This paper addresses learning in repeated stochastic games (RSGs) played against unknown associates. Learning in RSGs is extremely challenging due to their inherently large strategy spaces. Furthermore, these games typically have multiple (often infinite) equilibria, making attempts to solve them via equilibrium analysis and rationality assumptions wholly insufficient. As such, previous learning algorithms for RSGs either learn very slowly or make extremely limiting assumptions about the game structure or associates' behaviors. In this paper, we propose and evaluate the notion of game abstraction by experts (Gabe) for two-player general-sum RSGs. Gabe reduces an RSG to a multi-armed bandit problem, which can then be solved using an expert algorithm. Gabe maintains many aspects of the original game, including security and Pareto optimal Nash equilibria. We demonstrate that Gabe substantially outperforms existing algorithms in many scenarios.