If a woman seems popular with men would a guy who likes her play it super cool in order to stand out from the crowd?

Like if she goes on a lot of dates and has no problem dating and there is a guy in her friend group who has a crush on her which he has shown through flirting, teasing, body language, peacocking etc. but he does not really reach out to her do you think he might be clever enough to try to distinguish himself from the guys who are actively pursuing her by being cooler than them etc..
If a woman seems popular with men would a guy who likes her play it super cool in order to stand out from the crowd?
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