In short, the answer to the question posed is, "No, it's not okay to sleep with your friend's ex." However, please do notice that nowhere in there did I use the word, "never." Reason being, that there are in fact certain instances warranting this kind of behavior. By, "this kind of behavior" I mean the deceptive, back-stabbing kind that ruins friendships. Such is life! In the powerful words of Selena Gomez, "the heart wants what it wants."
I believe there to be two acceptable instances when you can sleep with a friend's ex. I'll go ahead and detail them for you now in the event you've been thinking about it like the real a**hole that you are. Additionally, I'm going to gear this specifically toward a male and his girlfriend, makes it easier than swapping back and forth between genders, but it's applicable to both.
When it comes to break-ups there is a sliding scale of intensity that ranges from a walk in the park to all out nuclear warfare. If your friend and his girlfriend broke up amicably because BOTH parties were no longer interested in each other, then yes, it's okay for you to make a move. Permitting you ask him first and he's cool with it. Yeah, it might be a little weird, but that's really the extent of it. Just because it didn't work out for them, doesn't mean you should ignore your feelings for his ex. Who knows? Maybe the two of you will hit it off better than they ever did and you'll live happily ever after! Here's the thing though, if you're just trying to get in and get out, don't bother. Sleeping with your friend's ex one time just because you want to get your rocks off is a waste, although in this particular instance, it's not the end of the world. Frowned upon, yes, but otherwise the world will keep spinning.
Say your friend and his girl ended it really terribly. You know what I mean—tears, broken glass, shattered hearts, the whole bit. He's distraught because he really still loves the girl and can't imagine moving on, but you know she's over it. IF and only IF you have strong, serious, love-like feelings for this girl is it appropriate for you to make a move—IN TIME. Does it break every aspect of bros before hoes? It sure does! But here's my take on it, relationships are complicated AF, love triangles being the most complicated of all. You can't please everyone and if you know deep down that this is the woman you want to be with, your friend will inevitably have to learn to accept it. If he doesn't ever come to terms with it, then you have to be prepared to lose him for good.
So that's about it. You can sleep with your friend's ex if he doesn't give a crap or if you're really in love with her and willing to sacrifice him beating you senseless followed by never speaking to you again. Make good decisions and choose wisely!
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