I don’t know if this is the right place to ask for these kind of things but here we go.

I have been cheating in public Minecraft servers (you can judge me), and every time I get IP banned (about once an hour), I restart my modem so it changes my PC’s IP (I think it’s called dynamic IP, correct me if I’m wrong).

So, the thing I’m worried about is: Is there a chance for me to run out of IPs I get banned in all of them? Is the amount of IPs that I can change limited? If it is technically I can get banned in all of them, right?

Sure. But the bigger “danger” to you here is getting thwarted by something more sensible than IP-banning like HWID-banning, which isn’t something you’ll feasibly be able to circumvent.

Do keep in mind that, depending on how seriously the admins on the receiving end take their jobs, continuous nefarious and undesirable activity from IP ranges is routinely tracked and reported. That chiefly concerns typical botnet activities like DDOS and spam but certainly isn’t limited to that. Less bandwidth-intensive but still undesirable behaviors like fraud, unauthorized to foreign systems and even video game cheating are still going to incur a risk of affecting your digital life and future. How freely one is able to use online services depends on the their repute. That’s the reason why, when using a Tor exit node, you may have to suddenly solve 6 consecutive CAPTCHAs when signing up for a random service while also not being able to use other services at all, e.g. banking access.

Don’t be smelly like a Tor access node u/HighZein.