This analysis is just wrong. There is no shame or misery in finding out that Carol already has a partner. The really bad outcome is that she's totally alone,

This analysis is just wrong. There is no shame or misery in finding out that Carol already has a partner. The really bad outcome is that she's totally alone, but she finds you such a dork, she humiliates you with a zinger that everyone around can hear. Also, women give their phone number to more than one man. They don't have a "first man only" rule. The reason a lot of guys, especially nerds, won't approach Carol is that they see her as holding higher social status than they do, so it feels extremely uncomfortable. The "popular" (high-status) guys will approach her confidently and playfully. People tend to group with others of approximately the same social status. To really learn about this stuff, you have to put the math book away and socialize with people.