Willingness-to-compete experiments typically use small stakes, which raises the question of whether the commonly observed lower competitiveness of women can be generalized to consequential real-world situations. The present paper examines gender differences in willingness to compete using a high-stakes TV game show. At several stages, contestants face a choice between continuing to compete and opting out in exchange for a comparatively modest prize. When strategic considerations are absent, we observe the well-known pattern that women are less likely to compete than men, but this difference derives entirely from women avoiding competition against men. When the decision is strategic and contestants should factor in the competitiveness of others, women again avoid competing against men. Men then seem to anticipate the lower competitiveness of female opponents, as evidenced by their greater tendency to compete against women. Ability differences are unlikely to explain these results. These findings show that the gender difference in willingness to compete also occurs in a setting with exceptionally high stakes, and underline the importance of the gender of competitors, a factor that is mostly ignored in the literature. Our results are particularly relevant for understanding the persistent gender gap at the male-dominated higher rungs of the career ladder.