We investigate the emergence of rationality in repeated games where, at each iteration, the players' payoffs are randombly perturbed (to account e.g. for the effects of fading or errors in the reading of one's throughput). We see that even if players start out completely uneducated about the game, there is a simple learning scheme that enables them to eventually weed out the noise and identify suboptimal choices, regardless of the noise level. More precisely, we show that strategies that are strictly dominated (even iteratively) become extinct in the long run, i.e. players exhibit rational behavior. As an application, we model a number of users that are able to switch dynamically between multiple wireless nodes and see that they are able to pick up which node works best for them, even in the presence of high performance fluctuations.