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 intracluster 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 per cent 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 subgrid processes, such as feedback.