Evolutionary tournaments have been used as a tool for comparing strategies. For instance, in the late 1970’s, Axelrod organized tournaments to compare strategies for playing the iterated prisoner’s dilemma (PD) game. While these tournaments and later research have provided us with a better understanding of successful strategies for iterated PD, our understanding is less clear about strategies for playing iterated versions of arbitrary single-stage games. While solution concepts like Nash equilibria has been proposed for general-sum games, learning strategies like fictitious play may be preferred for playing against sub-rational players. In this paper, we discuss the relative performance of both learning and non-learning strategies that embody some of the above approaches on an experimental testbed of all possible structurally distinct 2x2 conflicted games with ordinal payoffs. This set of bimatrices provides a baseline, neutral testbed for comparing strategies. We discuss the testbed, our choice of representative learning and non-learning strategies and relative rankings of these strategies ranked by cumulative score in tournaments. We also study the performance of the strategies in an evolutionary tournament. Finally, we provide some analysis of the observed results to highlight the advantage of learning strategies.