The symmetric 2x2 one-shot game is one of the simplest and most commonly used representations of strategic conflict. Among others, it includes the prisoner’s dilemma, the game of chicken, the volunteer’s dilemma, and the assurance game. All of these games share three characteristics: (1) both players have to make a single choice between two options; (2) they decide simultaneously; and (3) the payoff structure is symmetric. Typically, social scientists who examine (symmetric) 2x2 one-shot games either focus on one game or compare a small number of such games. There are comparatively few studies which analyzed (symmetric) 2x2 one-shot games in a more comprehensive manner. The goal of the present paper is to initiate research on the strategies people use to play any or all symmetric ordinal two-player two-moves games. We propose comparisons between eight different strategies. As will be shown, this analysis lays the groundwork for many possible follow-up projects.