Generally, anything beyond 125 to 150ms can introduce issues. That is hitting around 1/8 a second delay, which means the system needs to compensate for you being out of phase for up to 3 frames or more. Different types of games will have different tolerances, but that is an "ideal" target to shoot for when you can. Keep in mind, this is end to end latency, and not just to your head end or closest speedtest site.