"Back in the day"(just few years ago) I used to expose a port for RDP on my router, on a non-standard port. Typically it would be fine and quiet for a few weeks, then I assume some automatic scanner would find it and from that point onwards I could see windows event log reporting a log in attempt every second, with random login/password combinations, clearly just looking for something that would work. I would change the port and the whole dance would repeat all over again. Tens of thousands of login attempts every day, all year round. I used to just ignore it, since clearly they weren't going to log in with those random attempts, but eventually just switched to OpenVPN.
So yeah, the lesson there is that if you have a port open to the internet, someone will scan it and try to attack it. Maybe not if it's a random game server, but any popular service will get under attack.