This paper has a two-fold purpose. First, we attempt to outline the development of the turnpike theorems in the last several decades. Second, we study turnpike theorems in finite-horizon two-person zero-sum Markov games on a general Borel state space. Utilising the Bellman (or Shapley) operator defined for this game, we prove stochastic versions of the early turnpike theorem on the set of optimal strategies and the middle turnpike theorem on the distribution of the state space.