We examine gender differences in willingness to compete, using data from a TV game show where the winner of an elimination competition in expectation wins hundreds of thousands of euros. At several stages of this competition, contestants face a choice between continuing to compete and opting out in exchange for a comparatively modest prize. When there is no strategic interaction, we observe the well-known pattern that women compete less than men, but this difference derives entirely from women avoiding competition against men. When there is strategic interaction and contestants should factor in the willingness to compete of their opponent, women again avoid competing against men. Men then seem to anticipate the lower competitiveness of female opponents, as evidenced by their greater propensity to compete against women. Ability differences are unlikely to explain these results. Our findings show that the gender difference in willingness to compete that is well-documented in the experimental economics literature also occurs in a quasi-experimental real-world setting with exceptionally high stakes, and underline the importance of the gender of competitors.