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It depends on how CPU intensive the game is, and at what quality you're streaming
I need to factor in anything from indie to AAA titles; I don't tend to stick to just a couple of games. Likely 720/60, with potential for 1080/60 going forward during the lifespan of the CPU.
I'm not sure if OBS allows you to specify which CPU threads to use, I haven't used the new OBS Studio, but thanks to DXTory I can manage it all rather well.
I'm unsure if OBS has that; I can't remember off the top of my head, but I don't recall seeing it (at work at the moment). Though I know of Process Lasso, so I could always go down that route.
What I'd recommend in your situation is try and run it all now, and see how much your transcoding will use of the CPU. Although even then the 1700 should be a significant improvement for multi tasking like that.
I think that will be the best way. With all of that running, I'd imagine I'd be getting full use out of 8/16. I'd then be able to narrow down usage patterns, or throw around the idea of keeping Plex and/or game servers on my old 4690K system; freeing up the 1700 for gaming and streaming.
Just saw a 1700 for £274 and accidentally ordered it
Nice find!