We compare two concepts of stochastic stability in spatial games. The classical approach to stochastic stability, introduced by Foster and Young , involves single configurations in the zero-noise limit. Ensemble stability discussed in  refers to ensembles of configurations in the limit of an infinite number of players. The above two limits may not commute. We will discuss reasons of such behaviour. We review some results concerning the effect of the number of players and the noise level on the long-run behaviour of stochastic dynamics of spatial games.