The underrepresentation of women at the top of hierarchies is often explained by gender differences in preferences. We find support for this claim by analyzing a large dataset from an online card game community, a stylized yet natural setting characterized by self-selection into an uncertain, competitive and male-dominated environment. We observe gender differences in playing behavior consistent with women being more averse towards risk and competition. Moreover, we demonstrate how "shying away" makes female players less successful: despite no gender gap in playing skills, women accumulate lower scores than men due to their relative avoidance of risky and competitive situations.