Question Do not see 60 FPS

Feb 12, 2019
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I have Lenovo Legion Y-520 with 60Hz monitor. Whenever I play games, FPS counter reads 60+, but it looks very choppy and stuttering. However, when I watch videos in 60 FPS, they are smooth. Enabling VSync partly helps, but the input lag in competitive games is unacceptable. The fun thing, is that it does feel smooth, when I get to 120 FPS, for some reason.
CPU: IntelCore i5-7300HQ
GPU: GTX 1050
RAM:8Gb