Some games are graphics limited like fast action shooters.
Others are cpu core speed limited like strategy, sims, and mmo.
Multiplayer tends to like many threads.
You need to find out which.
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To help clarify your CPU/GPU options, run these two tests:
a) Run YOUR games, but lower your resolution and eye candy.
If your FPS increases, it indicates that your cpu is strong enough to drive a better graphics configuration.
If your FPS stays the same, you are likely more cpu limited.
b) Limit your cpu, either by reducing the OC, or, in windows power management, limit the maximum cpu% to something like 70%.
Go to control panel/power options/change plan settings/change advanced power settings/processor power management/maximum processor state/
This will simulate what a lack of cpu power will do.
Conversely what a 30% improvement in core speed might do.
You should also experiment with removing one or more cores/threads. You can do this in the windows msconfig boot advanced options option.
You will need to reboot for the change to take effect. Set the number of threads to less than you have.
This will tell you how sensitive your games are to the benefits of many threads.
If you see little difference, your game does not need all the threads you have.
It is possible that both tests are positive, indicating that you have a well balanced system,
and both cpu and gpu need to be upgraded to get better gaming FPS.
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I have little doubt that you will find the FX-6300 lacking.
The motherboard is not recommended for a FX-8...
http://www.tomshardware.com/forum/id-2384024/motherboard-tier-list-970-chipset.html
Not that it matters much, you get two more threads, but the power of each core is largely unchanged.
A upgrade to a more current ryzen or intel processor, motherboard and ddr4 ram will be required.
I could see a ryzen 2600 or a intel i5-8400 as a reasonable choice.
The 9th gen intel i5-9400 is likely to appear soon and should be even better price/performance.
If you will be running multithreaded apps, that is where the ryzen processors shine.
If you are a pure gamer, then the higher clocks of intel will usually be better.
You would be very pleased with either coming from a FX processor.
GTX960 is decent, but an upgrade should probably be a significant one to a GTX1060 or GTX1070.