I really need to get in contact with Brutus and get some more information on this. I was trying to write some software to diagnose these issues.
So here is my understanding of what could cause the issues you are experiencing:
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The pipe is too small. If someone is playing with a connection that is too slow (Mbs per second), the data will basically queue up until the other data is transmitted. Think of it like waiting it a queue of traffic. In my own testing a connection of 6Mb up and down the is minimum needed. Other people here that made the adapters say it will work with less but in my own testing 6Mb is the minimum. Even with 6Mb, if the person is doing something else like watching youtube, youtube will send micro bursts, which coupled with a poor router will increase ping times until the data is sent. In the UK I had a 300Mb connection and had no issues, but when trying with a 4Mb connection I could not play gap. Even if the speed test works great, well some ISPs do a thing called "traffic shaping". They degrade certain connections to prevent people using up too much of their network. I need to emphasis that the upload and download speed are both important. In Australia the connection speeds are awful. I'm currently limited to a 40Mb connection.
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Ports. Everyone connects using a thing called NAT. NAT means a public IP address is shared by multiple PCs. Think of it like having an apartment block. Your public IP address is the street address, then you will have an address in your building. Some cheaper ISPs (and Russians) use a thing called Global Carrier NAT. It means that the ISP is also using NAT. When you connect using FAF, the ports should get opened, but that is not always the case. Re FAF'ing means the ports are normally opened from the previous attempt.
It is also possible that another service is using those ports, hence why the relay is used. Check to see whether the ISP uses GC NAT. I may be wrong but if GC NAT is used, the connection will go via Nuremberg as GC NAT IP addresses are not strictly Australian ones, so it doesn't register the IP address as being Australian. I believe that if you speak to your ISP you may be able to get GC-NAT disabled.
https://www.aussiebroadband.com.au/help-centre/nbn/tech-support/cg-nat/
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Firewalls. There are loads of things that can block the ports. Antivirus comes with firewalls, as does windows. Either one of those can interfere. This is similar to the above NAT. It is possible to try disabling the firewall completely, then try. If it fixes the problem, you can add exceptions to your firewall.
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Wifi. If the signal gets interfered with, then the device will need to resend the information. Depending on what is around the device will mean that it might take a few hundred ms to get the information through. Make sure you only play games on ethernet.
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To the chap that said his BBC ping was okay but others were peaking, well a thing called "Quality Of Service" will prioritise the ICMP packet (ping request), so if you connection is maxed out as you download your strange porn, the Ping should come back without the delay.