This research focuses on the absence of women among academic staff in physics. To explore the causes of this gender imbalance, we focus on the decision-making junction between obtaining a Ph.D. diploma and pursuing a postdoctoral position. We use the mixed-methods paradigm, combining a nationwide representative survey of Ph.D. students in Israel (n=267 respondents out of 404 questioned) and interviews with Ph.D. students and postdoctoral fellows (n=38). The theoretical novelty that we propose is to view such career decision making as a "deal" that involves contextual, organizational, and individual variables and their intersection. Young women are examining the components of this deal: what it offers them and what prices they will have to pay, but their decision is made within a gendered power structure. Studying both context factors and agency, we reveal the multiple hidden ways in which gender operates as a power structure, putting up barriers to women's academic careers. This latent power structure influences women's decision making and experiences in several ways. In the academic field, it produces unequal competition in a male-dominated playground. In the social sphere, choosing a demanding academic career is seen as disrupting gender order. Within the family, women carry a greater burden of family work and give precedence to their husband's career and preferences. Within this social structure, women who decide to follow an academic career feel that they must excel, and this demand for "excellence" acts as a hidden mechanism within the gendered power structure that may prevent talented women from pursuing an academic career in physics.