Identifying the strategies that are played is critical to understanding behavior in repeated games. This process is difficult because only choices (not strategies) are observable. Recently, a debate has emerged regarding whether subjects play mixed strategies in the indefinitely repeated prisoner's dilemma. We use an experimental approach to elicit mixed strategies from human subjects, thereby providing direct empirical evidence. We find that a majority of subjects use mixed strategies. However, the data also suggest subjects' strategies are becoming less mixed over time, and move toward three focal pure strategies: Tit For Tat, Grim Trigger, and Always Defect. We use the elicited strategies to provide an empirically‐relevant foundation for analyzing commonly used mixture model estimation procedures.