However, it has recently been suggested, on the basis of
X-ray-optical scaling relations of galaxies in the field and the group/cluster
environment, that confinement pressure by the intra-cluster medium can actually
lead to an increase in the mass of hot gas surrounding these galaxies. We
investigate the competition between pressure confinement and ram pressure
stripping for satellite galaxies in orbit about galaxy groups and clusters
using simple analytic models and detailed cosmological hydrodynamic
simulations. It is found that, independent of host mass, ram pressure is
generally dominant over confinement pressure --- only ~16 % of galaxies find
themselves in the reverse situation. Furthermore, these galaxies have, on
average, less hot gas than ram-pressure dominated ones, contrary to simple
expectations. This is explained by the fact that the small number of galaxies
which are confinement dominated are typically at first or second apocentre and
have therefore already been maximally affected by ram pressure stripping around
first pericentre. Our results are shown to be insensitive to host halo mass; we
argue that the same is true for uncertain sub-grid processes, such as feedback.
