What happens when you see your ex with someone else?

I think most people have been here at some point. What happens when you see your ex with another guy? I know the obvious thing is to act cool and have a short conversation, but how do you do it mentally?

I saw an ex last night, and hadn’t seen her for three years, since then I’ve dated other women. But because I’m more or less single now, I’d kinda preferred it if I wasn’t at the same club, or if I was there with a GF. She said hello to me first, I didn’t really notice/see her at first. I had my friends around, mainly girls, and her friends were with me for most of the night, more than her, because I used to always get along with her friends well and I hadn’t seen them in three years either. Her new guy wasn’t talking to her friends, or anyone really, he just looked like a druggy. I don’t want to get back together or anything, I’m just trying to work out what the feeling is? I guess you don’t want to let your ex see that you don’t have a new GF? Any thoughts? Is it ego?

And I’m not sure why, I engaged her in conversation a couple of times when I was buying rounds of drinks, out of politeness, she was driving, so she declined anyway. But she asked me to dance, and I kinda made my excuses, like I’d already offered to dance with another girl. And then when she was leaving, she asked if I was out this Friday, and I said no, and she said see you next week then, and I was like “yeah ok, I might be out next week”.. but actually maybe I’m thinking about it because I probably don’t want to go out next week. I’d prefer to not see her, although her friends are ok, I’d hang with them. I’m kinda hoping she doesn’t just hang out at my regular place. But then another ex was there last night, but I see her regualrly and she’s a good friend now, so it’s kinda like the reason is also that I haven’t seen her in so long.