Recommended GPU for Asus H61M-K

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You didn't mention a budget or a monitor resolution and refresh rate. Without a limit on budget and assuming 1080p resolution I'd go with a GTX 1070. If your budget dictates your choice then go down from there, GTX 1060 6GB/RX 580 8GB, etc. or even further down to RX 570 4GB or even further to GTX 1050 Ti.

If you have a 1440p monitor then GTX 1070 Ti or GTX 1080. If you have a 4K monitor then either of those or even a 1080 Ti would be suitable. But, then you'd also want more RAM.

I'm just covering all the possible basis here. New Nvidia high-end GPUs are releasing next month, but there are already some pretty good deals on GTX 10 series GPUs you can go with which are more than capable of 1080p and even 1440p gaming.

*I may be placing...
You didn't mention a budget or a monitor resolution and refresh rate. Without a limit on budget and assuming 1080p resolution I'd go with a GTX 1070. If your budget dictates your choice then go down from there, GTX 1060 6GB/RX 580 8GB, etc. or even further down to RX 570 4GB or even further to GTX 1050 Ti.

If you have a 1440p monitor then GTX 1070 Ti or GTX 1080. If you have a 4K monitor then either of those or even a 1080 Ti would be suitable. But, then you'd also want more RAM.

I'm just covering all the possible basis here. New Nvidia high-end GPUs are releasing next month, but there are already some pretty good deals on GTX 10 series GPUs you can go with which are more than capable of 1080p and even 1440p gaming.

*I may be placing more confidence in your Sandy Bridge CPU than I should. It's older and fast enough for decent 60Hz gaming, but for higher refresh rates it will lack in performance. GTX 1060 is good enough right now, but looking at the next 3 years the GTX 1070 in my opinion will give you the best longevity for 1080p 60Hz gaming on high-ultra settings.

But given your system you may not can afford it. So don't be afraid to go with a cheaper option.
 
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